The Scientific Reinterpretation of Form 9781501734212

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The Scientific Reinterpretation of Form

CORNELL HISTORY OL SCIENCE SERIES

Editor: L. Pearce Williams

The Scientific Reinterpretation of Form by Norma E. Emerton

Geology in the Nineteenth Century: Changing Views of a Changing World by Mott T. Greene

THE SCIENTIFIC REINTERPRETATION OF FORM by Norma E. Emerton

CORNELL UNIVERSITY PRESS ITHACA AND LONDON

Copyright © 1984 by Cornell University Press All rights reserved. Except for brief quotations in a review, this book, or parts thereof, must not be reproduced in any form without permission in writing from the publisher. For information, address Cornell University Press, 124 Roberts Place, Ithaca, New York 14850. First published 1984 by Cornell University Press. Published in the United Kingdom by Cornell University Press Ltd., London. International Standard Book Number 0-8014-1583-7 Library of Congress Catalog Card Number 84-45139 Printed in the United States of America Librarians: Library of Congress cataloging information appears on the last page of the book. The paper in this book is acid-free and meets the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources.

A CAMBRIDGE TRIBUTE TO ARISTOTLE

When I contented liv’d by Cam’s fair streams, Without desire to see the prouder Thames, I had no flock to care for, but could sit Under a willow covert, and repeat Those deep and learned layes, on every part Grounded on judgment, subtil’ty, and Art, That the great Tutour to the greatest King, The shepheard of Stagira, us’d to sing: The shepheard of Stagira, that unfolds All nature’s closet, shows what e’ere it holds; The matter, form, sense, motion, place, and measure Of every thing contain’d in her vast treasure. How Elements doe change; What is the cause Of Generation; What the Rule, and Laws The Orbs doe move by . . . Thomas Randolph, Poems, 1638

(Aristotle came from Stagira, and was tutor to Alexander the Great.)

Foreword

of science, which it is the purpose of the Cornell History of Science Series to chronicle, is both fascinating and com¬ plex. In recent years, attention has focused upon those moments of rapid and unexpected change that are described by the term scien¬ tific revolutions. At such times, the world almost literally seems turned upside down. Old terms no longer mean what they did, old observations and experiments remain true but often irrelevant to the new theories that suddenly redefine reality and even percep¬ tion. Science itself reflects this concern, for science boasts that it is in an almost constant state of revolution, casting out the old and welcoming the new. And from science outward spreads the fashion that makes innovation both desirable and necessary. It is well, therefore, to be reminded occasionally that science is not only the most revolutionary of all intellectual systems but one of the most deeply conservative as well. Like all human beings, scientists are unwilling to abandon old habits and old ideas unless compelling reasons force them to do so. We may here cite the “discovery” of the neutrino in the early days of quantum mechan¬ ics; this, without a single piece of empirical evidence to support it, was introduced into physics because the principle of the conserva¬ tion of energy was lost without it. Some principles are just too fundamental to be abandoned. So it was with the principle of form, the subject of this second volume in the Cornell series. This work is, surprisingly, the first systematic account of an idea that was born with the idea of science itself in ancient Greece and that has been vital to its evolution ever since. This volume attempts to answer the question how brute matter, from whose actions only chaos could be expected, nevertheless is commonly found in an ordered and symmetrical form. Norma Emerton traces the answers The life

Foreword

[8]

given to this question from their origin in classical Hellas to the end of the Scientific Revolution of the seventeenth and eighteenth cen¬ turies, when crystallographers put forward views that permitted natural philosophers to penetrate into the very intimate structure of matter itself. The story is a fascinating one. The nature of form was central to ancient, medieval, and early modern societies, all of which relied upon it for far more than purely scientific results. Hence the evolu¬ tion of the idea of form reflects philosophical, religious, and even social concepts far removed from problems of matter and its orga¬ nization. But it was in the scientific realm that the idea was most important, and it is on this area that the author focuses. This book is an “internar history of science which illustrates well the fact that scientific ideas have lives of their own well worth investigating, describing, and analyzing. The result is a history that introduces one of the most important and central concerns of modern science. L. Ithaca, New York

Pearce Williams

Contents

List of Illustrations

11

Preface

13

1.

Form in the Mineral Kingdom

19

2.

The Development of the Concept of Form after Aristotle

48

3.

Mixtion and Minima: The Beginnings of a Corpuscular Approach to Form

4.

76

Minima and Atoms: The Corpuscular Reinterpretation of Form

5.

106

Atoms and Crystals: The Geometrical Approach to Form

126

6.

The Development of Form in the Platonic Tradition

154

7.

Spirit and Seed: The Chemical Reinterpretation of Form

177

8.

Salt, Earth, and Universal Acid: The Material Embodiment of Form

9. 10.

209

The Form and Origin of Crystals

233

Primitive Form: The Fleart of the Matter

258

Bibliography

289

Primary Sources Secondary Sources Index

[9]

289 300 311

List of Illustrations

Rock crystals and basalt

37

Salt crystals extracted from plants

46

Types of crystals: common salt crystallization and snowflakes

132

Seventeenth-century arrangements of rounded particles

134

Angular saline particles

149

Points and pores

152

The abyss at the center of the earth

202

Niter and sal ammoniac

215

Vitriol

216

Linnaeus’ saline classification of mineral crystals

241

Crystal forms known to Linnaeus when he made his classification

246

Early nineteenth-century arrangements of rounded particles

250

Early nineteenth-century arrangements of rounded particles

252

Swedenborg’s symmetrical particles

263

Constancy of angles; outlines of rock crystals

275

Forms of rock crystals and contact goniometer

276

The primitive form inside crystals

279

Decrements on rows of molecules

281

[11]

Preface

In

introduction to The Great Chain of Being, Arthur Lovejoy draws our attention to the fact that “most philosophic systems are original or distinctive rather in their patterns than in their components. . . . The seeming novelty [is] . . . the novelty of the application or arrangement of the old elements which enter into it." He enumerates some tasks and considerations for the his¬ torian in the quest for these elements, “the primary and persistent or recurrent dynamic units of the history of thought." He speaks of the necessity of tracing the “unit-idea" through various provinces of thought and in the writings of numerous thinkers of many gen¬ erations, and of undertaking “a study of . . . words and phrases . . . their ambiguities . . . their various shades of meaning . . . and an examination of the way in which confused associations of ideas arising from these ambiguities have influenced the development of doctrines, or accelerated the insensible transformation of one fash¬ ion of thought into another, perhaps its very opposite." In this book I have attempted such a study with regard to the concept of form, one of the most important and persistent ele¬ ments in natural philosophy. It is a study in the history of ideas of perhaps, to quote another phrase of Lovejoy’s, in the “history of confusions of ideas,” for the form was a concept in transition, moving from one context to another, gathering accretions and undergoing alterations on the way. The movement was not a sim¬ ple or straightforward one. In this flux of form, the concept borne along on the stream of human thought turned this way and that, exhibiting now one aspect of itself and now another, as each in turn came uppermost and displayed itself momentarily to view. Our task is to identify each aspect of the form and to investigate its

[13]

his

[Hi

Preface

changing relationships with other aspects, tracing the reinterpreta¬ tion and development of the form concept from classical times, through medieval and Renaissance thought, down to the scientific theories of the seventeenth and eighteenth centuries. In the pursuance of this task certain boundaries have had to be j set. To stray beyond them would be tempting, but some interesting ; topics must be ruled out of bounds in order to keep our study within reasonable limits. Such topics include the question of uni| versals and the conflict between realism and nominalism; the the¬ ological implications of form theory; a more detailed exploration of Arab natural philosophy, alchemy, and Hermeticism; the ramifi¬ cations of organic form; and the practical aspects of the sciences whose theoretical side we investigate. Some outstanding figures, such as Galileo, Newton, and Lavoisier, receive scant attention, because their contribution to form theory was slight. In this study, certain features stand out, and it is worth drawing attention to them here. First, I have been led to what some may think to be an undue emphasis on continuity between periods rather than on revolution or conflict between old and new. I be¬ lieve that what appears on the surface to be a sudden or violent change may often be the climax of an underlying gradual merger between traditional and innovating concepts. An example is the unexpected revival of form theory in the seventeenth century, when a loud outcry against the scholastic substantial form accom¬ panied a quiet, persistent reinterpretation of the form concept itself. Old concepts rarely die; instead of fading away they are transformed by amalgamation with other concepts. There is often a long overlap of earlier modes of thought continuing into later periods; given the long interaction of certain traditions, particular insights engendered by their cross-fertilization can reappear at dif¬ ferent periods. Second, it is important to establish the context within which a concept functions, which defines it in its own role and in relation to other concepts. An example is the way in which, from classical times, the rival particle theories of minimism and atomism flour¬ ished within a chemical and a physical context, respectively. Allied to this need for context is the significance that a concept or theory can gain from the background against which it is viewed. Platonic idealism and Democritan atomism both gained acceptance and au¬ thority because of their exposition in Aristotle’s writings. Third, the power of precedent must not be underestimated in determining the use and acceptability of a theory or concept. This

Preface

[15]

too is a consequence of the traditional context, and it led to the choice of minimism, not atomism, even by atomists, when a chem¬ ical particle theory was needed in the seventeenth century. Like¬ wise, we shall see that angular particles met with more favor than round ones because they fitted in better with precedents set by form theory, chemical tradition, and crystallography. Finally, I must stress the need, in a study of this sort, to pay attention to all the nuances of language and connotation displayed by the concept in question within many different contexts at differ¬ ent times. Only in this way can we understand its continuous trans¬ formation as it is remodeled and reinterpreted to qualify it for explanatory use in a succession of scientific theories. This book arose from an interest in the work of Haiiy and Rome de l’lsle inspired by my crystallographic studies, which led me to inquire into the sources of their ideas; I express my tribute to Professor Dorothy Hodgkin, who taught me crystallography at Ox¬ ford. Some of the material used here originally appeared in my Cambridge Ph.D. dissertation. I have rendered into English all quotations from works in other languages. For translations from Swedish I am indebted to Professor Bertil Albrektson and Elin Page. All other translations are my own, unless otherwise indicated. For advice on the knottier points of Latin I thankfully acknowledge the help of James Hunt; but all errors are mine alone. I am grateful to Carl von Sydow for helping me to use the Linnaeus archives at the Carolina Library, Uppsala; to the veteran crystallographer Mary Winearls Porter for the loan of material from the nineteenth and early twentieth centuries; to John Brooke for many useful suggestions; to Michael Hoskin for reading and commenting on the manuscript; and to others who have been helpful in various ways. Last, but not least, I wish to express my appreciation of my husband’s support, especially during the period of this study. Norma E. Emerton

Cambridge, England

The Scientific Reinterpretation of Form

CHAPTER

ONE

Form in the Mineral Kingdom In these crystalline structures, the formative forces of the earth seem to manifest themselves most directly, as if they were merely slumbering lightly beneath the rigid surface, resting from the First day of creation. Carl M. Marx, Geschichte der Crystallkunde

times people have inquired why natural ob¬ jects are characterized by a certain appearance and whether this outward shape is determined by a corresponding inward nature. The problem for the natural philosopher has been to define and explain how these two aspects of a thing are related, and how the internal character can give rise to the external configuration. The belief that the two are related is shown by the use of the same word “form,” like its equivalents eidos in Greek and forma in Latin, to signify both the outer shape of a thing and also its inner nature or essence. Hence Webster’s Dictionary defines “form” as not only “the shape and structure of something as distinguished from its material,” but also “the essential nature of a thing as distinguished from its matter.” If we understand the form in a broad sense as the order and pattern in nature, acting in and through matter but not to be identified simply with its exterior material embodiment, then we find that from classical times the concept of form has been almost perennial in philosophy. Aristotle commented that although many pre-Socratic philosophers, including the atomists, “thought the principles which were of the nature of matter were the only princi¬ ples of all things,” yet some of them introduced a formal cause of material order: Anaxagoras, for whom “reason was the cause of order and of all arrangement,” and the Pythagoreans, who “supFrom early

[19]

[2o]

The Scientific Reinterpretation of Form

posed the elements of numbers to be the elements of all things.”1 Plato’s transcendent forms or Ideas that provided the pattern of earthly things; Aristotle’s immanent forms shaping matter into spe¬ cific bodies; the Stoics’ all-pervading spirit giving rise to the hexis or formal nature of things—all these notions have continued to exert a profound influence on the thought of succeeding generations down to modern times. The concept of form became so deeply ingrained in the Euro¬ pean consciousness that it proved extraordinarily difficult to dis¬ place, even by those who abandoned the philosophical background from which it came. In the late eighteenth century Immanuel Kant wrote concerning matter and form: “These two concepts underlie all other reflection, so inseparably are they bound up with all em¬ ployment of the understanding. The one (matter) signifies the de¬ terminable in general, the other (form) its determination.”2 Even in the twentieth century new philosophies of form have been de¬ vised; some derive from the Platonic and Aristotelian traditions mediated by Catholicism, while others, more eclectic and owing much to Gestalt psychology, seek in the concept of form a principle of unity for science and the arts.3 Thus over the centuries philoso¬ phers have continued their efforts to construct form theories, and in the course of this development the concept of form has been constantly reinterpreted in order to make it relevant to new con¬ texts. With this process of reinterpretation our present study is concerned. The relation of a thing’s appearance to its innate form or es¬ sence, which successive form theories have tried to explain, is not always easy to discern in the world around us. But there are two classes of natural objects that are outstanding on account of their constant and specific outward form, which seems to presuppose as its source an equally constant and specific inward form. These are living creatures and crystals: a human being, an oak tree, or a rock crystal has an instantly recognizable characteristic appearance. A study of the meaning of form cannot afford to ignore organic and crystalline form. But since the subject of organic form involves a great many biological complexities that distract the mind from the 1. Metaphysics i 3, 983b; 4, 985a; 5, 986a. The translation of Aristotle’s writings used throughout the present book is The Oxford Translation of Aristotle, ed. William D. Ross. 2. Critique of Pure Reason, trans. by Norman Kemp Smith (London, 1929), p. 280; see also p. 66. 3. An example of the first class is Edward Watkin, A Philosophy of Form (London, 1935); in the second class are Lancelot Law Whyte, Aspects of Form (London, 1951) and Accent on Form (London, 1955).

Form in the Mineral Kingdom

[21]

concept of form itself, I have regretfully left it on one side and I have chosen the chemical and morphological study of crystalline minerals to illustrate the use of the form concept and its rein¬ terpretation in natural philosophy. Theories about crystals testify to their authors’ understanding of the relationship between inward and outward form in a way that few, if any, other areas of natural science can do. A twentieth-century crystallographer, Alfred Tutton, has pointed out the implications of crystalline form: “The great fundamental questions inevitably arise, ‘Why does a particu¬ lar substance crystallize in a specific characteristic form?’—‘What determines the choice of its form?'—‘Shall we ever be able to pre¬ dict from its chemical constitution what the crystalline form of a given substance will be?' ”4 As well as raising questions about the nature of form, the regular and beautiful shapes of crystals have also seemed to some writers to suggest answers to questions, to offer a key to understanding the meaning of form. For instance, Pliny the elder wrote in the First century a.d.: “In precious stones . . . the majestic might of Nature presents itself to us, contracted within a very limited space. ... It is quite sufficient to have some single gem before the eyes, there to behold the supreme and absolute perfection of Nature’s work.”5 In the early nineteenth century the same belief was expressed by the crystallographer Carl Marx, who wrote in the preface to his Geschichte der Crystallkunde the passage cited at the head of this chapter, and who concluded the same book with a verse in the style of Goethe, which may be rendered as follows: The wise man heavenward turns his questing eyes; To count the stars, measure the sun he tries. A miracle his gaze to earth doth draw, His measurements now fill his soul with awe— One crystal doth the cosmic law comprise!

In this way it has been supposed that the study of crystals can afford unique insights into “Nature’s work” or the “cosmic law,” that is, the universal patterning of matter by form. For these reasons, this first chapter examines the ways in which natural philosophers from classical times down to the late seven¬ teenth century approached the formation and figuration of miner4. Crystalline Farm and Chemical Constitution (London, 1926), p. 227. 5. Natural History, bk. 37.1, trans. by John Bostock and H. T. Riley (London, 1855), vol. vi, p. 386.

[22]

The Scientific Reinterpretation of Form

als and crystals, and how the form was seen as the source of speci¬ ficity. Chapter 2 depicts the philosophical background to these theories of mineral form and traces the evolution of the form concept in the same period, from Aristotle, via medieval scholas¬ ticism, to the seventeenth-century reinterpretations of form. In spite of the varieties of emphasis, much continuity can be seen throughout this development. Chapter 3 completes the study of Aristotle’s form in the physical world by concentrating on one area of form theory in the Middle Ages and the Renaissance, the elab¬ oration of a form theory of combination resulting in a form theory of particles, a nonatomistic corpuscularianism known as minimism. Chapter 4 follows the process by which minimism and atomism were blended by seventeenth-century natural philosophers to pro¬ duce eclectic particle theories that interpreted the form of a body in terms of the form of its particles. In chapter 5 we see how these particle theories borrowed from crystal geometry the insight that form could be interpreted as structure, the regular stacking of angular parts to make a whole. The next three chapters survey the development of the concept of form outside the Aristotelian tradition. Chapter 6 traces some of the many streams emanating from Plato: the Timaeus and its influ¬ ence on early scholasticism, the Neoplatonic tradition, and ancient and Renaissance Hermeticism. Chapters 7 and 8 examine the six¬ teenth- and seventeenth-century chemists’ interpretations of form, First in terms of chemical seeds and spirits, and then embodied in the saline or acid principle. Finally, the last two chapters demon¬ strate how eighteenth-century mineral and crystal studies united all these reinterpretations of form—crystal geometry, particulate structure, and chemical principles—and embodied them in the crystal nucleus. Chapter 9 illustrates this process in mineralogy and natural history, and chapter 10 depicts the culmination of the rein¬ terpretation of form in eighteenth-century crystallography. First, we turn to classical explanations of the formation of miner¬ als. According to Aristotle, “the question ‘why’ is answered with reference to the matter, to the form, and to the primary moving cause.”6 The material, the formal, and the efficient or moving causes, together with the final cause or purpose, brought about all phenomena and bodies, organic and inorganic. The complexity of life processes seems to call for a formal cause and to give wide scope for its application, whereas the simpler and less determinate nature of minerals might seem to be adequately explained by the 6. Physics 11 7, 198a.

Form in the Mineral Kingdom

[23]

material cause (the four elements in varying proportions) and the efficient cause (the action of motion and the four qualities, heat, cold, moisture, and dryness) without recourse to the form at all. In fact Aristotle restricted himself to the material and efficient causes and did not mention the form in his statement on mineral genera¬ tion, which provided the basis for most mineral theory for the next two millennia: We maintain that there are two exhalations, one vaporous, the other smoky, and there correspond two kinds of bodies that originate in the earth, “fossiles” and metals. The heat of the dry exhalation is the cause of all “fossiles.” Such are the kinds of stones that cannot be melted, and realgar, ochre, ruddle, sulphur, and other things of that kind. . . . The vaporous exhalation is the cause of all metals, those bodies which are either fusible or malleable such as iron, copper, gold. All these originate from the imprisonment of the vaporous exhalation in the earth, and especially in stones. Their dryness com¬ presses it, and it congeals. . . . Hence, they are water in a sense, and in a sense not. . . . They possess an admixture of earth; for they still contain the dry exhalation.7

The fact that Aristotle did not mention the formal cause here does not mean that he denied a form to minerals. He probably omitted it because it was difficult to explain, for he wrote in the same book: “Inanimate bodies like copper and silver ... all are what they are in virtue of a certain power of action or passion. But we cannot state their form accurately.”8 Plato, from whom Aristotle derived the notion of the watery nature of metals, postulated an aqueous or at least a water-borne mechanism for mineral generation, metallic “water” being “hard¬ ened by filtration through rock,” whereas “earth filtered through water passes into stone.”9 Theophrastus, Aristotle’s successor as head of the Lyceum, held that “of water are metals, while of earth are stones . . . formed of a pure and uniform matter, this matter being produced as a result either of a ‘conflux’ or of ‘filtering.’ ”10 Like Plato and Aristotle, Theophrastus made no mention of the 7. Meteorology 111 6, 378a—b. 8. Ibid, iv 12, 390a. 9. Timaeus 59, 60. The translation of Plato’s writings used throughout the pre¬ sent book is Benjamin Jowett, The Dialogues of Plato Translated into English, 4th ed. (Oxford, 1964). 10. De lapidibus, sects. 1—2, trans. by David Eichholz (Oxford, 1965). Eichholz challenges the traditional view that Aristotle meant the dry exhalation to be the material cause of stones, and holds that, like Theophrastus, Aristotle held earth to be the material cause of stones, the heat of the dry exhalation being the efficient cause (ibid., pp. 18, 43).

[24]

The Scientific Reinterpretation of Form

formal cause in this context. Theophrastus’ De lapidibus became an important source of facts for later writers, especially as a result of its extensive use by the elder Pliny (a.d. 23—79) in the mineralogical sections of his encyclopedic Historia naturalis, which was continuously available and enormously popular throughout the Middle Ages and through the sixteenth and seventeenth centuries. Pliny, too, took for granted the basis that Plato and Aristotle had provided for mineralogy. His very popularity, however, detracted from mineralogy in one respect, for his strong medical emphasis led to a shift away from the study of minerals for their own sake. The late classical and medieval writers who followed him were usually concerned more with the supposed magical and phar¬ macological uses of stones than with their formation and their mineral properties. This trend was reversed, however, by some of the Arab writers, who returned to the mineralogical and chemical study of minerals. Among them we may single out Avicenna (980-1037), whose adap¬ tation of Aristotle’s and Theophrastus’ mineral theory is of interest both for its own sake and because of its lasting influence on miner¬ alogy and geology. Arab chemistry interpreted Aristotle’s smoky and vaporous exhalations as sulfur and mercury, respectively, in the generation of metals, and as earth and water, respectively, in the generation of stones. Avicenna adopted this theory as the basis of his system, adding to it observations of his own. Like Theo¬ phrastus, he emphasized the role of water in the formation of minerals and stones. He wrote: “Stones are formed in two ways, by conglutination and by congelation. In the former, earth is domi¬ nant, and in the latter, water. In the first, mud is dried . . . and becomes stone. . . . The second is by the congelation of water fall¬ ing in drops, or by means of something deposited from running water, which remains at the bottom and becomes stone.’’11 Avicenna, like Aristotle, did not mention the form of stones. Like the chemists, he attributed the specificity of metals to their material cause, that is, to the varying proportions and degrees of purity of the sulfur mixed with their mercury. As the cause of the specificity of stones he suggested an earthy, mineral, or lapidific force acting by means of heat and cold. He never defined this force, but he seems to have thought of it as an efficient, rather than as a formal, 11. I translate the traditional Latin text of De congelatione et conglutinatione lapidum in Jean Manget, Bibliotheca chemica curiosa (Geneva, 1702), vol. 1, p. 636. For a translation from the Arabic, see Eric Holmyard and D. C. Mandeville, Avicennae de congelatione et conglutinatione lapidum (Paris, 1927), who also give a better Latin text.

Form in the Mineral Kingdom

[25]

cause, which thus probably does not feature in Avicenna’s account of mineral generation. Avicenna’s mineralogical work was translated into Latin in about 1200 and so it was available to Albertus Magnus (1206-80), who did a great deal to make known in the West the philosophy of Aristotle and the work of Avicenna. Albertus was far more than a mere popularizer, however; as a theologian, philosopher, man of science, and teacher of Thomas Aquinas, his influence on succeed¬ ing generations was immense. Here we must confine ourselves to considering the way he brought Aristotelian philosophy to bear on mineral theory. In his Miner aha he used mineral data from ancient writers, Avicenna, and his own observations, and he explained the data in terms of form theory. Why did Albertus, unlike his prede¬ cessors, find the material and efficient causes inadequate? Partly because, as his title of Doctor universalis suggests, he was working his way toward a synthesis of all knowledge within a framework of Christian Aristotelianism (a synthesis later achieved by his pupil Thomas Aquinas), and he felt that a basic philosophical concept such as form must be universally applicable. Partly because he was obliged to take into account some contemporary beliefs about for¬ mative forces such as astral influences and alchemical operations. Partly because he was grappling for the first time with the problem of mineral specificity and attempting to find a logically coherent answer to it. It is this attempt that we must now examine. Albertus argued that the material and efficient causes were inad¬ equate on their own to account for the specificity of minerals be¬ cause they were common to all minerals: A mineralizing power . . . does not seem adequate as the efficient cause of stones, since it acts in common not only upon stones but also upon all metals. . . . Practitioners of alchemy seem to say that all stones are produced entirely by accident. . . . They say that these stones have no real principle that produces specific form. . . . But the consequence of these [arguments] is intolerable error—namely that every stone would be of the same species as every other stone. . . . Moreover, stones would have to belong to the same species as metals, which also, being produced in the same way, have solidification and hardness instead of specific forms.12

In Albertus’ Aristotelian system, “the essential form in all things is what gives them being,’’ and specificity too, for Albertus often 12. The translation I use is that of Dorothy Wyckoff, Albertus Magnus’ Book of Minerals (Oxford, 1967), pp. 18-21; see also pp. 171, 177.

[26]

The Scientific Reinterpretation of Form

called the form the “specific form”; he wrote: “It seems madness to have any doubts concerning the substantial form of stones; for sight assures us that they are all solidified and their material is fixed according to a definite specific form. . . . Stones have substan¬ tial forms imparted by the powers of heaven and by the particular mixture of their elements.”13 The form, then, was seen by Albertus as being transcendent—“imparted by the powers of heaven”—and also immanent—“by the particular mixture of their elements.” It was a predetermined directing force working toward a particular end, immaterial and superior to the matter that it molded into a specific body; but at the same time it was embodied in matter suitable for its purpose, from which it could not be separated and through which alone it could act. This double character of the form, already implied by Aristotle but enunciated clearly for the first time by Albertus with respect to the mineral realm, was of great importance for the future understanding of the topic. An anonymous author writing soon after Albertus, and familiar with his work, also bore witness to the speculations about the for¬ mal cause of the mineral kingdom. He too was strongly influenced by Avicenna’s mineral theories, he was equally convinced of the important role of the powers of heaven, and although he had little to say about the specific forms of minerals, he was concerned to identify the formal cause. Concerning the formation of rock crystal he wrote: “The virtue is composite. . . . Crystal is made by an ele¬ mentary property which is the material cause, by a celestial proper¬ ty which is the efficient cause, and by the virtue of the Mover or Intelligence which is the formal cause.”14 He was fascinated by gems and speculated whether their virtue was caused by the ele¬ mentary qualities, as Alexander of Aphrodisias thought; or by the Intelligences, the movers of the heavenly spheres, as Avicenna thought; or by the corporeal forces of the heavens, as Hermes and Ptolemy thought; or by the soul, as Democritus and the Pythagore¬ ans thought; or by an Idea, as Plato thought; or by the substantial form of the stone, as Constantine thought. On this question he appealed to Albertus as the Final authority: “It seems to Albert of Cologne, who has spoken on this subject more definitely than any¬ one else, that the species is caused by the form, which is derived, on the one hand, from the celestial virtues of the Movers of the 13. Ibid., pp. 168, 24-5; see also p. 10. 14. Summa philosophiae Roberto Grosseteste ascripta, tractate 19.3, in Die philosophischen Werke des Robert Grosseteste, ed. Ludwig Baur (Munster-in-Westphalia, 1912), p. 629. This work is not now ascribed to Grosseteste.

Form in the Mineral Kingdom

[27]

spheres and the 48 stellar constellations and the signs [of the zodiac], and on the other hand, from the complex nature caused by the mixed elements.”10 But in spite of Albertus’ arguments, most medieval writers on mineral subjects continued to follow Aristotle, Theophrastus, Pliny, and Avicenna in confining themselves to the material and efficient causes. Precedent is always an important factor in scien¬ tific explanation. Some felt that the form, like the soul, should be reserved for biological and mental processes, not for inorganic phenomena. If a need was felt for formative causes in the mineral realm, astrological or alchemical forces seemed more accessible than philosophical concepts, in the view of most writers on mineral subjects. And as time went on, the gradual enlargement of knowl¬ edge about stones, gems, ores, and metals encouraged a belief that enough was known to explain minerals in physical terms alone. My purpose is not to trace the history of mineral theories, except insofar as this is relevant to the development and interpretation of the form concept in a mineral context. So a few examples will suffice to illustrate the types of mineral writings current between the time of Albertus and the sixteenth century. There were scholarly commentaries and questions on Aristotle's Meteorology, for in¬ stance by Albertus himself, Aquinas, and Themon Judaeus in the fourteenth century; these kept close to Aristotle’s treatment. On a more popular level there were lapidaries borrowing from Theo¬ phrastus, Dioscorides, and Pliny, and listing the medical and mag¬ ical uses and the symbolic meanings of stones; Albertus included two such lists in book 2 of his Mineralia. Then there were en¬ cyclopedic works describing all branches of knowledge in a tradi¬ tional manner, such as Bartholomew the Englishman’s De proprietatibus rerum and Vincent of Beauvais's Speculum naturale, both written at about the same time as Albertus’ Mineralia. Finally, there were alchemical books which treated mineral chemistry, mainly metals and their compounds, according to the sulfur-mercury the¬ ory of the Arab chemists; the most important of these was the Summa perfections of Geber. Because alchemists believed all metals to be impure approximations to gold, they could ignore specific forms and deal only with the material cause, the mixture of mercu¬ ry and sulfur. 15. Ibid. 19.6 (Baur, p. 633). Alexander was a Greek commentator on Aristotle about a.d. 200; Hermes was the legendary author of the third-century a.d. Her¬ metic books; Constantine the African was a translator of medical works in the eleventh century.

[28]

The Scientific Reinterpretation of Form

During the sixteenth century new sorts of writings on mineral topics emerged. There were books on natural history, openly im¬ itating Pliny but also showing their authors to be keen observers of the world of nature. Sitting lightly to established traditions, these works offered physical explanations based partly on the authors’ own observations and partly on an eclectic selection of sources. For instance, Jerome Cardan’s De subtilitate libri XXI showed his eclec¬ ticism by making use of Aristotle’s view of form, the sulfur-mercu¬ ry theory of metals, and the belief that minerals had occult and astrological significance and possessed a sort of life. His mineral explanations, like those of most of his contemporaries, were con¬ fined to the material and efficient causes. It must be repeated, however, that this was not tantamount to a denial of the formal cause, as we see from Alfonso Barba’s El arte de los metales, written a century later, which gave mineral explanations in terms of the material and efficient causes alone, but also insisted that “stones have their substantial forms to give them specificity.”16 The sixteenth century also saw the appearance of technical trea¬ tises on mining and metallurgy, such as those of Vannoccio Biringuccio, Georg Bauer (Agricola), and Lazarus Ercker. Practical in character, these works adopted an empirical approach and had little to say about theory; the most important were the writings of Agricola (1494—1555), which marked a step forward in miner¬ alogy. Agricola’s approach was reminiscent of that of Theo¬ phrastus in its factual nature, its interest in extraction techniques, and its emphasis on water-borne processes. Agricola objected to traditional mineral theories based on biblical passages, on al¬ chemical or astrological doctrines, and on Aristotle’s Meteorology (although, like all his contemporaries, he could not avoid being influenced by Aristotelian theory). Instead of Aristotle’s exhala¬ tions or the chemists’ sulfur and mercury, Agricola followed The¬ ophrastus and took earth and water as the material cause of miner¬ als. He introduced a degree of specificity into matter itself, without recourse to form, by postulating lapidific, saline, and metallic juices which solidified (either on their own or with varying proportions of earth and water) to produce all the varieties of minerals.17 He also allowed for an increased variety of efficient causes operating on and below the earth’s surface, which modified the matter in diverse ways; he particularly emphasized the role of water in dissolving and transporting mineral constituents. In this complex and all16. I cite the French translation, Metallurgie (Paris, 1751), p. 44. 17. De ortu et causis subterraneorum (Basel, 1546), pp. 9, 50, 71.

Form in the Mineral Kingdom

[29]

inclusive mineral system the formal cause could find no place; even the efficient cause was partly transferred to matter, which was portrayed as more active than in earlier systems. In addition, a new chemical doctrine was put forward in the sixteenth century by Agricola’s contemporary, Theophrastus Para¬ celsus (1493—1541), and his followers. This doctrine added salt to sulfur and mercury to constitute Paracelsus’ three fundamental principles of nature, the tria prima, and it emphasized the role of salt in the generation and crystallization of minerals. The Paracelsians also reintroduced the formal cause into the mineral kingdom by insisting on a formative force or agent to direct and mold mat¬ ter. This formative agent was given various names by different chemists; in its more formal aspect it was called form, archeus, star, and so forth, while in its material embodiment it was expressed in terms of chemical seeds, spirits, and principles. In chapters 7 and 8 we shall study these entities as chemical reinterpretations of the concept of form. For the moment it is enough to point out the contrast between the chemists who admitted, under whatever name, a formal cause in the mineral realm, and the majority of other writers who confined their mineral explanations to the mate¬ rial and efficient causes alone. Thus by the end of the sixteenth century diverse explanations had been advanced for the generation of minerals. There were purely mineralogical theories featuring Aristotle’s exhalations or the fluid mechanisms of Theophrastus, Avicenna, and Agricola; there were chemical theories of the old sulfur-mercury type or based on the new tria prima of Paracelsus; and there were eclectic theories of assorted origins. But the real point at issue was not the dispute about vaporous or fluid processes, or the roles of heat and cold, or chemical constituents. The fundamental cleavage of opin¬ ion concerned the need for a formative or formal cause, an essen¬ tial part of Paracelsian theory but passed over in silence so far as other systems were concerned. In affirming the need for a formal cause, the chemists, although not Aristotelians, were at one with Albertus Magnus. They held that “there would be no essential differences between any minerals if it were only a question of the matter and the universal efficient cause,” and that “in all genera¬ tions there must be a further power and vertue ... an internail and domesticall agent . . . proper to that which it produceth; otherwise there would be no distinction of species.”18 18. Etienne de Clave, Paradoxes, ou traittez philosophiques des pierres et pierreries, contre Vopinion vulgaire (Paris, 1635), p. 357; Edward Jorden, A Discourse of Naturall Bathes and Minerall Waters (London, 1633), p. 70.

[30]

The Scientific Reinterpretation of Form

In the mineral kingdom as a whole, then, the formal cause was often neglected except by the chemists; but what about crystal form? In antiquity and the Middle Ages there was little interest in the shapes of crystals and they were rarely mentioned save in the most cursory fashion, perhaps because gems were admired less for their shapes than for the decorative cameos and intaglios carved in them. But there were exceptions; Pliny’s Natural History described several crystal shapes, and a few medieval writers followed him. We may mention Vincent of Beauvais, Roger Bacon, and especially the fourteenth-century traveler Sir John Mandeville, who noted that Indian diamonds “ben square and poynted of here own kynde, bothe above and benethen, withouten worchinge of mannes hond. . . . As the perl, of his owne kynde, taketh roundnesse, right so the dyamand, be vertu of God, taketh squarenesse. . . . And sume ben six squared, sume four squared, and sum thre, as nature schapeth hem.”19 But in the sixteenth century, contemporary with Paracelsus and Agricola, came an upsurge of interest in crystallization. It cannot, I think, be ascribed to the chemists and metallurgists, who had as yet little contribution to make to the subject. Agricola took little notice of crystallinity except in De natura fossilium, and there he seemed more interested in the color, luster, and artificial shapes of cut gems than in their natural figuration. He gave several descriptions of the shapes of precious stones, but he held that “although gems have different forms, these do not constitute different species. . . . Gems are chiefly distinguished by their colors”; and one reason for this was his mistaken opinion that every precious stone, including the diamond, must resemble rock crystal in being hexagonally fig¬ ured.20 As for the chemists, their attention was mainly concen¬ trated on the volatile distillation products, so that solid residues of crystalline salts held little interest for them and were often dis19. Mandeville’s Travels, ed. P. Hamelius (London, 1919), chap. 18. Pliny de¬ scribed the shapes of sal ammoniac and common salt (Historia naturalis bk. 31.39, 41), and of the gems rock crystal, Indian adamas, and iris (bk. 37.9, 15, 52). He started the misconception, which persisted until the seventeenth century, that rock crystal was superfrozen ice (bk. 37.9); he misunderstood Plato’s mention of the formation of ice (Greek krustallos) in Timaeus 59 to refer to crystal. Roger Bacon’s descriptions of iris and rock crystal (Opus majus 4.12; 6.2) copied Pliny; Vincent of Beauvais borrowed from Pliny and other writers his accounts of diamond, beryl, rock crystal, and androdamas (Speculum naturale 8.40). 20. De natura fossilium, pp. 276, 282. Agricola described the shapes of ombria, marble, rhombites, emerald, cvanus, diamond, carbuncle, rock crystal, and beryl (ibid., pp. 262—4, 278, 283, 285—7, 292—3). Often it is not clear whether he was referring to the natural or cut chapes of precious stones.

Form in the Mineral Kingdom

[31]

carded without examination. Paracelsus, however, mentioned the shapes of common salt, niter, “salt of crystal.” and marcasite; and his follower Andreas Libavius mentioned those of alum, natron, and vitriol.21 What excited this new interest in crystals? For one thing, the invention of printing enhanced the popularity of Pliny’s Natural Histoiy, with its praise of rock crystal (quartz crystallizing in a hex¬ agonal prism). Always popular for ornament, this gem was highly esteemed for its transparency and because its freestanding forma¬ tion allowed a perfection of shape rarely achieved by the embed¬ ded gems with their pebble appearance when uncut. Such was its prestige that many writers assumed, as did Vincent of Beauvais and Agricola, that rock crystal was the basic gem to which others con¬ formed; and from the seventeenth century onward, the word “crystal,” originally the name of this variety of quartz alone, came to signify any transparent, angular stone or salt. Rock crystal is the chief precious stone to occur naturally in Europe; until the end of the Middle Ages jewels other than semiprecious stones had to be imported sparsely and with difficulty from the East. A second rea¬ son for sixteenth-century interest in crvstals and jewelry was the arrival of quantities of gems, especially the brilliant Columbian emerald, from the New World, whose mineral resources were now being opened up. Yet another stimulus was the virtuosity of Renaissance crafts¬ men. On a modest scale gem cutting was practiced before 1400, but the fifteenth-century breakthrough in diamond cutting, associated with the name of Louis Berquen of Bruges, promoted an enor¬ mous increase in the making of jewelry and the collecting of pre¬ cious stones in the sixteenth century, now that the beauty of jewels could be enhanced by facets. The fifteenth century also saw the manufacture of “crvstal” glass of unprecedented transparency, as well as enameled glass, attributed to Angelo Barovier of Venice. This not only prompted the wider use of the word “crystal,” but also encouraged the glassmakers to emulate the gemcutters by manufacturing artificial jewels. All these developments inspired interest in the natural as well as the cut shapes of gemstones. Less notice was taken of the shapes of salts than of precious 21. Paracelsus, The Economy of Minerals, 11 and 12; A Little Book Concerning the Quintessence; Preparations in Alchemical Medicine, 1; trans. by Arthur E. Waite, The Hennetic and Alchemical Writings of Paracelsus (London, 1894), vol. 1, p. too, vol. 11, p. 203. All references will be to this translation. Libavius, Alchemia (Lrankfurt, 1597), PP- 377’ 384-

[32]

The Scientific Reinterpretation of Form

stones. But Andreas Libavius, who, like Paracelsus, noted some shapes of salts, was probably the first to use the word “crystal” to signify salts as well as gems, and also the first to suggest that crystal¬ line shape depends on a certain mode of formation from solu¬ tion— “congelation,” which we now call crystallization. Libavius wrote: Indeed formation by congelation agrees with the crystalline form and consistency.

Therefore

although

other

things

also

possess

the

crystalline form and consistency, such as certain salts, repeatedly sub¬ limed mercury, etc., yet they are not properly called crystals unless the method of production also corresponds and it is an essential extract. Hence it is that most salts which are salts by nature fall into this class, and differ from alkalis both in manner of production and in form. Thus the foremost are alum, borax, sal gem, crystalline sugar, and others.22

But if most chemists and metallurgists had not a great deal to say about crystals in the sixteenth century, writers on natural history were more forthcoming. Attempts at a scientific classification of stones, far removed from the old lapidaries, were made by Agri¬ cola’s contemporaries Conrad Gesner (1515—65) and Hans Kentman. The latter made brief mention of the shapes of stones and gems, mostly listing the numbers of their angles; Gesner gave very detailed descriptions of their geometrical forms, with many il¬ lustrations, and even adumbrated the crystallographic principle of constancy of angles by his remark that “one crystal differs greatly from another by its angles and, in accordance with them, by its figure.”23 We should not assume from this that they were crystallographers in the later sense of the word. Both writers devoted much more attention to curiously shaped stones than to regular crystals. Of Gesner’s fifteen classes of stones grouped by shape, only one class concerned angular crystals; the other fourteen classes were characterized by shapes resembling the heavenly bodies, animals, plants, and other natural objects. Gesner and Kentman offered no explanation of the crystalline forms they described. Agricola spoke only of physical causes: 22. Alchemia, p. 377. 23. De rerum fossilium, lapidum et gemmarum maxime figuris et similitudinis liber, p. 19. This was published in the same volume, De fossilibus (Zurich, 1565), with Kentman’s Nomenclatura rerum fossilium and other works. Fossiles meant any subterranean bodies, minerals as well as fossils in our sense of the word.

Form in the Mineral Kingdom

[33]

“Stones differ in their shapes, which are given to them primarily by their situation, then by the efficient cause, and lastly by their mat¬ ter.” Paracelsus held that “their shape and species and angularity are bestowed upon them in proportion as the salt in them exists in a subtle or a dense state.”24 However, some of Gesnef s fellow natu¬ ralists, particularly Jerome Cardan (1501—76) and Andrea Cesalpino (1519—1603), had more to say. Cardan upheld the concept of form and used it in many contexts; he also believed that minerals possessed some sort of life. But when he sought to explain the geometrical shape of rock crystal, he did not follow either of these lines; he confined himself to the external efficient cause and to mathematical necessity: It must now be said why [rock] crystal has six surfaces. The reason is this: just as bees’ cells are surrounded by others, so parts of crystal are by other parts. But why should they be surrounded by others to make a hexagonal shape, when a sphere can be surrounded by 14 other spheres and not just by six? It is best to refer it to the force in the nature of a body, since every body enclosed by plane faces is dis¬ tinguished by length, breadth and height. Therefore crystal and the rest of this sort of gem, such as beryl, have six sides.25

These arguments were not difficult to refute. Cardan's opponent Julius Caesar Scaliger, a champion of the form, pointed out that the honeycomb analogy overlooked the fact that rock crystals were usually freestanding and that the other argument could be better exemplified by the six faces of a cube in three dimensions than by the six edges of a hexagon in two dimensions—“the worst mathe¬ matics slips out from the best and most skilled mathematician!”26 Cesalpino, who was equally distinguished in the life sciences and the earth sciences, proposed a comprehensive mineral system that united Aristotle's two exhalations, the sulfur-mercury theory of metals, and Agricola's mineral juices. Neither in his mineral system nor in his explanation of crystal shapes was there any room for the form, which seemed to him to be inapplicable to the mineral kingdom: 24. Agricola, De ortu et causis subtenaneorum, p. 62; Paracelsus, Concerning the Generation of the Elements, chap. 2 (Waite, vol. I, p. 225). 25. De subtilitate libri XXI (Lyons, 1554), p. 298. 26. Exotericarum exercitationum liber XV de subtilitate ad Hieronymutn Cardanum (Paris, 1557), p. 180. Nevertheless the bee cell argument was popular for a long time; it was still being repeated by Jacques Rohault in his Trade de physique (Paris, 1672), p. 212.

[34]

The Scientific Reinterpretation of Form

We see alum, vitriol, salt niter and white sugar congealed into angular faces when, after heating, the liquid is separated from the earthy dregs. So it is to be believed that the same thing happens to [rock] crystal. ... It is wonderful how [rock] crystal always shoots with a hexagonal figure and not otherwise, so precisely that it could never be imitated by art. . . . But it does not seem to be consistent with reason to ascribe a definite figure to inorganic bodies, for it is the property of the organic virtue to produce a definite figure, the soul acting for a certain purpose. ... In the drying up of a marsh by the sun, it is split into many cracks, making various figures. It is to be believed that something similar happens in the coagulation of [rock] crystal. For the lapidescent juice fills all the space where it is, its earthy parts splitting apart during the coagulation, attracted towards the walls of the rock. It agglutinates and makes a shape in little crystals suitable for filling the space.27

Mathematical necessity, Cesalpino thought, dictated the hexagonal cross section of rock crystal, for of the three space-filling shapes— triangle, square, and hexagon—the hexagon is nearest to the cir¬ cle, the perfect figure, and so it must be the best shape. Supporters of the formal cause were not slow to point out the lack of a firm basis for this explanation. For one thing, crystals separate out from liquid and are not formed by the splitting apart of a viscous space-filling mass. But there was also a more serious criticism: “If this splitting is accidental and not according to the laws of geometry, the form of [rock] crystals cannot arise in this way, for whenever and wherever they are generated, they always have exactly the same figure. . . . Nor can he give a reason why this should not happen for other gems as well as for [rock] crystal. For gems in fluors do not concrete into this figure, but into several other figures—globular, square, pentagonal, etc.”28 This criticism pinpointed the dilemma of those who excluded the formal cause: how can a constant and specific figuration arise accidentally or mechanically? If it is accidental, it cannot be constant when repeat¬ ed; if it happens by mathematical or mechanical necessity, a differ¬ ent cause must be assigned for each specific geometrical shape. The form, on the other hand, is both specific and constant. 27. De metallicis libri III (Rome, 1596), pp. 96-7. Cesalpino also mentioned, but did not explain, the shapes of niter or natron, limestone, selenite, diamond, and pyrites (pp. 49, 84, 86, too, 149). 28. Daniel Sennert, Tractatus de consensu et dissensu Galenicorum et Peripateticorum cum Chymicis, Opera omnia (Lyons, 1650), vol. hi, p. 767; based on Anselm Boetius de Boot, Gemmarum et lapidum historia, 2d ed. (Leiden, 1636), pp. 41—6.

Form in the Mineral Kingdom

[35]

Seventeenth-century writers who allowed for only external causes of crystalline shape did not come to any more satisfactory conclusions. Etienne de Clave, who insisted on the formal cause in the generation of minerals, ignored the figuration of stones until the last chapter of his mineral treatise, and then said only that “stones arise with angular figures because of the waters which, flowing round them, compact their matter by angles.”29 Nicolaus Steno’s detailed and exact observations of crystallization led him to some important results, including appreciation of the layered de¬ velopment of crystals and recognition of the constancy of their angles. His account of crystal formation, he claimed, was compati¬ ble with any matter theory—atoms, alterable particles, the four elements, the chemical principles—and with any formative agent— “the form, or the qualities proceeding from the form, or the idea, or the tenuous common substance, or the individual soul, or the world soul, or the immediate act of God.” But he was skeptical of such theories; formative agents were “known only by name,” and notions of shaped particles did not “accord with fact.” So he con¬ cluded that “as regards the formation of crystal, I would not ven¬ ture to declare in what manner its first shape is produced,” and his account of crystallization in terms of the motions of fluids and particles did not explain the shapes of crystals.30 Steno was a Cartesian; with Descartes’s views on crystallization we shall deal in chapter 5. Here it is sufficient to say that he as¬ signed the cubic shape of common salt to accidental factors, and for the stellate shape of snow crystals he invoked mathematical necessi¬ ty.31 That the mathematical necessity of surrounding a sphere by concentric rings of six equal spheres could just as easily give rise to a spherical snowflake as to a plane one was pointed out by Jacques Dortous de Mairan. The latter writer, after an attempt to combine Cartesian and Newtonian ideas on the architecture of matter, end¬ ed his review of observations and theories about ice and snow crystals with the admission that there must be “a sort of organiza¬ tion . . . which determines their constant arrangement, always rela¬ tive to angles of 60 or 120 degrees.”32

29. Paradoxes, p. 483. 30. Desolido intra solidum naturaliter contento dissertationisprodromus (Florence, 1669), trans. by John G. Winter, The Prodromus of Nicolaus Steno’s Dissertation Concerning a Solid Body Enclosed by Process of Nature Within a Solid (New York, 1968), pp. 216—7, 237; see pp. 238-40. 31. Les Meteores (Paris, 1637), discours 3 du sel; discours 6 de la neige. 32. Dissertation sur la glace, 2d ed. (Paris, 1749), p. 169; see also pp. 161—9.

[36]

The Scientific Reinterpretation of Form

If the reason for the figuration of crystals was not to be found in the material and efficient causes common to all minerals, or in the operation of accidental factors, or yet in mathematical or mechan¬ ical necessity, all that remained was to fall back on the traditional concept of the specific form, as Descartes’s contemporary, the chemist Edward Jorden, pointed out: “Every kinde [of salt] hath his severall manner or fashion of shooting, whereby a man may see the perfection of each kinde. . . . The reason hereof Scaliger saith cannot be drawne from the Elements . . . but only from the forme, anima, seed, etc., which frames every species to his own figure . . . according to the science, as Severinus termes it, which every seed hath of his own forme.”33 Whether couched in the Aristotelian language favored by Scal¬ iger, or in terms of the seed, the chemical reinterpretation of form employed by Paracelsians such as Severinus, the concept of form made a remarkable comeback in the sixteenth and seventeenth centuries. It was remarkable because since the time of Albertus Magnus the formal cause, although rarely denied, had suffered a virtual eclipse by the material and efficient causes in mineral expla¬ nations. When we seek a reason for this renewal of the concept of mineral form at a time when the scholastic substantial form had been coming under attack, we are forced to the conclusion that one of the reasons was the increasing interest in crystals, coupled with an awareness of the shortcomings of mechanical explanations of crystallization. Of course there were other reasons as well, which we shall explore in later chapters: the search for fresh interpreta¬ tions of the form concept to replace the scholastic substantial form, the use made of formative entities by the newly respectable chem¬ ical tradition, the concern of many corpuscularian writers to incor¬ porate a principle of form and order into their particle theories. But each of these concerns impinged upon the study of crystals, influencing crystal theory as well as drawing inspiration from it. Now, if mechanical explanations of crystalline shape were clearly inadequate, it had to be admitted that an appeal to the formal cause had its drawbacks too. The scholastic writers of the Middle Ages had been severely criticized for imagining that merely stating the substantial form as the cause for something exonerated them from the need to offer an explanation or mechanism for it, that is, an efficient cause. This was one of the chief objections made by later writers to the scholastic use of the substantial form, an objection of 33. Discourse of Naturall Bathes, p. 39.

Rock crystals (top and center) and basalt (bottom). (From A. B. de Boot, Gemmarum et lapidum historia, 3d ed., Leiden 1647. Courtesy of the History of Science Collections, Cornell University Libraries.)

[38]

The Scientific Reinterpretation of Form

which the sixteenth- and seventeenth-century champions of the formal cause were well aware. One of the first writers in the seven¬ teenth century to ascribe crystal figuration to the form was Anselm Boetius de Boot (1550-1632), who was an Aristotelian as well as a chemist. He had considerable influence on other writers, especially on his younger contemporaries Daniel Sennert and Etienne de Clave, and through them on the corpuscularian writers Pierre Gas¬ sendi and Robert Boyle. De Boot wrote: To the substance belong the form and the external figure which makes some stones angular and others round. Angular ones may have many angles, like basalt, or only six, like [rock] crystal. . . . The action of a thing seems to take its origin from a certain internal virtue, i.e. from the substantial form. . . . Any earth which hardens into a common or precious stone contains in itself a lapidific spirit . . . which is the cause, next to the form, of change and alteration.34

De Boot refuted Cesalpino’s mechanical explanation of crystalliza¬ tion and denial of a form to minerals, and put forward his own view: I do not see why one should deny a formative soul to certain stones such as [rock] crystal. . . . That faculty which always preserves the same figure in its species deserves the name of soul. ... It is not against reason, as he imagines, that a faculty in something, or a soul if you like to call it that, should produce a definite figure. ... It always uniformly allots a hexagonal figure to [rock] crystal. . . . Nor does it matter whether this happens by the expulsion of unwanted material or by the attraction of suitable material; either of these takes place by means of the faculty.35

De Boot did not make the mistake of exalting the formal cause at the expense of the efficient cause. On the contrary, he suggested several possible mechanisms by means of which crystallization might take place: mineral seeds and a lapidific spirit; expulsion or attraction of matter; the action of salt in minerals; and the motion of particles, a mechanism that was very advanced for its time: “The angular form happens when particles move to the center with un¬ equal speeds and forces . . . the particles that are more subtle than others, or more aerial, or slower in reaching the center, are left at

34. Gemmarurn et lapidum historia, pp. 18, 25. 35. Ibid., pp. 43-4.

Form in the Mineral Kingdom

[39]

the corners or pushed there by others.”36 But whether the efficient cause be chemical or mechanical, “either of these takes place by means of the faculty.” Each mechanism was based upon the con¬ cept of form, for the specific form directed and determined the action of salt, spirit, and seeds, or the transfer of material, or the nature and speed of the particles. Every efficient cause was con¬ trolled by the formal cause. The German physician Daniel Sennert (1572-1637), who ad¬ mired de Boot as “the most diligent investigator into the nature of stones and gems,” also insisted that the formal cause must be taken into account for minerals and crystals. Aristotelian, but with eclec¬ tic sympathies, Sennert played an important part in uniting the various approaches to the form in the early seventeenth century, and it is no coincidence that the form of crystals excited his interest. He made use of some of the mechanisms that de Boot had sug¬ gested for crystallization and, like him, believed that these were no more than the vehicle of the form. He wrote: “Always in vain does anyone resort to external causes for the concretion of things; rather does it concern the internal disposition of the matter. . . . On account of their forms . . . things have dispositions to act. . . . They receive their perfection from their form, not from an external cause. Hence also salt has a natural concretion . . . not from heat or cold, but from its form, which is the architect of its domicile.”37 According to Sennert, not only the act of concreting but also the resultant crystalline shape was the act of the form; indeed, the external figuration of a crystal was the outward and visible sign of the inward form and the proof of its presence and activity: Every form of any perfect mixt, like diamond, even though it is not a soul, is a quintessence, quite different from the four elements ... a plastic principle directing to a definite form. . . . When various stones and gems are generated, this proceeds from some specific form. For each gem has its own specific form which distinguishes it from all others and which it gets from a seminal principle of its own species. . . . The differences between forms are recognized only by the differences between their faculties, operations, and qualities. Hence [rock] crystal and Hungarian and Silesian diamond are hexagonal in shape; western emeralds are quadrangular; Bohemian garnet and the geode are spherical; and other gems have other figures.38

Gems may be the most outstanding, but they are not the only, examples of specific figuration, as Sennert pointed out: 36. Ibid., p. 45; see also pp. 23-5, 28-9, 31-2, 44, 49, 540, 543-6. 37. Tractatus, p. 765. 38. Epitome scientiae naturalis, Opera omnia, vol. 1, pp. 77, 81.

[40]

The Scientific Reinterpretation of Form

Individual metals as well as gems possess specific forms ... as appears from this, that each individual possesses not only its own colors and other qualities, but most of them also possess their own special shapes. . . . Since some forms and natures are specific to niter, others to vitriol, others to alum, others to common salt, each salt concretes in this or that shape according to its form, by the formative spirit proper to it, just as gems too concrete in definite shapes.39

De Boot and Sennert, with others who shared their views, were standing within the Aristotelian tradition, however much it might be expanded and liberalized by the acceptance of other influences. Others among their contemporaries, however, felt more at home within the Platonic tradition. We shall have more to say about this in chapters 2 and 6; at present it suffices to indicate that Platonic doctrine emphasized transcendent forms or Ideas and a universal form or world soul, and that Plato’s vision of the cosmos, as ex¬ pressed in his Timaeus, envisaged it as being geometrical both in form and matter. Not only was the world soul geometrically de¬ signed, but the four elements, the building blocks of matter, were characterized by their own regular polyhedral shapes. Earth was a cube, water an icosahedron, air an octahedron, fire a tetrahedron; the quintessence or ether, the heavenly element, was a dodecahe¬ dron. Thus the five regular Platonic solids were the framework of the universe. Now, since crystalline shapes too are symmetrical polyhedra, and some of them coincide with the Platonic solids, it would seem natu¬ ral to look for some theoretical link between crystals and Platonic doctrines, and this was, in fact, the approach of some seventeenthcentury writers. The first to enunciate a Platonic theory of crystals was the astronomer Johann Kepler (1571 — 1630). He was also the first to call attention to the regular sixfold stellate form of snow¬ flakes and to try to explain it; the earlier passing references to snowflake “stars” or “flowers” by Themon Judaeus in the four¬ teenth century and Olaus Magnus in the sixteenth century seem to have aroused no interest. Kepler’s advocacy of the form concept did not make him oblivious of the material and efficient causes. He recognized that heat and cold must play their part, and also the regular stacking of ice pellets in geometrical patterns.40 39. Tractatus, pp. 745, 766. 40. Strena seu de nive sexcnigula (Frankfurt, 1611), trans. by Colin G. Hardie, The Six-cornered Snowflake (Oxford, 1966). “Equal pellets ... in the same horizontal plane . . . come together either in a three-cornered or a four-cornered pattern. . . . If four-cornered . . . the pellets will become cubes or rhomboids . . . comparable to the octahedron or pyramid. ... If three-cornered . . . the pattern will be compara¬ ble to the prism or pyramid” (p. 15).

Form in the Mineral Kingdom

[41]

But these factors could not be the source of crystal figuration, for they were general causes that account neither for the constant sixfold symmetry of snow crystals nor for their individual variety; the true cause must be specific: The cause of the six-sided shape of a snowflake is none other than that of the ordered shapes of plants and of numerical constants. ... I do not believe that even in a snowflake this ordered pattern exists at random. . . . There is then a formative faculty in the body of the Earth . . . the faculty of earth is in itself one and the same, but it imparts itself to different bodies and cooperates with them. It en¬ grafts itself on to them, and builds now one design, now another, as the inner disposition of each matter or outer conditions allow. . . . The whole realm of spirits is akin to the regular geometrical or world¬ building figures. . . . The authentic type of these figures exists in the mind of God the Creator, and shares his eternity.41

Thus Kepler was able to combine the notion of a universal form or formative faculty with differing specific applications of it, in miner¬ al crystals as well as in snow crystals: “The same faculty of soul that clothed the diamond within the earth in the form ... of the oc¬ tahedron . . . clothed with the same shape the snowflake. . . . For our cause other products of this formative faculty can speak. [Rock] crystals, for instance, all six-cornered, whereas octahedral diamonds are exceedingly rare. But the formative faculty of earth does not take to her heart only one shape; she knows and is prac¬ tised in the whole of geometry.”42 In addition to the stellate snow crystal, Kepler mentioned mineral crystals in the shape of the Pla¬ tonic solids octahedron, icosahedron, and dodecahedron, as well as the hexagonal prism of rock crystal and also salt crystals: rhombohedral vitriol and hexagonal prismatic niter. With reference to Paracelsus' attribution of crystallinity to salt, Kepler remarked: “Let the chemists tell us whether there is any salt in a snowflake, and what kind of salt, and what shape it assumes otherwise.”43 On the whole, the chemists contemporary with Kepler failed to take up his challenge to account for snow crystals, but there was one who shared not only Kepler’s interest in crystals but also his Platonic notion of crystal form. Phis was the Scot William David¬ son, who became professor of chemistry at the Jardin du Roi in 41. Ibid., pp. 33—5. “World-building figures” are the Platonic solids. 42. Ibid., pp. 43—5. “The same shape” means no more than that octahedra and snowflakes both have six points. 43. Ibid., p. 45.

[42]

The Scientific Reinterpretation of Form

Paris in 1648. Besides the traditional association of the five Platonic solids with the four elements and the quintessence, he linked the three chemical principles of salt, sulfur, and mercury with the three isosceles triangles into which the pentagonal faces of the dodecahedron can be divided; he also compared the four elements with the four groups of three faces in the dodecahedron, and the three chemical principles with the three planes composing each solid angle, for “as a solid body cannot be made without three planes, so a natural body cannot be made without salt, sulfur, and mercury.”44 He illustrated his book with the five Platonic solids and their derived forms, accompanied by geometrically symmetrical natural objects among which crystals predominated. There were fig and vine leaves; rose and peach blossoms; a bee and its cells; snowflakes; sal gem, iron and copper vitriols, salt of hartshorn, cooking salt, niter, gypsum, amethyst, and rock crystal. Most seventeenth-century chemists, while not sharing de Boot’s, Sennert’s, and Davidson’s interest in crystalline form, would have agreed on the role of the salt principle in causing mineral genera¬ tion and crystallization. This was a view that was sharply criticized by some writers outside the Paracelsian chemical tradition, such as Robert Boyle (1627-91). Boyle and the earlier French atomist Pierre Gassendi (1592-1655) were in the forefront of the mechan¬ ical philosophy movement and were committed to promoting parti¬ cle theory; at the same time they both had a keen interest in crys¬ tals. In a philosophy that claimed to explain all phenomena in terms of matter and motion there might seem to be no place for either the salt principle or the formal cause, but when crystals were taken into account the formal cause could not be dismissed. Even the mechanical philosophers could not fail to be impressed by de Boot’s influential Gemmarum et lapidum historia, which pointed out the flaws in Cesalpino’s mechanical account of crystallization and replaced it not only by chemical agents and the formal cause but also by particle theory. Study of the well-known writings of de Boot and Sennert raised the question of how the specific form might be understood in relation to corpuscular and saline theories of crystal¬ lization, and this led to new interpretations of the form concept in particulate terms. We shall deal in detail with these reinterpretations of form in

44. Philosophiapyrotechnica (Paris, 1633), which was translated into French in 1651 as Les elemens de la philosophie de I'art du feu ou chimie. On Davidson, a little-known figure, see works by John Read listed in the bibliography.

Form in the Mineral Kingdom

[43]

chapter 5; here we shall examine briefly how the study of crystals led up to them in the thought of Gassendi and Boyle. Gassendi observed the shapes of stones, gems, salts, snowflakes, and, using the newly invented microscope, dust particles and bladder gravel. In every case, he found, they were geometrically shaped, so that “even in this [mineral] creation Nature seems to have aimed at something regular.”45 His conviction of mineral regularity was also encouraged by reading de Clave’s mineral treatise Paradoxes, which was inspired by de Boot’s work and which emphasized the formal cause in minerals even though it did not connect it with crystal form. Gassendi’s Epicurean atomism had nothing to say about reg¬ ularity in nature—on the contrary, it laid all the stress on random¬ ness; but his study of crystals forced him to admit that this reg¬ ularity could not be accidental: Look at a mass elegantly divided and separated into several crystals, not accidentally made but identical and regular with a hexahedral form. . . . Does it happen by chance? No, rather because of a constant cause, a sort of seminal virtue. ... By reason of their constant regular figure, gems seem in a special way to come from a seed . . . which fits the corpuscles together . . . into little masses . . . and shapes them uniformly.46

This crystal “seed,” “constant cause,” or “seminal virtue” was none other than the formal cause. It was envisaged by Gassendi partly in terms of the formative chemical principle that he had learned from de Boot and de Clave, and partly in terms of a regular arrange¬ ment of geometrically shaped atoms that he had devised with crystals in mind. His crystal observations led him to a new under¬ standing of the form that could do justice to nature’s regularity and that could be applied to chemical and corpuscular theories. Boyle’s approach to the formal cause in particle theory had much in common with Gassendi’s. He questioned the validity of the scho¬ lastic substantial form and the chemists’ salt principle as causes of crystallization, but he recognized that chance alone could not ac¬ count for the specificity and constancy of crystal shapes. Boyle was both a better chemist and a keener observer than Gassendi, and his observations of salt and mineral crystals were supplemented by 45. Syntagma philosophicum, De lapidibus ac metallis, Opera omnia (Paris, 1658), vol. 11, p. 115. On the angular shapes of minerals, see vol. 1, pp. 170—3; vol. 11, pp. 34, 36-8, 41, 80-1, 114-5, n746. Ibid., vol. 11, pp. 114, 117.

[44]

The Scientific Reinterpretation of Form

laboratory experiments. The geometrical shapes of crystals sug¬ gested to him, as they did to Gassendi, that the internal construction of crystals must also be geometrically regular. He set himself the task of investigating “that remarkable property of being endowed with exact and curious shape and figure . . . for which salts have been, by modern philosophers especially, so much admired.”47 In the labora¬ tory he found that the same acid with different metals, or the same alkali with different acids, produced differently shaped crystals, and he was able to reproduce artificially the natural crystallization of salts and gems. Hence each acid, alkali, and metal must have its own specific internal form which was modif ied by the other in compound salt crystals. “And this I shall add in favour of the comparison I lately intimated betwixt the coagulation of [salt] petre and that of gems, that having made an odd menstruum wherein I was able to dissolve some precious stones, there shot in the liquor crystals . . . that might well have passed for crystals of nitre.” Moreover, careful inspection assured Boyle that uncut gems had geometrical shapes, suspected by few people at that time, and that even their apparent roughnesses and irregularities consisted of minute geometrical figures, indicat¬ ing a regular internal texture.48 It seemed clear to Boyle, then, that gems and natural and ar¬ tificial salts all had the same cause of crystallization, although their shapes were specifically different and constant. He could not avoid the question what this universal yet specific cause might be, a ques¬ tion to which diverse answers had been given: The chymists ascribe the firmness and hardness of bodies to salt. . . . The greater number of contemplators ascribe the effect under con¬ sideration to a certain substantial form. . . . But what this form is, and by what means it unites the parts so strongly in a diamond or a ruby ... is as difficult to conceive, as to imagine without it a cause of cohesion in a dry body. Other learned men there are among the modern naturalists, have recourse some of them to a spirit . . . but others fancy rather a certain cement or glue.49 47. The Origin of Forms and Qualities, according to the Corpuscular Philosophy, Works of the Honourable Robert Boyle (London, 1744), vol. 11, p. 478. Here Boyle most likely had Gassendi in mind. 48. An Essay about the Origin and Virtues of Gems, Works, vol. in, p. 218. See also pp. 219—20, 226—7; Experimenta et observationes physicae, vol. v, p. 83; A Physico-Chemical Essay, Containing an Experiment, with some Considerations Touching the Differing Parts and Redintegration of Saltpetre, vol. 1, pp. 231-2; Origin of Forms and Qualities, vol. 11, pp. 481-2, 486, 490-1. 49. The History of Fluidity and Firmness, Works, vol. 1, pp. 254, 261.

Form in the Mineral Kingdom

[45]

In addition to these versions of the formal cause, attention had to be paid to the opinion of the mechanical philosophers, which Boyle shared, that all phenomena were explicable in terms of the sizes, shapes, and motions of particles. Like Gassendi, he reconciled this opinion with the formal cause by his belief that the shapes and arrangements of particles within bodies were not random but reg¬ ular and that this regular internal structure embodied the form, causing the external shape and properties. He held that “divers known salts would, when broken, appear to be geometrically fig¬ ured, even in the lesser corpuscles, as well as they are evidently so in their entire bulk."50 This regular internal structure seemed to Boyle, as to Gassendi, the best model for understanding the formal cause that bestowed specific pattern and order; it produced crystal¬ line figuration, and it even made sense of the possible mineralizing role of salt by interpreting this as the effect of the geometrical shapes of saline particles. So through their study of crystals Gassen¬ di and Boyle both arrived at a corpuscular reinterpretation of the form. A similar view was held by Boyle's contemporary, the botanist Nehemiah Grew (1628-1711). Like Boyle, Grew emphasized the order and regularity of nature that manifested God's design. He detected it not only in living beings but also in crystals, which he described in detail; and from his observations he deduced, like Steno, the constancy of angles in any crystal species. He held that “Nature doth everywhere geometrize" and that “the regularity of Principles discovers itself more apparently in Consistent Bodies. . . . Gemms . . . Stones . . . and sometimes Metals themselves . . . are naturally figured. . . . Their Salts are always so: and always comformable to themselves. . . . Ice will, upon freezing, always shoot regularly . . . always at the same angles ... as there wou'd be in Snow. . . . From all which Instances, it is evident that the Princi¬ ples of Bodies are regularly figured. '51 Grew’s firm belief in the geometry of nature made the concept of form congenial to him; thus he could affirm: “It is their Form, by which they are what they are. . . . We all say, Forma dat esse [form gives being].’’52 As we shall 50. Origin and Virtues of Gems, Works, vol. in, p. 226. 51. The Anatomy of Plants, 2d ed. (London, 1682), p. 160; Cosmologia sacra (Lon¬ don, 1701), pp. 14—17. See also Anatomy of Plants, pp. 261—8; A Treatise of the Nature and Use of the Bitter Purging Salt contain'd in Epsom and such other Waters (London, 1697), pp. 12—13, 20, 22. 52. Anatomy of Plants, pp. 21, 222.

[46]

Tab $3

1 he Scientif ic Reinterpretation of Form

THJ/ent: Salt/ of QLaatr . c'

h-

ITLanru. Salts of Plants fS-

Salt crystals extracted from plants. (From N. Grew, Anatomy of Plants, ist ed., London 1682. Courtesy of the History of Science Collections, Cornell University Libraries.)

see in chapter 5, he followed Boyle in understanding the form in terms of geometrical particle figuration based on the shapes of crystals. Thus even the mineral kingdom was not without its witness to the order, pattern, and specificity in nature that were the visible expression of form. Snowflakes in the sky, mineral crystals in the earth, salts in the laboratory, all by their constant and specific ap¬ pearance seemed to call for some sort of formal cause, and this was asserted by many writers in Platonic, Aristotelian, chemical, or cor¬ puscular language. Let Gassendi have the last word, exploring the various approaches to the formative cause of snow crystals:

Form in the Mineral Kingdom

[47]

Should one resort to a world soul which, taught to geometrize by the supreme Creator, makes this wonderful structure by which the most beautiful material in a perfect number produces six rays from the center? . . . Or should one say that it reveals the eternal Wisdom which, playing in the circle of the earth, fashions regular figures above the earth in the same way as it forms men, fishes, or other sorts [of fossils] out of stony material inside the bowels of the earth? Or should one say that since the seeds, and hence the figures, of all natural things are specific, therefore in the same way that animals, plants and stones are delineated by definite forms, so are other things delineated by the necessity of their seeds? For we see diamond, [rock] crystal, amethyst, and other gems, as well as alum, salt, arsenic, and all minerals, shaped with invariable forms as soon as they are coagulated or sublimed. Thus snow could be similarly configured by its own solidification. This is worthy of consideration; imagine part of sea¬ water to be evaporated and solidify into snow, and part to be com¬ pressed and change into salt. Just as the latter is formed into cubes with six faces, the former is formed into stars with six rays. Or should one say that when sea foam hardens it contracts into itself in various ways, and because there is a certain uniform tension, it has to contract into something like strings forming the sides of equilateral triangles, whose outermost side breaks ... so that the parts nearer the center contract towards the other sides? Or should one say that the moment a droplet hardens, six others at once sur¬ round it, touching both it and each other on all sides; six more, and others beyond them, adhere to the central region and harden, and thus six rays are created which seem to project from the center? But whilst some droplets join these rays, others fall off, or fail to adhere, or melt; how can one say the same about them as about the former ones? Indeed, whatever we say, we will not claim that there is a single proper cause, since there are so many things that can justly be ob¬ jected about each of them.53 53. Syntagma philosophicum, De rore, pruina, nive, grandine, glade, melle ac man¬ na, Opera omnia, vol. 11, p. 81. The first paragraph refers to the Platonism of Kepler’s Strena; then to the Bible, which in the Vulgate translation of Proverbs 8.31 speaks of the divine Wisdom playing in the circle of the earth. To this “play” oddly shaped stones and fossils, called “sports of Nature,” were popularly ascribed. The second paragraph refers to the chemists' beliefs, which Gassendi shared, that the form was associated with a mineral seed and that crystallinity was caused by salt. Gassendi held that “salt niter is the cause of cold and also of solidification” (p. 80), as did his contemporaries Erasmus Bartholinus (De figura nivis, 1661) and Claude Berigard (Circulus Pisanus, 1643). The third paragraph criticizes the mechanical theories of Isaac Beeckman, who had much influence on Gassendi (see Beeckman's Journal for 1623), and of Descartes (Les Meteores, discours 6).

CHAPTER TWO

The Development of the Concept of Form after Aristotle “Form” for Aristotle embraces a variety of meanings. Sometimes it is used of sensible shape. . . . But more often, perhaps, it is thought of as something which is an object of thought rather than of sense, as the inner nature of a thing which is expressed in its definition, the plan of its structure. . . . And in nature, the form which is to find fresh embodiment is already present and is the cause of movement. William D. Ross, Aristotle

of form that developed in the West and became normative for European philosophy was based upon Aris¬ totle’s statements as elucidated by the Greek and Arab commen¬ tators and the Latin schoolmen of the Middle Ages. His conception of form was a rich and varied one, operating at different explana¬ tory levels and bringing together many aspects of his thought. Aristotle approached the form in many ways. In the passage of which part is cited at the head of this chapter, Ross identifies eidos, logos, and to ti en einai, Aristotle’s main terms for the form, as “intelligible structure,” “formula or definition,” and “what it was to be so-and-so,” respectively.1 Perhaps the simplest approach is Aris¬ totle’s definition of form as “that by reason of which the matter is some definite thing,” that is, as the source of specificity.2 It should be noted that the form of a thing is the form of the species, not of the individual; two individuals of the same species “are different in virtue of their matter, for that is different, but the same in form.”3 Aristotle’s starting point was the specific nature or substance of a The doctrine

1. William D. Ross, Aristotle (Oxford, 1923), p. 74. 2. Metaphysics vii 17, 1041b. 3. Ibid., vii 8, 1034a.

[48]

The Concept of Form after Aristotle

[49]

thing, which exists only potentially in the matter, for matter pos¬ sesses only the passive capacity to be structured. The structuring of matter is wrought by the form, the pattern and active principle that bring the substance to actuality so that it reaches its fulfillment or realization in matter. The two aspects of substance, matter and form, constitute an indivisible unity, not two separate entities; they can be separated only in thought, for “the proximate matter and the form are one and the same thing, the one potentially, the other actually.”4 The matter in a body is always infused by a form, even though in the process of change one form may replace another, and the form infuses and acts upon only that kind of matter which is suitable to it, so that matter and form are always fitted to each other. Aristotle was well aware of his predecessors' beliefs about the form, and it was partly in reaction against them that he formulated his own system. He criticized both the materialistic atomists who ignored the form and the Platonists who overemphasized it: “Some thought the nature of the [Platonic] forms was adequate to account for coming-to-be. . . . Others thought the matter was adequate by itself. . . . Neither of these theories, however, is sound.”5 The mate¬ rialists’ fault was simply one of neglect: “It was only very slightly that Empedocles and Democritus touched on the forms and the essence.”6 It was not so much this as Plato’s idealistic emphasis that Aristotle was concerned to refute and that helped him to define his own position in contrast to it. The basic inconsistency in Plato’s doctrine of forms or Ideas was, according to Aristotle, that they were held to give form to sensible bodies and yet they were believed to exist, unchanging and at rest, in a transcendent world remote from the world of sense and hence unable to affect it: What do the [Platonic] Forms contribute to sensible things? . . . For they cause neither movement nor any change in them. . . . And to say that they are patterns and that the other things share in them is to use empty words and poetical metaphors. . . . Again, it would seem im¬ possible that the substance and that of which it is the substance should exist apart; how, therefore, should the Ideas, being the substances of things, exist apart?7 4. Ibid, viii 6, 1045b. 5. On Generation and Coiruption n 9, 335b. 6. Physics 11 2, 194a. 7. Metaphysics 1 9, ggia-b. Aristotle described Plato’s theory of Ideas in Meta¬ physics 1 6, 7. Plato spoke of the Ideas as “absolute beauty and goodness and great¬ ness” (Phaedo 100b), whose realm was “the heaven which is above the heavens. . . . There abides the very being with which true knowledge is concerned; the colorless, formless, intangible essence, visible only to mind” (Phaedrus 247c).

[50]

The Scientific Reinterpretation of Form

In Aristotle’s opinion, then, Plato depicted the form as pattern but not as cause or act and, in presenting it as transcendent, he lost sight of the matter it informed. Conscious of these defects, Aristo¬ tle insisted that form and matter were united and not separate, and that the form not only supplied the pattern of a body but also actively directed and achieved that pattern in its material embodi¬ ment. “Form and matter are not separate from the thing,” for “the form ... is a kind of power immersed in matter.”8 Aristotle was not altogether fair to his teacher, for Plato’s interest in form theory was concerned primarily with the soul and its perceptions and values rather than with accounting for the specificity of bodies. But Aris¬ totle’s achievement was considerable, for by tightening up the structure of form theory and drawing together various strands of meaning—substance, causality, teleology, actuality and poten¬ tiality, logical definition—he made the concept of form into a powerful, flexible, and universally applicable explanatory tool. However, Aristotle’s form theory was not perfect, and there were some valuable aspects of the Platonic form for which it could find no place and which eventually caused it to be altered in order to accommodate them. One such aspect was the relevance of the en¬ tities of mathematics (numbers and geometrical concepts) which, if not actually forms themselves, were ranked with them by Plato as part of the same transcendent world of being. We shall see in the following chapters that late scholastic and postscholastic attempts to apply the concept of form to theories of the structure of matter and crystal figuration revealed that in these contexts a geometrical understanding of form was essential, and this gap in the Aristo¬ telian form theory had to be filled by recourse to Platonism. But even at an earlier period the need to fill this gap was already recognized, and the way was prepared for a geometrical under¬ standing of form. As so often happened, the Platonic tendencies of some of the Church Fathers played a part here, Augustine being, as usual, the chief transmitter of notions such as the dependence of forms upon divinely ordained measure, number and order, and the preeminence of light as the most perfect “first form.” At the threshold of the scholastic age, this “metaphysic of light” was clear¬ ly expressed by Robert Grosseteste (1168—1253), Chancellor of the newly founded university of Oxford and later Bishop of Lincoln, who was one of the first to appreciate the importance of Aristo¬ telian thought and to try to combine it with the Platonizing Au8. Physics iv 2, 209a; On Generation and Corruption i 5, 322a.

The Concept of Form after A ristotle

[51]

gustinian tradition. He wrote: “The first corporeal form which some call corporeity is in my opinion light. . . . The extension of matter in three dimensions is a necessary concomitant of cor¬ poreity ... by [light] multiplying itself and diffusing itself in every direction instantaneously and thus extending matter. . . . For the form cannot desert matter, because it is inseparable from it, and matter itself cannot be deprived of form.”9 Thus light provided a geometrical paradigm for the material universe; as the First cor¬ poreal mover, it produced universal motion and alteration by its tridimensional action. All natural effects should be understood, like light, in a geometrical manner, “by means of lines, angles, and Figures,” Grosseteste believed.10 His pupil Roger Bacon, arguing physically rather than metaphysically, drew the same conclusion, as we shall see in the next chapter. As the philosophical importance of Augustine waned after the thirteenth century, the metaphysical signiFicance of light as the first form counted for less, but its legacy of understanding the action of the form geometrically remained within scholastic thought. There was another approach to a geometrical, or at least spatial, understanding of form, and once again it took its ultimate origin from Plato. Some of the earlier writers on Aristotle had felt that the gap between totally unformed prime matter and the forms of the elements was too great, and they had postulated a partly formed matter, “common matter,” between the two. The form of common matter could not be specific in Aristotle’s sense; what sense then could be given to it? It was identified with extension, the common property of all bodies, and was called the “material form,” “cor¬ poreal form,” or “form of corporeity.” The Arab commentators Averroes and Avicenna expressed it in their different ways in terms of tridimensionality.11 Like the metaphysic of light, this ap¬ proach emphasized the three dimensions of matter and encour¬ aged a spatial understanding of form; both theories took for 9. De luce, trans. by Clare C. Riedl, On Light (Milwaukee, 1942), p. 10. The Latin text is in Die philosophischen Werke des Robert Grosseteste, ed. Baur, p. 51. 10. De lineis, angulis et figuris sen de fractionibus et reflexionibus radiorum, and similar¬ ly De rnotu corporali et luce (Baur, pp. 59—60, 90-1). See also Alistair Crombie, Robert Grosseteste and the Origins of Experimental Science (Oxford, 1953), pp. 107, 110. 11. Concerning the corporeal form, Averroes wrote: “The three dimensions which are believed to constitute the nature of body are the first state in matter. . . . Matter is that which receives these three dimensions and their existence is inter¬ mediate between that potentiality in which matter subsists and the actual three dimensions, which are the substratum of alteration” [Averroes Middle Commentary on Aristotle’s De generatione et corruptione, trans. by Samuel Kurland [Cambridge, Mass., t958], p. 26).

[52]

The Scientific Reinterpretation of Form

granted Plato’s account in Timaeus 31-37 of how the world was created in a geometrical manner. But whereas the Augustinian theory awarded to light, the first corporeal form, a most exalted status reaching out on the theological level to God and the angels, the material form, as its name suggests, was of a low and almost material nature, scarcely to be classified with other forms. The soul of the world was another aspect of Platonic doctrine that Aristotle could not fit into his system, for the specificity of Aristotelian forms precluded any notion of a universal form for the whole world. Nor could Aristotle see the need for any metaphysical principle of unity for the cosmos, since he had no doctrine of creation or of a definite origin of the world; he was content to acknowledge that the world had a “unity of order” like that of an army or a household.12 Unlike Aristotle, Plato held a doctrine of creation that necessitated a metaphysical principle of unity, as did the Jews, Christians, and Muslims. But whereas these monotheists naturally identified this principle with the almighty Creator, Plato’s demiurge or creator god in the Timaeus was a shadowy figure who was soon eclipsed by his first creation, the world soul, whose origi¬ nal function was to impart motion to the cosmos. The Neoplatonists exalted the world soul to divine status; it was held to be not only the Idea or transcendent pattern of the world, but also the creator.13 At this point the reader may well be inclined to echo Edward Gibbon’s words in The Decline and Fall of the Roman Empire: “The new Platonists would scarcely deserve a place in the history of science.” But in fact, as we shall see later in this chapter, and in chapter 6, Neoplatonic concepts such as the world soul, which were never altogether lost sight of in some medieval circles, returned to prominence in the sixteenth and seventeenth centuries. Then a renewed search for a universal principle of unity would focus at¬ tention on such concepts once again in order to supply a feature lacking in the Peripatetic tradition of form, and the world soul would play a part in unifying the principles of natural philosophy for the reinterpretation of the form concept. This revival of interest in the world soul still lay far in the future, however, when the Peripatetic form theory was being elaborated by the Greek and Arab commentators on Aristotle and by the medi¬ eval schoolmen. From the early centuries of our era, when the

12. Metaphysics xii 4—10. 13. Compare Plato’s Timaeus 36c! with Plotinus’ Enneads v 1.2.

The Concept of Form after Aristotle

[53]

writings of Aristotle began to have a wider influence, the Aristo¬ telian system was nearly always presented with an admixture of Platonism. The middle Platonists' view that Aristotle was one of themselves; the Neoplatonism of some of the Greek and Arab com¬ mentators; the attribution to Aristotle of two Neoplatonic works (the so-called Theology of Aristotle, which was really based on Ploti¬ nus’ Enneads, and Proclus’ Liber de cansis); the use of Platonism to interpret the Jewish, Christian, and Muslim religions—all these led to an eclectic approach that sought to harmonize the views of the Lyceum and the Academy and to minimize their differences. When the Aristotelian form theory first appeared in the West in the twelfth century, a strong Platonic tradition already existed there, fostered by Calcidius’ fourth-century Latin translation and commentary on Plato’s Timaeus, by patristic and theological writ¬ ings, and by some Platonizing works of the Latin authors Boethius and Macrobius. When the schoolmen at Chartres, for instance, learned from Boethius of Aristotle's theorv of form and matter, they added it to the Platonic doctrine they already knew. As we shall see in more detail in chapter 6, they believed in the world soul and the Platonic Ideas, and they had adopted from Calcidius the theory that the Aristotelian specific forms were the active formal cause linking the Ideas to the world of matter. In the thirteenth century too, many writers, including Robert Grosseteste and Roger Bacon, held together the Platonic Ideas and the Aristotelian specif¬ ic forms of bodies. But there was a contrariety too. The twelfthand fourteenth-century debates about nominalism, questioning whether general forms, or universals, exist apart from particular things, were evidence of an antithesis between the Platonic and Aristotelian conceptions of form. In addition to this alreadv familiar Platonism, the Latin translations of Aristotle appearing in the twelfth and thirteenth centuries were followed by translations of the Greek and Arab commen¬ tators, often bringing with them a Neoplatonic bias. This, then, was the matrix from which Aristotelian form theory was born in the West. From the outset, the Peripateticism of the Latin schools, even though it was based on an exhaustive examination of the Aristo¬ telian texts, was permeated by aspects of Platonism to which the schoolmen were so accustomed that they took them for granted. The chief intention of the schoolmen was to amplify and eluci¬ date Aristotle’s terse statements and to codify his ideas into a closely knit system of propositions designed to cover any eventuality. They underlined and shaded in heavily what he had been content to

[54]

The Scientific Reinterpretation of Form

sketch lightly. From the point of view of the present study the main result was that the formal cause and the form concept became more important in explanations, and received a more exalted sta¬ tus, than in the thought of Aristotle himself. Some extracts from a typical scholastic tractate by Thomas Aquinas (1225-74) will dem¬ onstrate how closely it follows Aristotle (it is based on Metaphysics xii 1-5), but at the same time how much it expands his account and exalts the form: Anything from which a thing derives existence, whether substantial or accidental, can be named form. . . . Because form brings existence into actuality, we state that form is act. Whatever brings substantial existence into actuality is called substantial form, and whatever brings accidental existence into actuality is called accidental form. . . . Gener¬ ation is motion towards form. . . . Form does the generating, while from [matter and privation] generation takes place. . . . Since all definition and knowledge takes place through form, prime matter can only be defined and known through its relationship to form. . . . Since [prime matter] contains no form in its definition, it cannot actually exist;

actual existence comes only through the

form. . . . In respect to temporal generation, matter is prior to form . . . but in respect to substance and completeness form is prior to matter, since only through form does matter have complete existence. . . . The material and efficient causes are therefore prior in the process of generation, but the form and aim are prior in the process of perfec¬ tion.14

Many aspects of the form are expounded here; it is represented as the source of existence, as the act that brings about actualization, as the cause and aim of generation, as the essential definition that alone gives knowledge of a thing, and as ontologically prior to matter. The author sides with Aristotle against Plato in stressing the active, causal character of the form and its involvement with matter; he goes beyond Aristotle, however, in his insistence on the form’s predominance and superiority to matter. These views of Aquinas’s commanded widespread acceptance, but not all writers were in complete agreement with him, even though all allotted an important place to the form. For instance, John Duns Scotus (1265—1308) made many criticisms of Aquinas’s 14. De principiis naturae, trans. by Mary T. Clark, An Aquinas Reader (London, 1974).

PP- l64~5> 167-8, 172-3.

The Concept of Form after Aristotle

[55]

system, and some of them concerned the form. Scotus’ severely logical approach, and his principle that all unnecessary multiplica¬ tion of entities must be avoided, made him exclude concepts that he considered superfluous, such as inchoate forms (seminal rea¬ sons) latent in matter, or the presence of the forms of the elements in compounds. Scotus did not award matter such a lowly status as Aquinas did, but allowed it a certain limited degree of existence, actuality, and intelligibility in itself apart from the form. Even so, he still regarded the form as the dominant partner. In the century after the death of Aquinas, the role and status of the form was always a paramount theme in natural philosophy. Discussion usually tended to follow the lines already indicated, and differences of opinion often concerned the distribution of func¬ tions between matter and form and the degree to which the form should be exalted above matter. But there were two topics on which scholastic form theory underwent considerable development, and these both concerned processes of change. One was mixtion theo¬ ry, the study of combination, which we shall examine more closely in the next chapter; the other was the form theory of motion, a complicated and confusing area of scholastic speculation to which we must now briefly turn, although an investigation of its complex¬ ities would be out of place here. Aristotle did not speak of motion in terms of matter and form; but he embraced it within the general class of change, which in¬ cluded alteration (change of quality), growth (change of quantity), and sometimes generation (change of substance), as well as local motion (change of place). Averroes (1126—98) pointed out that there were two ways of considering motion. On the one hand, “motion is nothing other than the generation of part after part of that perfection towards which it is tending”; on the other hand, “motion is a way from potentiality to actuality.” Averroes inferred: “So motion has a twofold significance. With respect to its matter it is in the same category as that towards which it is proceeding. But with respect to its form, according to which it is a change conjoined with time, it is in its own category of passivity.”15 Averroes re¬ marked that although the definition according to form, viewing motion as an entity in itself, was the more famous, he believed that the definition according to matter, defining motion as the gradual acquisition of a final state, was more correct. 15. Digression on Physics 111 text 4, v text 9. Aristotle treated motion in Physics in, v, vi. Aristotle’s ten categories of being were substance, quantity, quality, relation, place, time, position, habit, action, passivity.

[56]

The Scientific Reinterpretation of Form

Both these views were expressed in terms of form theory by the Latin schoolmen. It was Albertus Magnus, in the century after Averroes, who bestowed the names by which scholastic writers al¬ ways referred to them afterward. Motion understood according to form he called a flux of form (fluxus formae), defining it as a process of change; and motion understood according to matter he called a flowing form (forma fluens), implying its appropriation of a final complete form.16 Following Averroes and Albertus, most thir¬ teenth-century schoolmen adopted the forma fluens. In the four¬ teenth century it was still popular, but increased interest was shown in the fluxus formae as well, partly because of the new understand¬ ing of the kinematics and dynamics of motion that was being reached at Oxford and Paris, and partly because of a growing appreciation of the successive nature of change, which we shall mention in the next chapter.17 It was an adherent of the forma fluens theory, William of Ockham (1280—1349), who initiated a new approach. Although in many respects an opponent of Duns Scotus, he shared the latter’s princi¬ ple of avoiding the multiplication of unnecessary entities (often called “Ockham’s razor”). In conformity with this principle and with his nominalist view that only singular things and not abstract universals should be taken into consideration, he insisted that “matter and form are not universals but singulars. . . . Different formal beings are really the forms themselves. . . . Potentiality is not a thing existing in matter, but it is matter itself in relation to form.”18 When applied to motion and change, such an approach entailed the consequence that “change is not distinct from acquir¬ ing a form or from the form that is acquired” and that “change or motion is not something distinct from the permanent thing [that is changed or moved]”; so Ockham proposed that the superfluous abstract words, change and motion, should be replaced by concrete phrases, changing or moving thing and the verbs to change or to move.19 But, as we have just seen, he did not hold the form to be a superfluous concept, and for Ockham, as for other schoolmen, the form was the dominant partner. 16. Paraphrase on Physics in 1.3. 17. For developments in motion theory, see Anneliese Maier, Die Vorlaufer Galileis im 14 Jahrhundert (Rome, 1949), and “Forma fluens oder fluxus formae?” in Zwischen Philosophic und Mechanik (Rome, 1958), pp. 59—154. 18. Summulae in libros physicorum 1 14, 15, 16; Latin text in Philosophia naturalis, ed. Bonaventura Theulus Veliternus (Rome, 1637), pp. 18-20. 19. Summulae in 4, p. 51; the second phrase quoted is repeated in in 2, 3, 4, 5, 6, 7, 15, 16, 25, 27. The linguistic proposals are in in 3, 7.

The Concept of Form after Aristotle

[57]

The scholastic emphasis on the role of the form and its superi¬ ority to matter gave it a status above Aristotle’s conception, and some schoolmen exalted it to a very high degree. In this respect Plato’s transcendent Ideas and world soul were influential, not only because of the traditions already cited, but also because Aristotle’s own frequent references to them, although critical, tended to draw the reader’s attention to them and make them familiar, which was certainly not Aristotle’s intention in mentioning them. Because Pla¬ to’s theories occurred in Aristotle’s text, there was an almost un¬ noticed tendency to assimilate them into the Aristotelian system. Later we shall notice this happening with Democritan atomism as well as with Platonic idealism. Another factor tending to exalt the form was the scholastic readiness to associate it with the human soul, partly for theological reasons, and partly following Aristotle himself in On the Soul, so that beliefs about the soul colored the concept of form. Yet another reason was the complex set of beliefs linking the form with the heavens. Physically, according to Aristo¬ tle, their motion and that of the sun was the ultimate cause of all change; in popular astrology, astral influences affected earthly af¬ fairs; theologically, the heavens represented the almighty power of God; metaphysically, they were the realm of Plato’s forms or Ideas; and in the philosophical tradition associated with Avicenna, the Intelligence of the lunar heaven was the giver of forms.20 So scho¬ lastic writers commonly imputed the activity of the form to the “power of the heavens” and thereby exalted it yet higher. An example of this complex of associations was Albertus Mag¬ nus’ view that “substantial forms are imparted by the power of the heavens,” which he linked with the motion of the sky in Aristotle’s manner, and with the doctrine of Plato too; he also interpreted it astrologically as the power of the stars and planets.21 Two later examples of the same tendency were the sixteenth-century Aristo¬ telians Jean Fernel and Julius Caesar Scaliger, who stressed the form’s celestial origin by naming it “quintessence” and “fifth ele¬ ment,” that is, the incorruptible ether or matter of the heavens. Both of them associated the form and the soul; Fernel called the form divine, and Scaliger followed the fourth-century Greek com¬ mentator Themistius in calling the form, like the soul, “the archi20. Lynn Thorndike writes: “It cannot be too strongly emphasized that for scho¬ lastic writers the active principle is the heavens. This rule of the heavens should be kept constantly in mind by every student of the history of science before Newton” (“The True Place of Astrology in the History of Science,” Isis 46 [ 1955]:275). 21. Mineralia 1 1.6, also 3, 5, 8, 9; and in 1.6.

[58]

The Scientific Reinterpretation of Form

tect of its domicile.” Fernel stated that “the origin of forms is proximately from the heavens, then from the Intelligences, and ulti¬ mately from God.” Scaliger championed the superiority of form to matter by insisting that since “the form has the power of acting . . . it is stupid to attribute to matter the force and affection by which the form is distinguished.”22 However, this exaltation of the substantial form was not the only possible interpretation of Aristotelian form theory, and it did not pass unchallenged. Throughout the three centuries between Albertus and Scaliger a lower or more material view of the form, such as that of Duns Scotus, was also common, a view against which Scaliger waged a constant battle. The low view of the form assimi¬ lated it much more closely to matter; in closer conformity to the opinion of Aristotle himself, this view stressed the union between matter and form, and the fact that matter must always be in posses¬ sion of some sort of form, and it emphasized the contribution of matter as well as form to the composite substance. If the elevated view of the form was molded by a preoccupation with theology, metaphysics, and astrology, it could be said that the low view was often encouraged by the study of the physical world. The Galenic medical tradition, for instance, assimilated forms to qualities and derived the form from the temperament or harmony of qualities. And Arab philosophy, with its strong medical and chemical interests, could go the same way; Averroes, for instance, regarded the forms of the elements as being not fully substantial forms but intermediate between these and the accidental forms of qualities. In fact the low view of form tended to blur the distinction between substantial and accidental forms. The low view of form could be formulated in various ways. It was said that “matter seizes a form for itself,” thus giving matter an active role; or that the form emerges from “the battle of the elements” or, as the Galenists said, from the temperament, that is, from the proportions of the in¬ teracting elements and their qualities; or that “form is educed from the potency of matter,” in other words, it is determined by and emerges from a particular sort of matter.23

22. Jean Fernel, De abditis rerum causis libri n, i 8, n 2, Universa medicina (Paris, 1567), pp. 47, 66; Julius Caesar Scaliger, Exotericarum exercitationum liber XV (Paris, 1557), ex. 6 and 346, pp. 14, 456. 23. For accounts and refutations of these views, see Scaliger, Exotericarum exercita¬ tionum liber XV, ex. 6, 17, 101, 346, pp. 13, 35, 145, 456; and Sennert, Hypomnemata physica, Opera omnia, vol. 1, pp. 142-3, 164—7, an(i Tractatus, Opera omnia, vol. in, pp. 738,

774> 777’ 779-

The Concept of Form after Aristotle

[59]

Some writers insisted that matter possesses in its own right a latent or inchoate form that needs only to develop to actuality, not to have a form imposed upon it. This notion was derived from the seminal reasons (logoi spermatikoi) which the Neoplatonists had adopted from the Stoics and which Latin scholasticism had learned about from Augustine. Here too the power of the heavens could be invoked, not as giver of forms but as the agent ripening in the fullness of time an embryonic seed form in matter, just as the sun’s heat germinates plant seeds in the earth. In the thirteenth century this was maintained by Bonaventure and, under the name “active potency of matter,” by Roger Bacon.24 The difference between the lower and the higher views of form was one of degree rather than of kind. Both recognized four causes operating in the world of phenomena, but the former laid more stress on the material and efficient causes, whereas the latter view emphasized the formal and final causes. Then again, those who exalted the form knew that it must be “immersed in matter,” as Aristotle said, but they saw it in the light of transcendent entities such as the soul and the heavens; and the proponents of the low view were aware that in the same passage Aristotle denoted the form as “the active principle,” but they were more conscious of the lower echelons of forms, such as those of the elements.25 Many would have agreed with Thomas Aquinas, the greatest of the schoolmen, when he summed up the question in his usual balanced manner: “After the form which is the soul there are other forms having more potentiality and closer to matter insofar as their exis¬ tence is not without matter. In these also we find an order and gradation down to the primary forms of the elements, which are closest to matter, and they have no operation except that of those active and passive qualities.”26 Throughout the Middle Ages the debate concerning forms continued, about their relations to matter and to one another, and about their roles in metaphysics and phys¬ ics. Much of the discussion repeatedly went over the same area, but sometimes it broke new ground, as in motion and mixtion theory. This debate was not abandoned when scholasticism came to an end. For one thing, as Robert Boyle wrote as late as 1661, “the

24. On these notions, and the similar ones of Heinrich Bate and Dietrich of Freiburg, see Anneliese Maier, “Die Struktur der materiellen Substanz,” in An der Grenze von Scholastik und Naturwissenschaft (Rome, 1952), pp. 46—68. 25. On Generation and Corruption 1 5, 322a. 26. De ente et essentia, trans. by Clark, Aquinas Reader, p. 43.

[6o]

The Scientific Reinterpretation of Form

vulgar philosophy [Peripateticism] ... is still in great request with the generality of scholars.”27 But apart from this, the form re¬ mained a topic of great interest to the sixteenth- and seventeenthcentury writers of many diverse philosophical positions who were trying to identify their own stance by differentiating themselves from their scholastic predecessors, much as Aristotle had done visa-vis Plato. It is a mistake to think that the concept of form faded away when the supremacy of Aristotle was challenged; the evi¬ dence is to the contrary. The opponents of scholasticism were hos¬ tile to the schoolmen’s hairsplitting arguments over abstruse and irrelevant details, and to the use of the substantial form as a deus ex machina to solve all problems or as an all-enveloping blanket phrase that appeared to offer an explanation but was no more than empty verbiage. But they did not usually reject the concept of form as such, and in fact the denials of the form, however vehemently stated, were more apparent than real. The continuing interest in the form is shown by the many discussions of it and by the habit of listing the scholastic variants of form theory; indeed, the very vari¬ ety of the older views was a stimulus to those who were trying to work out their own position. Thus the seventeenth-century atomist Etienne de Clave wrote:

Scarcely three philosophers together can reach accord on this subject, even though they all agree that the form is what gives being to a thing. . . . Some hold that the form is educed from the potency of matter; others, from the diverse mixture of the elements; others, from the temperament . . . others, that it is enclosed in a seminal spirit . . . some hold that the form is purely celestial and comes from the stars. . . . They have taught me only one thing, that the form is the principal essence which gives being to the thing.28

Similar lists were compiled by de Clave’s contemporaries, the atomists Sebastian Basso and Pierre Gassendi and the Aristotelian Daniel Sennert. Sennert drew on some different sources:

27. Some Specimens of an Attempt to make Chymical Experiments Useful to Illustrate the Notions of the Corpuscular Philosophy, Works, vol. 1, p. 228. 28. Paradoxes, pp. 404-6, 414.

The Concept of Form after Aristotle

[61 ]

There are the greatest disagreements among the philosophers con¬ cerning the true origin of the form. . . . Aristotle and his commen¬ tators say that neither matter nor form is generated but a com¬ posite. ... If you ask a Peripatetic . . . where the form comes from, he will say it is educed from the potency of matter. . . . Others hold, with Plato, that the Ideas are the effective cause of forms, and from him later writers introduced the world soul. Avicenna thought the cause was the tenth Intelligence, in his language called Cholcodea. . . . Fernel, and others with him, stated the heavens to be the effective cause of forms. . . . Some Peripatetics say that matter does not actually con¬ tain forms in itself, but that there is in matter a certain disposition towards a form which, when completed, becomes in actuality what it already was potentially.29

To de Clave, Sennert, Basso, Gassendi, and many other seven¬ teenth-century writers who were grappling with the recent devel¬ opments in natural philosophy, it seemed clear that the new theo¬ ries that were needed could not be constructed without some sort of form concept. These writers did not necessarily lean toward the philosophies of Aristotle or Plato. Many of them were self-con¬ fessed atomists or mechanical philosophers, but they were aware that in certain contexts, such as chemical combination and crystalli¬ zation, the order and pattern in nature could not be expressed in terms of matter alone. Few of them were willing to dispense with the concept of form altogether; most of them would have agreed with the atomist Pierre Gassendi when he wrote, “What one seeks to know is matter and form,” and with Francis Bacon’s statement that “the invention of forms is of all other parts of knowledge the worthiest to be sought, if it is possible to be found.”30 But the new scientific discoveries needed fresh interpretations of the concept of form. The new writers severely criticized their predecessors, es29. Epitome scientiae naturalis, Opera omnia, vol. 1, pp. 10—11; Tractatus, p. 738. Avicenna’s “Cholcodea” should probably be understood as a transliteration of the Arabic kull qadiya, meaning “all things”; I owe this suggestion to Dr. Malcolm Lyons of Cambridge University. The tenth or lunar Intelligence was held to be the giver of forms to all things on earth. The last of the opinions refers to seminal reasons or Roger Bacon’s active potency of matter. Similar lists were given by Sebastian Basso, Philosophiae naturalis adversus Aristotelem libriXII, pp. 148—59, 162—79, anfi by Pierre Gassendi, Syntagma p kilos op hicum, Opera omnia, vol. 1, pp. 469—70. 30. Gassendi, Exercitationes paradoxicae adversus Aristotelicos, 1 5.6, trans. by Ber¬ nard Rochot, Pierre Gassendi: Dissertations en forme de paradoxes contre les Aristoteliciens (Paris, 1959), p. 124. Bacon, The Advancement of Learning, Works, ed. James Spedding, Robert Ellis, and Douglas Heath (London, 1857), vol. 111, p. 355; “invention” means discovery. All references to Bacon’s works are to this edition.

[62]

The Scientific Reinterpretation of Form

pecially the schoolmen who had obscured the real merits of Aristo¬ tle’s theories by trying to oversystematize them, but it was hoped that they could be made to yield insights that might help to build up a fresh understanding of form relevant to the new needs. To the new reinterpretations of form we must now turn. We can distinguish several approaches to the form in seven¬ teenth-century thought, some of which were continuations of trends within the Aristotelian tradition. First, the low or more ma¬ terial view of the form adopted by some scholastic writers recom¬ mended itself to later writers who similarly emphasized the mate¬ rial and efficient causes in natural phenomena. Sometimes they went so far as to identify the formal and efficient causes, as did the late Peripatetic Sir Kenelm Digby, who was content to interpret the formal cause as “the ordered series of naturall causes and not an intrinsecall formative virtue. . . . There needeth not to be supposed a forming virtue or vis formatrix. ... Yet we shall not quite banish that terme from all commerce with us; so that what we mean by it be rightly understood, which is the complex assemblement, or chain of all the causes, that concur to produce this effect, as they are set on foot to this end by . . . God Almighty, whose instrument Nature is.”31 A more moderate, although still low, view of the form was adopted by the chemists Anselm Boetius de Boot and his fol¬ lower Etienne de Clave, the former being an Aristotelian and the latter an atomist. Both of them accepted the traditional definition of form; they both wrote that “the form is that which gives being to the thing.”32 As we shall see in chapter 7, they linked the form closely to the chemical spirits and seeds which were believed to be the agents of mineralization. Their position had much in common with the scholastic opinion that the form was educed from the potency of matter, emphasizing the material involvement of the form without denying its character as the source of being and specificity. At the other end of the scale were those seventeenth-century writers who found an exalted view of the form, like Fernel’s and Scaliger’s, congenial to their outlook, although usually with an ad¬ mixture of Platonism that Scaliger would not have admitted. Two contrasted examples are the late Peripatetic Daniel Sennert and the anti-Aristotelian atomist Sebastian Basso. Both of these owed much to Scaliger. Sennert was his follower and frequently referred to

31. Two Treatises (London, 1644), PP- 2&6, 289. 32. De Boot, Gemmarurn et lapidum historia, p. 31; de Clave, Paradoxes, p. 414.

The Concept of Form after Aristotle

[63]

him with approbation; and although Basso regarded Scaliger, whom he called “Aristotle’s trumpeter,” as his chief antagonist, yet he borrowed Scaliger’s physical explanations and benefited from some of his ideas about the form. Like de Clave, Sennert, and Gassendi, Basso listed and examined the various form theories. He demonstrated to his own satisfaction that the doctrine of substantial form was untenable and absurd. But he never denied the necessity of the form concept itself for explaining the marvels of nature. He was deeply impressed by nature's “order in position, proportion in size, symmetry in space, and harmony in number. What workman, however skilled and however often he tried, could produce the work that the form directed, made and completed without any premeditation, hesita¬ tion, or error?”33 lire concept of form constituted an important part of Basso's thinking; four out of the twelve books of his Philosophia naturalis were devoted to it. Basso’s repudiation of substantial form was grounded in his be¬ lief, reminiscent of Scaliger's, that the scholastic low view of form was inadequate and unworthy of the phenomena it was designed to explain. The only answer consonant with the dignity of creation, he thought, was to accept a universal form, created by God, moved by him, and acting as his agent in the world: “Why do they seek in individual things individual substantial forms, when one universal cause extended through everything suffices for individuals? . . . The universal bond is the continual operation of the presence of God, which theologians call natura naturans; impressing impetus on the material principles that are suitable to it, it joins like matter to like.''34 This was a Christianized version of Plato's world soul, and Basso admitted that “divine Plato'" was his mentor. Yet Basso's conception of form was not only Platonic; in spite of his repudiation of the substantial form, his understanding of form had strongly Aristotelian features as well. It was not just a transcen¬ dent Idea or pattern, but also an “internal active principle” im¬ mersed in matter: “There is a principle within each thing that forms it little by little, nourishes it when formed, and increases it, and is the author of all motion and rest. It is indeed the principle which Aristotle and his followers called the nature of a thing or the sub33. De forma. Philosophiae naturalis adversus Aristotelem libri XII (Geneva, 1621), p. 196. 34. Ibid., pp. 267, 269. Basso repeatedly exalted the form as God’s direct creation (pp. 136, 148, 151, 158, 269) and his instrument (pp. 197, 237, 269, 304, 341), and criticized the low view of the form (pp. 149—51, 166—71, 174—7, 195—7)-

[64]

The Scientific Reinterpretation of Form

stantial form.”35 Basso saw no incompatibility between a universal form and a variety of operations and bodies, because “the universal form operates in various ways by means of varied instruments”; we shall see in chapter 4 that he was able to understand these “varied instruments” by the aid of the Peripateticism whose substantial form he was so eager to deny.36 Basso’s contemporary, Sennert, likewise had an exalted concep¬ tion of the form. He agreed with “the many learned Peripatetics and physicians who think more sublimely of the generation of things. . . . They do not assign the constitution of things to the battle of the elements, but chiefly to the soul instructed in its fac¬ ulties and to the specific form. . . . The form or soul is the architect of each thing and the prime mover in mixtion. . . . For forms are the divine and immutable principle which determines all the ac¬ tions and passions of a natural thing, and they are as it were instru¬ ments in the hand of the most wise Creator.”37 Among those “who think more sublimely” Scaliger held a prominent place in Sennert’s opinion. Sennert applied to the form Scaliger’s titles “fifth ele¬ ment” or “quintessence” and “architect,” and he took care to re¬ fute, as Scaliger had done, any notion that impugned the predomi¬ nance of the form, which he often called “the superior form.”38 Sennert’s reasons for exalting the form were not only philosophical but also, like Basso’s, theological. His insistence on the paramount status of the form was firmly based on the biblical doctrine of creation, for “God at first in the creation gave things their forms, through which the order of generation is continued and com¬ pleted.”39 Sennert’s eclecticism, like Basso’s, contained Platonism as an important ingredient. He wanted to reconcile Plato’s world soul with his Peripateticism, but he was aware that his mentor Scaliger had objected against it that “the world is not one by the unity of one informing form. ... If one form informed the world, either the remaining forms would be part of that form, or else they would be informed by it, either of which is most absurd. For forms are not all of one type among themselves. . . . Since they differ so much in

35. Ibid., pp. 181-2. 36. Ibid., p. 255. 37. Tractatus, pp. 777-8. 38. Epitome, pp. 11, 77, 81, 86; Hypomnemata, pp. 142—3, 146—7; Tractatus, pp. 738, 740, 745, 765, 774, 777-8. 39. Hypomnemata, p. 142. For the form’s preexistence and its role as the instru¬ ment of God, see Epitome, p. 11; Tractatus, pp. 729, 735, 774.

The Concept of Form after Aristotle

[65]

type, they cannot all be parts of one. . . . Their unity is a unity of order.”40 Anxious to make use of the universal form to bridge the gap between Aristotelianism and chemical theory, Sennert twisted Scaliger’s argument, ingeniously quoting Scaliger’s remark that “their unity is a unity of order" for the purpose of proving, with Plato’s help, that this order could be equated with the heavens, with the form of the world in the sense of its shape, and with the form of the world in the sense of the universal form or world soul—“this opinion is not pleasing to the Peripatetics," he confessed.41 Like Basso, he was using the world soul, the metaphysical principle of unity, to unite the different scientific approaches that he wanted to combine in his eclectic form theory, as we shall see in chapter 4. Similarly, when commenting on the opinion that “one thing [prime matter] actually contains all forms,” Sennert remarked that “this makes better sense if we understand it as a seminal force implanted by God in all things at the creation ... or as the Platonic world soul. . . . Some speak of a common vital spirit diffused through the whole world. . . . Some call it the heaven of heavens.”42 Once again he admitted that “most Aristotelians do not like this idea." For Basso and Sennert, Platonism was but one ingredient in an eclectic blend that also included Aristotelianism and chemical and corpuscular theories. But some proponents of the exalted form concept took their stand upon what they regarded as a substantially Platonic platform, even though it might not have been recognized as such by the founder of the Academy. Among these were the astronomer Johann Kepler and his contemporary William Gilbert, the pioneer in magnetism; the chemists, followers of Paracelsus and van Helmont; and those whose Platonism was impregnated with Hermetic and occult views, such as Marsilio Ficino and Gior¬ dano Bruno. We shall postpone consideration of these fundamen¬ tally Platonic positions to chapter 6. The enigmatic language and imagery of the Neoplatonic, chem¬ ical, and Hermetic writers exerted a sort of fascination on many people in the seventeenth century. But equally there were those of a more rationalist outlook who were repelled by it, and who sus¬ pected that obscurity of expression often concealed muddled thinking. Yet these more skeptical writers too were usually con¬ vinced of the value of the form concept, and they sought some way

40. Exotericarum exercitationum liber XV, ex. 6, pp. 10—11. 41. Epitome, p. 28. 42. Tractatus, p. 729.

[66]

The Scientific Reinterpretation of Form

of expressing it that should be free from the rigid logical frame¬ work of the Peripatetics, the metaphysical connotations of Pla¬ tonism, and the fantastic conceits of the chemists and the Hermetic writers, without abandoning altogether the best insights of the ear¬ lier traditions. For instance, Francis Bacon (1561-1626) was highly critical of the Platonists, Aristotelians, and chemists, but he stated his intention “to ground a sociable intercourse between antiquity and proficience . . . and to retain the ancient terms, though I some¬ times alter the uses and definitions.”43 Far from being an advocate of the abolition of the form concept, Bacon attached great importance to the form, and he devoted much space to discussing it in The Advancement of Learning (1605) and Novum organum (1620). As a starting point for his arguments about form, he turned first not to the philosophers but to the Bible: “In the creation we see a double emanation of virtue from God . . . the one expressed in making the subsistence of the matter, and the other in disposing the beauty of the form . . . the one carrying the style of a manufacture, and the other of a law, decree, or counsel.”44 Bacon understood the form in terms of an ordered disposition of matter and also as a law, the divine fiat “Let there be . . . ,” which established and determined the order. Bacon also spoke of the study of form enabling mankind to “embrace the unity of Nature,” hoping that the human intellect would not rest content with the discovery of “particular forms” but would “pro¬ ceed to the legitimate discovery of the great Form,” by which he meant the divine law or plan for the world.45 Bacon was determined to avoid Plato’s error in “considering of forms as absolutely abstracted from matter,” and his own approach was by means of a low view of the form “confined and determined by matter . . . immersed into matter.”46 In his emphasis on the material involvement of the form and on its character as the es¬ sence of a thing, his thought as well as his language was close to Aristotle: The form, or true specific difference, or nature-engendering nature, or source of emanation . . . these are the terms which come nearest to

43. 44. 45. 46.

Advancement of Learning, pp. 353, 265-6. Ibid., pp. 295-6. Novum organum, Works, vol. iv, pp. 120, 162. Advancement of Learning, pp. 355, 359-

The Concept of Form after Aristotle

[67]

a description of the thing. . . . The form of a nature is such, that given the form the nature infallibly follows. Therefore it is always present when the nature is present, and universally implies it, and is con¬ stantly inherent in it. . . . The true form is such that it deduces the given nature from some source of being which is inherent in more natures. . . . The form of a thing is the very thing itself.47

But the character of the form as the source of being was only one aspect of its definition; equally important, to Bacon as to Aristotle, was its activity as the determinant cause of the qualities and actions of a thing, and in this context Bacon’s definition took on a rather different look: In Nature nothing really exists besides individual bodies, performing pure individual acts according to a fixed law. ... It is this law, and its clauses, that I mean when I speak of forms. . . . When I speak of forms, I mean nothing more than those laws and determinations of absolute actuality, which govern and constitute any simple nature, as heat, light, weight . . . thus the form of heat or the form of light is the same as the law of heat or the law of light.”48

This equating of form with law was in line with Bacon’s account of matter and form at the creation; it meant the continual ordering of matter so that it fulfilled the nature imparted to it by the Creator. The twofold nature of the form as essence and as law or act had important consequences in Bacon’s system; it offered the possibility not only of theoretical knowledge but also of practical applications. “From the discovery of forms results truth in speculation and free¬ dom in operation”; on the one hand, “of a given nature to discover the form ... is the work and aim of human knowledge,” and on the other hand, “whosoever knoweth any form, knoweth the utmost possibility of superinducing that nature upon any variety of mat¬ ter.”49 Whereas the ontological aspect of form is difficult to investi¬ gate, the phenomenological aspect, Bacon believed, should be ac¬ cessible to physical inquiry by the examination of the “vehicle of the form,” which is the material and efficient causes: “The form of a thing is to be found in each and all the instances in which the

47. Novum organum, pp. 119, 121, 137. 48. Ibid., pp. 119, 146. 49. Ibid., pp. 120, 119; Advancement of Learning, p. 357.

[68]

The Scientific Reinterpretation of Form

thing itself is to be found; otherwise it would not be the form. . . . The form is found much more conspicuous and evident in some instances than in others; namely in those wherein the nature of the form is less restrained and obstructed and kept within bounds by other natures.”50 Book n of Novum Organum gives examples of the study of various “simple natures,” especially heat, comparing the bodies and phenomena in which they occur in order to Find their more conspicuous and evident instances. The distinction Bacon made between form as essence and form as an active simple nature exemplifying a law corresponded more or less to the scholastic distinction between substantial and acciden¬ tal form. He did not imagine that forms were made up from qualities; the simple or accidental forms were true forms, but lim¬ ited to a single mode of action, and they had to exist as components of a higher form in the way that heat or color could not exist on its own apart from a body. Like some of the schoolmen, Bacon adop¬ ted the idea of a hierarchy of forms in which the simple or acciden¬ tal forms were part of the higher or substantial forms: “To inquire the forms of sense, of voluntary motion, of colors, of gravity and levity, of density, of tenuity, of heat, of cold ... of which the es¬ sences (upheld by matter) of all creatures do consist ... is that part of metaphysics which we now define of ... . The simple forms and differences of things are few in number, the degrees and coordina¬ tion whereof make all this variety.”51 A bridge between form and matter, or between substantial and accidental forms, was made by that expression of material order, deriving from the form as law, which Bacon called “structure,” “texture,” or “configuration.” “The latent process [is] carried on from the manifest efficient and the manifest material to the form which is engendered; and in like manner . . . the latent configura¬ tion. . . . [On] the true textures and configurations of bodies ... all the occult and . . . specific properties and virtues in things de¬ pend.”52 This linking of the form with the internal disposition of bodies was an insight that had already occurred within scholas¬ ticism, in the writings of William of Ockham, Nicole Oresme, and Agostino Nifo, as we shall see in the next chapter. In the seven¬ teenth century it was developed by other writers besides Bacon, but

50. Novum organum, pp. 149—50. 51. Advancement of Learning, pp. 355—7. 52. Novum organum, pp. 119, 125.

The Concept of Form after A ristotle

[69]

they gave it a particulate interpretation, whereas he was content to leave it in general terms. Bacon’s conception of form stood somewhat apart from the views of many of his contemporaries on this subject. In some ways it was more abstract, expressed in terms of law rather than as some easily visualized mode of material structure, but at the same time it was more practical, suggesting ways in which the activity of the form might be investigated experimentally. Bacon was able to com¬ bine a critical attitude to scholasticism with an appreciation of the value of Aristotelian insights; indeed, he was often close to Aristo¬ tle in his approach. From this tradition he obtained his emphasis on the material involvement of the form; his understanding of the form as law, as order, and as act; his use of internal configuration; his recognition of the material and efficient causes as vehicles of the form; and his hierarchy of lower and higher forms. There was another seventeenth-century writer whose approach to form resembled Bacon’s in some respects: in standing aloof from contemporary preoccupations with chemical and corpuscular theo¬ ries, in seeking to reconcile Aristotle and the “reformed philoso¬ phy,” and in tracing back the form to the law of creation. This was Gottfried Wilhelm Leibniz (1646—1716), who was born twenty years after Bacon’s death. In his early years Leibniz was much influenced by the criticisms of scholasticism voiced by Bacon, Des¬ cartes, Gassendi, and others, but later he recognized that some Peripatetic doctrines, notably the substantial form, were of great value to philosophy.53 He had little use for the uncritical eclec¬ ticism of some of his predecessors and contemporaries, and he firmly ruled out their equivalents of the form, especially the uni¬ versal form: In accounting for natural phenomena ... it is as vain here to intro¬ duce the perceptions and appetites of an archeus, operative Ideas,

53. I cite all Leibniz’s works, with the exception of Protogaea, from the translation by Leroy E. Loemker, G. W. Leibniz: Philosophical Papers and Letters (Chicago, 1956). Leibniz expressed his desire to reconcile Aristotelian and modern philosophy in his letter to Thomasius of 20 April 1669 and in Specimen dynamicum. In the latter work, in his Discours de metaphysique sect. 11, and in his letters to Arnauld of 14 July 1686 and to Remond of 10 January 1714, he recorded his change of heart over the substantial form. Leibniz, like Francis Bacon, came to reject atoms and the void; compare his De ipse natura, p. 823, with Bacon’s Novum organum, p. 126.

[7°]

The Scientific Reinterpretation of Form

substantial forms, and even minds, as it is to call upon a universal cause of all things, a deus ex machina to move individual natural things. There is no world soul. ... I consider the omniscient heat of Hippo¬ crates, the soul-giving Cholcodea of Avicenna, the most wise plastic power of Scaliger and others, and Henry More’s hylarchic principle, to be in part impossible and in part superfluous.54

In words similar to Bacon’s, he gave the reason for this superfluity: “In creating things from the beginning, God willed that they should observe a certain law in their progression. . . . Things have been so formed by the command that they are made capable of fulfilling the will of him who commanded them.”55 Leibniz was not denying the reality of the form in these passages; he was limiting its philosophical role. He disallowed the use of the form as an explanation of individual phenomena, but he main¬ tained it as the metaphysical basis for physical explanations, be¬ cause it was the law of creation. Conversely, he held mechanistic doctrines to be invalid at the metaphysical level, but mechanical explanations to be adequate at the phenomenal level:

I fully agree that all the particular phenomena of Nature can be explained mechanically . . . but we must also consider how these me¬ chanical principles and general laws of Nature arise from higher principles and cannot be explained by quantitative and geometrical considerations alone; there is rather something metaphysical in them. . . . Nature has as it were an empire within an empire, a double kingdom, so to speak, of reason and necessity, or of forms and of the particles of matter.56

But Leibniz’s form theory was not a mere abstraction remote from the world of matter and motion. He was able to show that it was relevant to the new science of dynamics, of which he himself had laid the mathematical foundations: “The concept of forces . . . for whose explanations I have set up a distinct science of dy¬ namics, brings the strongest light to bear upon our understanding of the true concept of substance. Active force . . . contains a certain

54. Animadversiones in Cartesium, p. 675; De ipse natura, p. 810. 55. De ipse natura, p. 813. 56. Animadversiones in Cartesium, pp. 674—5. See a^so the letter to Arnauld of 14 July 1686.

The Concept of Form after Aristotle

[71 ]

action or entelechy. ... It is carried into action by itself and needs no help.”57 This active force, the equivalent of the Aristotelian substantial form that had been defined as pure act, was the essence of the body, which imparted specificity and caused the body’s actions, motions, and qualities. Leibniz explicitly held that he was rein¬ terpreting the form in terms of force. But at the same time he maintained a high view of the form and believed that it was neither generated nor corrupted, for having been created by God, it could be destroyed only by him. In fact, like Fernel, Leibniz looked upon the substantial form as a substance in itself. Leibniz elaborated this view of form as substance into his theory of monads. Described in the opening words of the Monadologie as “a simple substance . . . without parts,” the monad or self-sufficient unit of substance was defined elsewhere by Leibniz in terms of form and force: This substantial principle itself which is called the soul in living beings and substantial form in other beings, inasmuch as it truly constitutes one substance with matter . . . makes up what I call a monad. ... [To] primary matter . . . must be added a soul or a form ... a first en¬ telechy, that is, or a kind of nisus or primitive force of action which is itself the inherent law impressed upon it by divine command. . . . This I customarily call a monad.58

Although the monad was a unity, it had an active and a passive aspect; the active force functioned as form with respect to the subordinate passive force and was known by the Aristotelian name “entelechy” (actualization). Leibniz also held that monads aggre¬ gated to form an organism, which he called a “natural machine,” under the control of a dominant monad which functioned as form with respect to the subordinate monads. This hierarchy of monads owed much to the scholastic theories of hierarchies of forms, which had also appealed, in a different way, to Francis Bacon. Leibniz’s form theory, then, was squarely based on a Peripatetic foundation, as is shown by his use of the terms “substantial form” and “entelechy”; his view of the form as substance, act, and source of specificity; and his hierarchy of forms. His was the last great philosophical system to have the concept of form explicitly as its 57. De primae philosophiae emendatione et de notione substantiae, p. 709. 58. Monadologie, p. 1044; De ipse natura, pp. 818—20.

[72]

The Scientific Reinterpretation of Form

main feature. But he had little influence on the general ideas about the form concept that were circulating in the late seventeenth cen¬ tury, not only because of the difficulty of some of his ideas and the fact that many of his writings remained unpublished, but also be¬ cause his theory was out of the mainstream of contemporary spec¬ ulations about the form, which were concerned mostly with cor¬ puscular and chemical theories on which he turned his back. During the seventeenth century corpuscular opinions gradually gained in importance and influence. It is often supposed that those who embraced atomism or some other particle theory necessarily rejected the traditional understanding of bodies in terms of matter and form. But this is so only in a few cases. In their mature work Galileo, Descartes, and Thomas Hobbes omitted all consideration of form from their theories and pursued a mechanistic approach in terms of matter and motion alone, but each of them passed through a stage when they made use of the form concept, as William Wallace has shown for Galileo, and as we shall indicate for Descartes and Hobbes in chapter 5.59 The majority of their fellow corpuscularians admitted the concept of form to a greater or lesser degree. Their particle theories as well as their form theories were of varied types. Of those whom we have already mentioned in this chapter, de Clave and Basso were atomists; Digby, de Boot, Sennert, and Bacon oc¬ cupied a more eclectic position with respect to particle theory. Basso and Sennert had a high view of the form; Digby, de Boot, and de Clave had a low view; and Bacon and Leibniz had their own versions. Basso and Sennert devised particulate reinterpretations of form; de Boot and de Clave, as well as Sennert, employed chemical form theories. Many possibilities existed for incorporating the concept of form into current scientific theories and reinterpreting the form in a manner suitable to each context. We shall explore these possibilities in the following chapters. In the formulation of the new theories certain problems had to be faced. Whatever view is taken of the nature of bodies, there are two questions that always crop up and that are difficult to answer. One is concerned with the cause of the specificity of bodies, and the other with the physical mode in which order is established in mat¬ ter. The former was a particular stumbling block to mechanistic writers; the latter was the weak point of most form theories, as our 59. William Wallace, Galileo's Early Notebooks: The Physical Questions (Notre Dame, Ind., 1977). The young Galileo compiled questions in the traditional manner on Aristotle’s works, using, and apparently accepting, scholastic doctrines including form theory.

The Concept of Form after Aristotle

[73]

study of mineral and crystal theories in the previous chapter clearly showed. Robert Boyle enunciated the problem with respect to crystallization, the crux of the mineral kingdom so far as the form is concerned: I know, that not only profest chemists, but other people, who are deservedly ranked among the modern philosophers, do with much confidence entirely ascribe . . . the lapidescence of bodies to a certain secret internal principle, by some of them called a form, and by others a petrifying spirit. And for my part ... I am very forward to grant that (as I elsewhere intimate) it is a plastick principle implanted by the most wise Creator in certain parcels of matter, that does produce in such concretions as well the hard consistence as the determinate fig¬ ure. We deny not, then, that these effects depend most commonly upon an internal principle; but the difficulty consists in conceiving how that internal principle produces its effects, which these writers not pretending to explicate intelligibly, we thought it not amiss to survey.60

There was indeed a “difficulty ... in conceiving how that inter¬ nal principle produces its effects," especially when that principle was envisaged as the exalted form which Sennert had inherited from Scaliger, and Basso from Plato. Nevertheless, it was Sennert in particular who was able to point the way to the direction that Boyle and others followed in integrating the form more closely with matter—the reinterpretation of form in corpuscular terms. This approach was based upon the belief that at the creation the primal particles received forms, “implanted by the most wise Creator,” that determined their qualities and activities and hence the natures of all the complex bodies that would be made by their combination throughout the history of the world. The biblical doctrine of creation was the focal point of every kind of reinterpretation of form propounded in the seventeenth cen¬ tury. It not only supplied a metaphysical principle of unity, but also offered a unique occasion for the interpenetration of the realms of body and spirit, matter and form, for in the divine act of creation nothing was impossible. Boyle saw the advantage of this. He felt the attractive plausibility of the form or “architectonick principle,” but he was inclined to restrict it to the beginning of the world. The physical phenomena of the present day might seem to be ade¬ quately explained by the mechanical philosophy; Boyle wrote: “I 60.

History of Fluidity and Firmness, Works,

vol. 1, pp. 275—6.

[74]

The Scientific Reinterpretation of Form

suspected the principles of the world, as it now is, to be three, matter, motion, and rest.” But within a page of writing these words, he added the following passage, showing how these phenomena were the effects of the primeval form: I have sometimes thought it not unlit, that to the principles ... we should . . . add another, which may conveniently enough be called an architectonick principle or power, by which I mean those various determinations, and that skilful guidance . . . which were necessary at the beginning to turn that confused chaos into this orderly and beau¬ tiful world. . . . For I confess I cannot well conceive, how from matter, barely put into motion, and then left to itself, there could emerge such curious fabrics.61

The appeal to the creation was more than a convenient escape route, however; in a satisfying way it firmly tied the properties of matter and the physical world to the God-given orderliness im¬ parted to the world from the beginning. It found widespread sup¬ port among very different schools of thought for another reason too; as well as agreeing with Christian doctrine, it also reached back to another ancient and commonly held belief, the Neoplatonic sem¬ inal reasons implanted in matter by God and awaiting develop¬ ment. The question naturally arose: What could be the nature of the form bestowed by God on the primary particles at the creation— chemical affinity, motion, size, shape, mass? Whichever answer was given, one thing was certain: the form had to be expressed mate¬ rially. Once again we find Boyle proposing a definition that would have been accepted by most other corpuscularians: “The form is . . . the matter itself of a natural body, considered with its pecu¬ liar manner of existence ... its speciFical or its denominating state, or its essential modification, or ... in one word, its stamp.”62 With its emphasis on the involvement of the form in matter, this defini¬ tion was not very far from the original form concept of Aristotle, when we remember that the latter wrote: “The proximate matter and the form are one and the same thing, the one potentially, the other actually.”63 Sometimes it is said of Boyle, as of Bacon, that he reduced the form to qualities, but this is not true. What is true of both of them is that they blurred the distinction between the sub61. 62. 63.

The Sceptical Chymist, Works, vol. 1, p. 361. The Origin of Forms and Qualities, Works, vol. Metaphysics vm 6, 1045b.

11, p. 470.

The Concept of Form after Aristotle

[75]

stantial and the accidental form, a distinction more characteristic of the schoolmen than of Aristotle, so that there was an immediacy of connection between the form and the qualities arising from it, indeed between form and matter. For, as Bacon pointed out, forms are only known by the qualities and actions that they produce, just as people’s characters are only shown by their behavior. This was meant by Aristotle’s calling the form “act” or Boyle’s calling it “the stamp.” So the corpuscular understanding of the form had much in common with the low view of form held by Aristotle and some of the schoolmen, form “immersed in matter” or “educed from mat¬ ter.” But at the same time the exalted nature and heavenly origin of the form were guaranteed by the imprint of the Creator’s hand upon matter “to turn that confused chaos into this orderly and beautiful world.” In this chapter we have seen the vigor of seventeenth-century efforts to reinterpret the form, coming at the end of a long devel¬ opment of Aristotelianism and benefiting from some of its insights, but also drawing inspiration from Platonism, chemical and cor¬ puscular theories, and the biblical doctrine of creation. The con¬ cept of form had an important part to play in the scientific theories of this century, and, resting on a foundation of traditional form theory, it was now being reconstructed to fit it for its new role.

CHAPTER

THREE

Mixtion and Minima: The Beginnings of a Corpuscular Approach to Form Contributing to the rapid alteration and blending of moist bodies is their easy divisibility; for they divide one another before being united, and arejuxtaposed together as corpuscles, thus interacting more easily and more quickly, and they rapidly become one body both in substrate and in quality—a body not in actuality any of the bodies that have been mixed, but in potentiality all of them. . . . The constituents First divide one another and then by their jux¬ taposition as corpuscles become malleable and are unified and assimilated in form and likeness. Alexander of Aphrodisias, De mixtione

of the concept of form to explain the specificity of bodies seemed straightforward enough in cases where there was no substantial change, such as the constant angularity and trans¬ parency of crystals, for there was clearly a single permanent form. But this simple approach could not cover more complex cases where there was change in the substance itself, such as generation and corruption or chemical combination, where new substances appeared and old ones disappeared. The question of specificity was raised by chemical change in a different way from crystalliza¬ tion. Aristotle took seriously the problem of change of substance, and he criticized “all our predecessors [because], with the single excep¬ tion of Democritus, not one of them penetrated below the surface or made a thorough examination of a single one of the problems.”1 The use

i. On Generation and. Corruption i 2, 315a.

[76]

Mixtion and Minima

[77]

He distinguished between mere alteration (“when the substratum is perceptible and persists, but changes in its own properties”), total change or generation and corruption (“when nothing persists in its identity as a substratum”), and the intermediate phenomenon of combination, in which the components of a new substance “neither persist actually . . . nor are they destroyed."2 The medieval school¬ men called combination “mixtion,” the constituents “miscibles,” and the compound a “mixt,” and henceforth I shall use these terms. Mixtion (e.g., of two molten metals to form an alloy) differs from mechanical mixture (e.g., of two sorts of grains) because the latter involves no change but in mixtion the miscibles change into a single homogeneous mixt. Mixtion also differs from generation (e.g., conception) in the continuity and similarity between the mixt and the miscibles and the possibility of reconstituting the miscibles from the mixt. Now the usefulness of these distinctions was, of course, limited by the rudimentary state of chemistry in Aristotle’s time, which could not furnish him with more notable examples of chemical change than alloying. The Stoics in the century after Aristotle add¬ ed another category of change to fill the gap between mixtion and generation: total fusion from which the constituents could not be regained, such as the compounding of drugs. But since their classi¬ fication was never widely adopted, and the atomists’ explanation of combination by mere juxtaposition of atoms was inadequate, Aris¬ totle’s theory of mixtion held the field without a rival. Its limita¬ tions in face of the increasingly wide variety of chemical phe¬ nomena that became known during the Middle Ages was undoub¬ tedly a reason why mixtion theory rarely emerged from the study into the laboratory, but remained a topic for abstract debate until the end of the scholastic period. Writers rarely went beyond Aristo¬ tle’s own examples of mixtion; among the few who illustrated mix¬ tion theory by fresh examples were Alexander of Aphrodisias, Albertus Magnus, Roger Bacon, and the anonymous author of the Summa philosophiae. Of these few, Albertus tried hardest to apply mixtion theory to mineral chemistry. He chose as his examples the “intermediate minerals” (i.e., slags, salts, alum, vitriols, marcasites, etc.), which were neither stones nor metals, but were formed in the earth from stony and metallic materials, to which they could again be reduced.

2. Ibid. 1 4, 319b; 1 10, 327b.

[78]

The Scientific Reinterpretation of Form

Everything which in some ways shares the passive [properties] of stones and in other ways those of metals, we call an intermediate. . . . Nature does not pass directly from one extreme to the other . . . and has made many things intermediate between infusible stones and fusible metals. ... It is a property of all intermediates that their spe¬ cific forms seem to be incomplete. . . . An intermediate, strictly speak¬ ing, possesses only in an unformed state that nature which in the extremes is distinct and perfect. . . . The extremes are in some man¬ ner present in the intermediate but only in confused forms. . . . Marcasite has the nature of both stone and metal . . . the metal in it has not completely attained its specific form . . . thus it vanishes by evap¬ oration when assayed by strong heating.3

The mixtion theory developed by Albertus and other schoolmen was based upon the words of Aristotle: It is obvious that mixtion must differ from coming-to-be and passing-away. . . . Since, however, some things are-potentially while oth¬ ers are-actually, the miscibles combined in a mixt can “be” in a sense and yet “not-be.” The mixt may be-actually other than the miscibles from which it has resulted; nevertheless each of them may still bepotentially what it was before they were combined, and both of them may survive undestroyed. ... It is evident that the combining misci¬ bles not only coalesce, having formerly existed in separation, but also can again be separated out from the mixt. The miscibles, therefore, neither persist actually . . . nor are they destroyed (either one of them or both), for their power of action is preserved. . . . When there is a certain equilibrium between their powers of action, then each of them changes out of its own nature towards the domi¬ nant; yet neither becomes the other, but both become an intermediate with properties common to both.4

3. Book of Minerals, pp. 238-9, 246. Alexander took over from his Stoic oppo¬ nents the examples of burning incense, precipitated gold, fire in heated iron, the action of drugs, etc. (De mixtione, in Robert B. Todd, Alexander of Aphrodisias on Stoic Physics [Leiden, 1976], p. 119). Roger Bacon gave mineral examples in his Communium naturalium 1 (Opera hactenus inedita Rogeri Baconi, ed. Robert Steele, [Oxford, 1911], fasc. 2, pp. 2, 18; fasc. 3, pp. 274-5). The Summaphilosophiae gave numerous examples of metals, minerals, and stones in tractates 17 and 19 {Die philosophischen Werke des Robert Grosseteste, pp. 604, 625—9; see a^so PP- 629—43). 4. On Generation and Corruption 1 10, 327b—328b. In order to show the relevance of this passage to scholastic mixtion theory, I have substituted the words “mixtion,” “mixt,” and “miscible” for the words “combination,” “compound,” and “constitu¬ ent” or “combinable” used by Harold Joachim in The Oxford Translation of Aristotle. I am grateful to the Oxford University Press for permission to make this change of wording here and on p. 86.

M ixti on and Minim a

[79]

By using the notions of potentiality and actuality and by postulat¬ ing powers exerted by one body on another, Aristotle attempted to solve some problems of mixtion: how bodies can disappear into a mixt and yet be regained from it; whether the miscibles are invisi¬ bly present in the mixt; what determines the nature of the newly formed mixt. He did not express mixtion theory in terms of matter and form, but when it became the subject of debate among the medieval schoolmen, with their greater stress on the form, it was natural that mixtion should be discussed in the light of Aristotelian form theory. The emergence in Arab and Latin scholasticism of many differ¬ ent form theories of mixtion, all based on the words of Aristotle, bore witness to the difficulty of understanding the relationship between miscibles and mixt in terms of their substantial forms. All these theories were designed to explain this relationship, but no single solution that worked along the lines suggested by Aristotle could satisfactorily do justice to the facts of mixtion as well as to the Peripatetic doctrine of form. The problem of mixtion became one of the most widely discussed philosophical questions of scholastic times. The most hotly debated points were whether the forms of the miscibles or elements remain in the mixt and, if they do, whether they undergo strengthening or weakening (intension and remission, in the scholastic terminology). There are too many rami¬ fications of the various theories to enumerate here, but they can usefully be grouped around the positions of certain well-known authors to obtain an overall view of the subject, as was done by the sixteenth-century Peripatetic Jacopo Zabarella the elder in his Liber de mistione: Avicenna thought that the forms of the elements remain intact in the mixt, not damaged in any way, but that their qualities do not remain intact but are limited and broken by their mutual activity and pas¬ sivity . . . for substantial forms cannot be strengthened or weakened like qualities. . . . Averroes thought that, just as the substantial form actually remains in the mixt, so do the qualities, but both [forms and qualities] are broken, limited, and reduced to a mean state. . . . He hoped to avoid Avicenna’s difficulties by stating that the forms of the elements can be strengthened, weakened, broken, or limited, so that from all of them is made one intermediate form. . . . Scotus thought that both the forms and the qualities of the ele¬ ments are entirely destroyed in mixtion, and a new form of the mixt J

J

[8o]

The Scientific Reinterpretation of Form

generated, also a new quality which is the temperament of the mixt. . . . Thomas [Aquinas] and the more recent philosophers say that the forms of the elements are not preserved at all in the mixt, but are wholly destroyed, whilst the qualities remain, weakened and reduced to a mean state.5

Each of these versions had its own advantages and disadvan¬ tages. Avicenna’s theory, which was the earliest, transgressed the basic Aristotelian tenet that a body can possess only one substantial form at a time, but it allowed for the possibility of decomposing mixts into their miscibles. The theory of Averroes, Avicenna’s fel¬ low Arab and opponent, mitigated the difficulty of holding a plu¬ rality of forms by allowing them only a weakened state as part of the form of the mixt or subordinated to it. But it violated the Aristotelian doctrine that the form was immutable and hence inca¬ pable of weakening or strengthening. The Thomist and Scotist versions avoided all these philosophical pitfalls, but they under¬ mined the theory of mixtion as a whole by losing sight of the continuity between the miscibles and the mixt and the possibility of regaining the former from the latter. "These theories of mixtion were really form theories. Their in¬ terest for the schoolmen lay in the possibilities they opened up of exploring the form, rather than in any explanations they might offer of natural phenomena, the structure of matter, or chemical change. This was a reason why Albertus’ application of theories of form and mixtion to minerals found little response. In general, mixtion theory was treated abstractly with reference to the study of form. But even though it did not usually deal with the combina¬ tions and changes investigated by medieval chemists, it produced some important insights into the nature and role of the form in mixtion which would in time become relevant to chemical theory. We must now examine some of these insights and the ways in which they developed. In many ways the Averroist form theory of mixtion proved to be the most fruitful in producing new insights and suggesting new lines of thought along which the study of mixtion might be pur5. Liber de mistione, in De rebus naturalibus hbri XXX (Cologne, 1590), cols. 40911. For a detailed account of scholastic mixtion theory, see Maier, “Die Struktur der materiellen Substanz,” pp. 1 — 139. A brief account is given in Eduard Dijksterhuis, The Mechanization of the World Picture (Oxford, 1961), pp. 200—4.

Mixtion and Minima

[81 ]

sued. Averroes’ teaching that the forms of the elements undergo strengthening and weakening (intension and remission) could be interpreted in various ways and gave rise to some interesting sug¬ gestions. He held that substantial forms did not vary, but that the elementary forms were not fully substantial; being intermediate between substantial and accidental forms, they could vary in inten¬ sity as accidents or qualities did. He expressed this state of weak¬ ness or remission as being between actuality and potentiality: “Out of each of the miscibles, as they become mixed, there emerges a third thing in actuality, which is uniform in its properties but dif¬ ferent in form from each of the miscibles, in that each one of the latter exists in it with a potentiality bordering on, not remote from, actuality.”6 This idea was taken up by several schoolmen in their attempt to understand the presence of the miscibles in the mixt. Some writers, including Roger Bacon, posited degrees between potentiality and actuality through which the forms passed on their way from the elementary state to their union in the form of the mixt. This had the consequence that it was possible to understand mixtion as a gradual and successive process, a series of stages. The weakened state of the form in its intermediate stages could be thought of as a form whose capacity for acting, rather than its existence, was im¬ paired. For writers with a leaning toward the Platonic tradition there was the possibility of going outside Aristotelianism and of drawing upon the notion of seminal reasons or embryonic forms latent in matter, which Augustine transmitted from his Neo¬ platonic background to Latin Christendom. This was favored by some of Aquinas’s contemporaries, such as Bonaventure, Roger Bacon and others, although it wras frowmed upon by Duns Scotus. Concepts based on seminal reasons regained popularity in seven¬ teenth-century chemical reinterpretations of form theory, but they should not be regarded as innovations, for they had already been accommodated within Aristotelian mixtion theory in the Middle Ages. We may take as an illustration of scholastic speculation on this subject the form theory of mixtion propounded by Roger Bacon (1214-94), which presented some interesting features. Inspired by

6.

Epitome, in Averroes’ Middle Commentary and Epitome on Aristotle's De generatione et corruptione, trans. by Kurland, p. 121.

[82]

The Scientific Reinterpretation of Form

Averroist mixtion theory to some extent, but often pursuing an independent line, Bacon displayed some consistent tendencies. One was a preference, like his contemporary Albertus Magnus, for considering concrete examples rather than abstract relations; an¬ other was a care to preserve the balance between matter and form without overemphasizing either of them. Since God had created matter and form together, Bacon held that each species had its own specific matter as well as its specific form; thus there must be a hierarchy of matters and of forms, the higher absorbing or per¬ haps building on the lower. Even generation and corruption or substantial change such as mixtion did not involve decomposition as far as unformed prime matter, as Aquinas and most others thought. The material substrate, which Bacon called “natural mat¬ ter,” was not without its own forms, to which higher forms were added; this conception was similar to Avicenna’s and Averroes’ material or corporeal form in matter prior to its reception of ele¬ mentary and higher forms. Bacon’s notion of mixtion as a gradual process envisaged a series of related forms, each higher and more specific than its predeces¬ sor, which led up to and prepared for the final form of the mixt, into which they were assimilated. He differed from writers such as Aquinas, who admitted a gradual process in which the earlier forms disappeared, by his Averroist insistence that the previous lower forms were still present in the form of the mixt, although they were weakened and subordinated to the latter. For Bacon, the final form itself, as well as the lower forms composing it, was in some sense present from the beginning, since it was the perfection toward which the lower forms were tending. Matter had a part to play in this process; the seminal reason or preexistent state of the form was called by Bacon the “active potency” (potentia activa) of matter from which the form of the mixt developed. We have seen in chapter 2 that the study of the form in the inorganic realm presented a temptation to unbalanced views: either to exalt or to depreciate the formal cause unduly in relation to the material and efficient causes. Bacon’s insistence on the joint existence and col¬ laboration of matter and form at all levels was a reminder that the material and formal causes were mutually necessary to each other and not alternatives. The Averroist view that the weakened elementary forms were absorbed or dominated by the form of the mixt was later affirmed by Scaliger:

Mixtion and Minima

[83]

The nature of the elements [is understood] not only with respect to themselves but also with respect to their mixts. With respect to itself, it has a form which it gives up in order to obtain a nobler form [in the mixt]. Thus neither do the forms remain, nor are the qualities de¬ prived of their forms, but in a different way they are accommodated to the substance of the mixt. For a new generation it is necessary that the forms of the parts, subdued by one another’s qualities, should have laid aside the original inflexibility of nature under the dominion of one [form] that is more powerful.7

In this view there was a causal continuity between the forms of the miscibles or elements and the form of the mixt, since the former were part of the latter. This continuity was weakened by the Thomists and lost by the Scotists. In the teaching of Aquinas, the forms of the miscibles vanished, but their surviving weakened qualities fused into a single intermediate quality. This prepared the matter for the new form of the mixt, which was suitable to this quality but was not derived from it. Thus the role of the miscibles was preparatory rather than constituent, and the causal aspect was very weak. The relinquish¬ ment of a role for the-elementary forms was balanced by a stronger emphasis on the qualities, and on the intermediate quality, the sole point of contact between the miscibles and the mixt. This led to the recognition, especially by Giles of Rome and Jean Buridan, that although matter and qualities are altered during mixtion, they must stay numerically constant in the miscibles and the mixt as a whole. This insight has been seen by some historians as an early intimation of the principle of conservation of matter, but more relevant to its own time was its reminder that mixtion should not be discussed in terms of the form alone and that attention should also be given to matter, its qualities and quantity. But if Aquinas disposed of the forms of the elements, how could their qualities survive? The logical Duns Scotus did away with both of them. Even the weak causal connection of the Thomists was abandoned, and all that could be said about the relationship of the mixt to the miscibles w^as that the former was suitable to the latter. In view of the lack of continuity between the miscibles and the mixt, the question naturally arose, Where did the form of the mixt come from? Now it wras admitted by all schoolmen that the four natural causes, although necessary, were not in themselves suffi7. Exotericarum exercitationum liber XV, ex. 16, pp. 34—5.

[84]

The Scientific Reinterpretation of Form

cient for the emergence of forms; the concurrence of a superior cause was also required. This was the power of the heavens which, as we have seen in chapter 2, had theological, astrological, and metaphysical aspects. For most schoolmen the natural causes in mixtion were the instruments of the celestial cause, but for those who shared the Scotist view of mixtion it was difficult to see how any cause other than the heavens could logically be assigned. The medieval discussions about mixtion succeeded in formulat¬ ing some valuable insights about the roles of forms, qualities, and matter. Albertus’ application of form theory to concrete mineral phenomena; Bacon’s insistence on the joint activity of matter and form; the Averroists’ view of the subordination or absorption of lower forms by higher ones; the Thomists’ recognition of a numer¬ ical constant persisting through qualitative change; even the Scotists’ bleak realization that the logical conclusion of mixtion the¬ ory, when shorn of all its inconsistencies, was a denial of natural causation and hence a dead end—all these insights, emerging from the very defects and ambiguities of Aristotelian mixtion theory, would contribute to the reinterpretation of the concept of form in the context of mixtion during the sixteenth and seventeenth centuries. T hat reinterpretation, however, still lay in the future. By the second half of the fourteenth century a thorough exploration of all the varieties of mixtion theory had reached a stalemate. As Anneliese Maier writes: “The schoolmen did not solve the problem because for them it was insoluble. . . . This problem was one of the decisive points at which scholastic natural philosophy came to a point of no return, and it was here that a bitter struggle was waged against the philosophy of forms and qualities, a fight for which scholasticism itself had already forged the weapons.’’8 It must not be thought that the development of mixtion theory was a waste of time just because it ultimately failed to find one conclusive, logically consistent answer to the problem. On the con¬ trary, it exerted an important influence on the history of the form concept, not least because its inconsistencies forced writers to pay attention to alternative points of view. The fact that Aristotelian philosophy took seriously the problem of substantial change and attempted to answer it in terms of the form meant that it was not possible to overlook the material involvement of the form or to separate its active role as the agent of change from its passive role 8. “Die Struktur der materiellen Substanz,” pp. 138—9.

Mixtion and Minima

[85]

as the pattern for the end product, in the way that Plato had done. Nor could the form be restricted to a static function; Aristotle’s understanding of change as motion implied the necessity of a dy¬ namic role for the form. Up to the early fourteenth century it seems that the main empha¬ sis in mixtion theory had been on the status, and the presence or absence, of the elements or miscibles in the mixt. But the Scotists had shown that no consistent explanation of this could be given, at least on Aristotle’s terms. Now it seems that the emphasis shifted from the miscibles to the mixt itself; the nature and function of the form of the mixt promised, and indeed proved, to be a more fruit¬ ful subject of inquiry than the elementary forms. As Albert of Saxony wrote in the second half of the fourteenth century: “[Mix¬ tion cannot take place] unless there is in the mixt a form other than the form of an element, a constructing, regulating, figure-giving form. . . . There must be one ruling form in the mixt. . . . The mixt requires a due figure and a due organization, and this is the dif¬ ference between an element and the mixt.’’9 Another shift in em¬ phasis was toward consideration of the process of mixtion, seen from the point of view of the form of the mixt rather than the miscibles. How did the ruling form of the mixt perform its con¬ structing, regulating, figure-giving functions? A new approach was needed that could utilize the partial insights achieved in the scho¬ lastic exploration of mixtion and make sense of some of the more puzzling aspects of mixtion theory. In short, what was called for was nothing less than a fresh in¬ terpretation of the form concept. This would be a corpuscular reinterpretation of form, and it would renew not only mixtion theory but also the whole postscholastic understanding of chem¬ istry, matter theory, and crystal studies. The approach to it, taking into account the particulate nature of matter, started from the mixtion theory of Aristotle himself. This contained a corpuscular, but not atomistic, understanding of mixtion; for the fact that Aris¬ totle held matter to be a continuum and that he opposed atomism did not mean that he totally ruled out particulate explanations, though admittedly they played a very small part in his thought. He held that a temporary and preliminary division into particles took place in mixtion and in the growth of living creatures. So he made occasional references to particles of flesh and, more to our pur9. Quaestiones in duos libros de generatione et corruptione 1.19, 2.7, in George Lokert, Quaestiones et decisiones physicales insignium virorum (Paris, 1518), fols. 143a, 150c!.

[86]

The Scientific Reinterpretation of Form

pose, of miscibles. His treatment of mixtion, of which we have already seen a part, included the following particulate account: So long as the miscibles are preserved in small particles, we must not speak of them as combined. ... If mixtion has taken place, the mixt must be uniform in texture throughout—any part of such a mixt being the same as the whole, just as any part of water is water; where¬ as, if mixtion is mixture of the small particles, nothing of the sort will happen. . . . Only those agents are miscible which involve a contrariety, for these are such as to suffer action reciprocally. And, further, they combine more freely if small pieces of each of them are juxtaposed. For in that condition they change one another more easily and more quickly. . . . Hence . . . those whose shape is readily adaptable have a tendency to combine; for they are easily divided into small parti¬ cles. . . . Mixtion . . . depends upon the fact that some things are such as to be reciprocally susceptible, and readily adaptable in shape, i.e. easily divisible. For such things can be combined without its being necessary either that they should have been destroyed or that they should survive absolutely unaltered. . . . Anything is miscible which, being readily adaptable in shape, is such as to suffer action and to act. . . . Mixtion is unification of the miscibles, resulting from their alteration.10

In the original text, this passage and the one cited earlier in this chapter are twined together into a single account, of which the two parts belong together and illuminate one another. For instance, the statement that the miscibles “neither persist actually . . . nor are they destroyed” makes better sense when one thinks of particles mutually altering one another and then merging into the con¬ tinuum of the mixt. I have detached the two parts, because that is how the schoolmen seem to have looked at Aristotle’s account. The first part distinguishes mixtion from generation and explains the presence of the miscibles in the mixt in terms of potential existence and powers of action; the second differentiates mixtion from mix¬ ture and explains the union of the miscibles in terms of interacting particles which then blend into one. Preoccupied with the first part, explaining it in terms of the form concept that Aristotle had omit10. On Generation and Corruption i 10, 327b—328b. The First paragraph of this passage comes after the First paragraph of the passage on p. 78, and the second paragraph comes after the second paragraph of the earlier passage. On the altered wording, see note 4. On divisibility and mixtion, see also Physics vi 1,4, 6, 10, and On Sense and Sensibility 440b.

Mixtion and Minima

[8?]

ted from his account, the schoolmen had less attention to spare for the seond part. Nevertheless, they did not overlook the question of particles altogether; they accepted the existence of particles on Aristotle’s authority and, although they did not often use particles in explanations, they discussed the possibility in various contexts, and thus the way was opened for a corpuscular reinterpretation of form at the end of the scholastic period. To the development of Aristotle’s notion of particles we must now turn. What sorts of particles did Aristotle envisage in this passage? Not the atoms of Democritus and Leucippus, or the geometrical units of Plato, but just conveniently small portions of matter that enabled the miscibles to mingle and interact. Their size, their shape, their very existence were indeterminate; once mixtion was complete they merged into the homogeneous continuum and lost their existence as particles, for if they remained separate, they would constitute a mixture, not a mixt. They were a useful explanatory device for showing how certain sorts of change could take place, but their use in such contexts had no special significance for matter theory and certainly did not imply a permanent corpuscular structure of matter. Aristotle’s commentators were not content to let the question rest at this simple level. They conflated the mixtion particles mentioned in this passage with the particles of flesh mentioned by Aristotle in a biological context. He had suggested that in organic growth “par¬ ticle after particle comes to be, and each successive particle is dif¬ ferent”; moreover, since living creatures' sizes vary only between certain limits, he held that this must be true of their parts as well, and hence there must be “the minimum quantity of flesh [from which] no body can be separated out; for the flesh left would be less than the minimum of flesh.”11 From this commonsense notion the commentators and the schoolmen elaborated the conception that to every sort of substance there must correspond, in Averroes’ words, “particles than which there can exist none more minute,” each species being ruled by its own form, so that “flesh cannot exist smaller than the minimum because the form of the flesh cannot be preserved in a smaller quantity”; and the consequence was the doctrine that “the natural minimum ... is that ultimate [state] in which the form is preserved in the division of a natural body.”12 11. On Generation and Corruption 1 5, 321b; Physics 1 4, 187b. “Different” here means “distinct.” See also On Generation and Corruption 1 3, 317a, where dissociation into “relatively small parts” is opposed to division into atoms. 12. Averroes, Middle Commentary 1.5 (Kurland, p. 38); Jacopo Zabarella the elder,

[88]

The Scientif ic Reinterpretation of Form

Thus the minimum naturale or minimum natural part, the material unit that embodied the form, was postulated and came to be associ¬ ated with Aristotle’s indeterminate mixtion particle. This Peripatetic corpuscular theory, known to us as minimism, was distinguished from atomism by the Greek and Arab commen¬ tators and by the schoolmen. For instance, Alexander of Aphrodisias showed how Democritan and Epicurean atomism, Stoic phys¬ ics, and Aristotelian hylemorphic minimism each gave rise to its own distinct theory of mixtion; and Averroes, with his unswerving devotion to Aristotle, came into conflict with the version of Epi¬ curean atomism that had been revived in the Muslim world as an anti-Aristotelian move.13 In the Latin West the schoolmen were equally aware of atomism, but here it was the atomism of Demo¬ critus that counted, not that of Epicurus and Lucretius whose names, although known, were not often mentioned before the sev¬ enteenth century. Why was Democritus always acknowledged as the atomist par excellence? It was because Aristotle represented him as such. Democritus’ atomic theory was known through Aristo¬ tle’s presentation of it in his Physics, On Generation and Corruption, On the Heavens, and On the Soul. Aristotle’s qualified praise of him and serious discussion of his views made him familiar and accept¬ able to those whose intellectual formation was shaped by Peripateticism. This illustrates the overwhelming importance and authority of the Aristotelian writings during and even after the scholastic era; one cannot exaggerate the extent to which writers up to the late seventeenth century viewed philosophical questions through Aristotelian spectacles whether or not they agreed with him. It could happen that the reader who encountered Democritan views in, say, the Physics could assume almost without noticing it that, in spite of Aristotle’s criticisms of them, they were to be count¬ ed as part of the Aristotelian heritage. We have seen in chapter 2 that this happened in the case of Aristotle’s descriptions of Plato’s form theory. The result could be an eclectic willingness to absorb into one’s understanding of Peripateticism some of the features of Democritan atomism, as had already happened with Plato’s doc¬ trine of Ideas. For instance, Albertus Magnus encountered the

In Aristotelis librosphysicorum commentaria (Basel, 1622), p. 126, and Liber de mistione, in De rebus naturalibus libn XXX, p. 423. 13. Alexander, De mixtione; Averroes, Epitome and Middle Commentary 1.18 (Kurland, pp. 63-4, 121-2). On the atomism of the Arab Mutakallimun, see Harry Wolfson, The Philosophy of the Kalam (Cambridge, Mass., 1976), pp. 466-517.

Mixtion and Minima

[89]

views of both Plato and Democritus in his reading of Aristotle’s On Generation and Corruption, and he displayed more willingness than most schoolmen to find common ground between Aristotle and Democritus, although he was well aware that the concept of form was entirely lacking from the system of Democritus: [Flesh] is composed of minima which possess the action of the form. . . . There is held to be flesh so small that if it were any smaller the function of flesh would not be fulfilled; this is the minimum body . . . and Democritus called it the atom. . . . He was not wrong, if he was thinking of quantitative physical composition; but he was wrong in not seeing that the primary essential composition is of mat¬ ter and form, for the flesh particle (homoiomere) is composed of matter and form. . . . He was wrong in saying that the minima of physical bodies are indivisible (atomalia); if they are divided further they do not possess any physical action.14

As long as the rigor of scholastic logic was still in force, however, a total reconciliation of minimism and atomism was unlikely, al¬ though the eventual amalgamation of the two systems after the end of the scholastic period owed much to the habit of reading about atomism in an Aristotelian setting. The line between the two theo¬ ries was usually drawn carefully by the schoolmen, some of whom inserted rebuttals of atomism into their commentaries. Roger Bacon, for instance, refuted it by means of Euclidean geometry as well as by Aristotelian logic, and denied, like other schoolmen, the view that there could be permanent minima.15 Modern writers sometimes loosely give the name of atomist to medieval writers who expressed particulate views, for instance, William of Conches in the twelfth century, Giles of Rome in the thirteenth century, or the fourteenth-century Paris terminists. But this is inaccurate; William held a Platonic view of matter and the others were minimists. Corpuscularianism from 1200 to 1600 was minimistic rather than atomistic; the few exceptions, notably Nicholas of Autrecourt in the fourteenth century and Giordano Bruno in the sixteenth century, adopted atomism as part of a deliberate rejection of Aristotelianism, and this is clear from their language and beliefs. What, then, were the criteria that differentiated minimists from atomists? First, their language was different; minimists used the 14. Tractatus de generatione et corruptione i 1.12, Opera omnia, vol. v. 15. Communium naturalium 2 (Steele, fasc. 4, pp. 317—21); Questiones supra libros octo physicorum Aristotelis 1, 3, 7 (Steele, fasc. 13, pp. 31—3, 160—1, 369-70).

[9°]

The Scientif ic Reinterpretation of Form

words pars, minima pars, minimum naturale, particula, corpusculum, homoiomere, and did not use the word atomus except when referring to Democritan views.16 Second, this distinction of language indi¬ cated different conceptions of the particles. Atoms were held to be indivisible, impenetrable, and unchangeable, combining by contact alone and possessing no properties except size, shape, and motion. Minima were held to be physically divisible, although when divided they lost their form; in mixtion they underwent interaction and change and finally lost their separate existence; and they possessed the qualities of the body they composed. Atoms were the ultimate building blocks of all matter, solid and indestructible, whereas min¬ ima were not fundamental particles but a temporary state of matter enabling change to take place, and their function was to be the vehicle of the form—a conception that was meaningless in atom¬ istic terms. In the third place, atomism and minimism were designed for different purposes and were used in different contexts. Atomism offered an all-embracing and self-contained account of the uni¬ verse in general and the structure of matter in particular in strictly materialistic and nonmetaphysical terms, substituting random mo¬ tions in a void for form and order. Theoretically, atomism had a universal scope, but in practice it was strongest in matter theory and physical explanations. Minimism had a strictly limited context and function; it supplemented the other kinds of explanation (mat¬ ter and form, elements and qualities) in the case of chemical and biological processes, which were, as Aristotle pointed out, the sub¬ jects with which atomism was least competent to deal. Hence there was a striking divergence in the explanatory contexts in which these two particle theories were used—physical for atomism, chem¬ ical for minimism. Unlike atomism, minimism was not an indepen¬ dent matter theory; it was a small part of Aristotelian philosophy, which defined it and designated its explanatory role within the total framework. Only when minimism is understood as part of this 16. Corpusculum was sometimes used by atomists too. Aristotle used homoiomere to mean a part similar to the others and to the whole (e.g., a part of homogeneous bodies like metals or flesh) and to mean Anaxagoras’s particle, which had this characteristic. Some schoolmen used it to mean the minimum particle, as Albertus did in the passage just cited. Note that not every scholastic use of the words “atom” and “minimum” implied particles. Both words also had well-attested meanings in logic with reference to the individual, infima species, and summum genus, and it is in this logical context that they must be interpreted in Roger Bacon’s Questiones supra libros prime philosophie Aristotelis 10 (Steele, fasc. 10, pp. 322-32); and Questiones supra libros octo physicorum Aristotelis 7 (Steele, fasc. 13, pp. 361-70).

Mixtion and Minima

[91]

greater whole, integrated with the fundamental categories of mat¬ ter and form, can its conceptual content, its special contribution to mixtion theory, and its role in the reinterpretation of form be appreciated. Of all the distinctions between minimism and atom¬ ism, the most important and fundamental was that minimism was indissolubly tied to the concept of form, which supplied the basic definition of the scholastic minimum naturale as the unit material embodiment of the form. This is a point that cannot be too strongly emphasized. The schoolmen did not do much to develop minimism. If we take a typical minimistic explanation of mixtion, penned by Albert of Saxony in the fourteenth century, and compare it with Aristo¬ tle’s exposition cited above and with the account by Alexander of Aphrodisias which stands at the head of this chapter, we see that the only way in which the scholastic version advanced beyond its predecessors was in the prominence it gave to the substantial form: How does mixtion take place? . . . The miscibles, divided into small particles, act and react on each other until the substantial elementary forms of all those particles are corrupted. Then from the total mass composed of these particles the substantial form of the mixt is edu¬ ced, by whose eduction those matters become continuous, which were formerly contiguous when they were subordinated to the elementary forms. . . . For mixtion or the generation of mixts, mere juxtaposition of the parts is not enough; continuity is necessary as well. . . . Division of the miscible does not proceed to infinity but stops at the minute parts. . . . That any part of the mixt is mixt takes place, first, through juxtaposition, next, through their corruption, then through the intro¬ duction of the substantial form of the mixt.17

Here we see clearly the dose integration of minimism and mixtion theory with the Aristotelian doctrine of the form. Throughout the Middle Ages minimism was known and accept¬ ed by writers of all schools, and it was mentioned as a matter of course in questions and commentaries on Aristotle’s works. It gave rise to some speculations about the status, nature, and functions of minimum parts and their role in mixtion and organic growth—Do minima have sizes or shapes? Are they the same as points? Does divisibility have a limit? Do all things have a maximum and a mini¬ mum? In mixtion, are minima generated all at once or one after another?—but these stayed dose to Aristotle and had little to say 17. Quaestiones in duos libros de generatione et corruptione 1.20 (Lokert, fol. 144c!).

[92]

The Scientific Reinterpretation of Form

that was new. John of Jandun, Albert of Saxony’s Averroist con¬ temporary, was unusual in giving a novel minimistic explanation of condensation and rarefaction, brief as it was: Of any natural thing there is some quantity so small that its form cannot be preserved in a lesser quantity. . . . The matter of water can be brought to such a quantity that the form of water cannot exist in it; similarly air by condensation can be so diminished that it is corrupt¬ ed. . . . When minimum parts are divided, they take the form of what surrounds them; if they are in air, they take the form of air, and so on.18

Such questions demanded more searching consideration, howev¬ er, and they began to receive this in the sixteenth century when the pace of development quickened and minimism came into its own. The scene of this late flowering was the university of Padua, a stronghold of Averroist Aristotelianism and scientific method. The writers who did most to develop minimism were Agostino Nifo (1473—1538), Julius Caesar Scaliger (1484—1558), and Jacopo Zabarella the elder (1532—89). Nifo and Zabarella both taught at Padua, but Scaliger, after his training there, made a name for himself outside the university and obtained a wider audience. In their efforts to develop particle theory, these writers were able to draw upon the form theories of mixtion and other insights of scholastic philosophy that had not originally concerned minimism but were now seen to be capable of contributing to it. Some of these ideas we have already mentioned in passing, and we shall now examine their relevance to the corpuscular reinterpretation of form. First, there was the Averroist belief in the intension and remis¬ sion of forms, the elementary forms changing by degrees, which implied an understanding of change as being successive rather than instantaneous—in fact, as being particulate with respect to time, matter, and form. Thus generation, mixtion, or lesser changes such as heating were said to take place “in succession from part to part.” The idea of successive change was congenial to mini¬ mism. In the thirteenth century Roger Bacon viewed change as a series of steps by which the new substance gradually arose through 18. Super octo libros de physico auditu subtillissimae quaestiones (Venice, 1575), 1.16, fols. 26a,b. Rarefied water exceeds its minimum size and becomes a larger air particle; condensed air shrinks below its minimum size and becomes a smaller water particle.

Mixtion and Minima

[93]

ascending degrees of form from the lowly active potency of matter up to perfect actuality, and he expressed this in corpuscular terms: “When the substance of the agent touches the substance of the patient without anything in between, the substance of the agent, since it is active, can transmute a certain adjacent minimum, the first minimum part according to sense, and when that is trans¬ muted, it transmutes the second one similarly, and the second a third one, and so on.” A century later Albert of Saxony made the analogy: “One part being generated helps towards the generation of other parts, just as when one part of tow catches fire it sets fire to other parts.'"19 This approach was followed by Nifo in the sixteenth century, who never tired of pointing out that “Averroes held that growth, generation, and alteration take place by means of minima. . . . He held that there are maximum and minimum degrees of any natu¬ rally intensible form. . . . Averroes everywhere upheld minima naturalia.” Nifo wrote: “The agent can alter the first minimum part of the subject by one degree of quality, then by means of the first it will alter the second to one degree; while it alters the second to one degree, it will push the first up to two degrees; while it alters the third to one degree, it alters the first to three degrees and the second to two degrees.”20 Zabarella too spoke of particles being changed by degrees: If a mixt is to be generated which should belong by six degrees to the nature of earth and by two degrees to the nature of air, there must be a mutual action between the particles of earth and air. Hence air diminishes by two degrees the nature of earth ... so that six degrees remain; whilst earth being dominant subtracts six degrees from the nature of air, so that two degrees remain. . . . Hence the particles of both earth and air will become of the same nature, since each will be tinged by six degrees of the nature of earth and two of the nature of air; and each will be no longer earth or air, but something intermedi¬ ate such as gold. Thus in this way any part of the mixt is mixt. . . . The broken and damaged forms migrate into an intermediate state which is the form of gold.21 19. Roger Bacon, Communium naturalium 1 (Steele, fasc. 2, pp. 19—20); Albert of Saxony, Quaestiones in duos libros de generatione et corruptione 2.7 (Lokert, fol. 150c!). 20. Expositio super octo Aristotelis Stagiritae libros de physico auditu: Averrois . . . in eosdem libros proemium ac commentana (Venice, 1552), fols. gyv, ii2r, 2i3r. 21. Liber de mistione, De rebus naturalibus, pp. 423—4. Proportions were tradi¬ tionally expressed as parts of eight; see Aristotle, On the Soul 1 5, 410a. They had long been used in medical literature, but became popular in philosophy in the fourteenth century.

[94]

The Scientific Reinterpretation of Form

In addition to this quasi-arithmetical treatment of degrees of form, a geometrical understanding of form also made its contribu¬ tion to minimism. We have already seen in chapter 2 that this was a gap in Aristotelian form theory which had to be filled by recourse to Plato, and that one attempt to do this was made by Robert Grosseteste in his metaphysic of light. The schoolmen were also familiar with Plato’s theory that the tetrahedron, octahedron, ico¬ sahedron, and cube were the forms of fire, air, water, and earth in both the physical and the metaphysical sense, because they read of it in Aristotle’s critical presentation in On the Heavens.22 As hap¬ pened in the case of Plato’s Ideas and Democritus’ atomic theory, the Aristotelian setting of this geometrical account of the elements ensured for it an entry into the scholastic world view. The time was not yet ripe for the acceptance of geometrically shaped particles, but a general geometric approach to matter became part of the medieval tradition and contributed to the understanding of the form concept. Its first effect seems somewhat trivial. The imagination of read¬ ers was caught by the fact that fire not only has the sharp penetra¬ tion of its form, the tetrahedral pyramid, but its flame has a pyra¬ midal shape too; this led them to concentrate their attention on the pyramidal figure and to use it in their explanations. Grosseteste’s pupil, Roger Bacon, echoed his master’s words when he said that every force is “with respect to lines or angles or figures,” and he used the geometrical mode of action of light as a pattern for other forces, acting along the radii stretching from the agent to every point of the patient and composing an infinite number of pyra¬ mids:

I shall demonstrate a proposition in geometry in respect to the effi¬ cient cause. For every efficient cause acts by its own force which it produces on the matter subject to it, as the light of the sun produces its own force in the air. . . . This force is called species. . . . This spe¬ cies causes every action in the world. ... It is this [pyramidal] figure that Nature especially selects in every multiplication and action, and

22. Timaeus 53—7. This was not included in Calcidius’ Latin translation of the Timaeus, but it was mentioned in his commentary, chaps. 20-2, 326. However, the much more extended account in On the Heavens in 5, 7 was a more important source for the schoolmen.

Mixtion and Minima

[95]

not any pyramid at all, but that one whose base is on the surface of the agent and whose vertex falls on some point of the surface acted on. ... So that force comes from the whole agent to each point of the surface acted on.23

The application of geometrical categories, especially the pyra¬ midal figure, to the changes of forms and qualities was carried a stage further a century after Bacon by Nicole Oresme (1325—82) at Paris. Although Bacon suggested that all species or forces had a geometrical mode of action, he did not work this out for any except light. Oresme took as the subject of his geometrical method of form latitudes many different examples of the variations in intensity of forms and qualities: for instance, time and motion; heat; sound; magnetism; medical, biological, and psychological phenomena. He expressed the constant (e.g., the subject body) as the horizontal axis (longitude or extension) of a graph, and the variable (the varying intensity of a quality throughout the subject) as heights on the vertical axes (latitude or intension). The perimeter enclosing the base and the tops of all the verticals formed a figure that repre¬ sented the configuration or distribution of the varying quality. So far this method did not differ from the graphing of motions and speeds, for which it was mainly used. A rectangular configura¬ tion meant uniform intensity, a trapezium or triangle a “uniformly difform” or regularly changing intensity, and an irregular figure a “difformly difform" or irregular change. But Oresme went on to claim that the configuration corresponded to something in the subject, a sort of internal configuration, and that it was therefore possible to gain information about the nature of the subject, its qualities and actions, from the shape of the graph. As so often happened in medieval thought, symbol and reality tended to pass into each other, and it is not at all easy to be sure how objectively Oresme meant the internal configuration to be taken. On the one hand, he contrasted with a body’s “true” three-dimensional cor¬ poreity “another [corporeity] that is only imagined from the inten¬ sity of this quality taken an infinite number of times”; but on the

23. Opus majus iv 2. 1—3, trans. by Robert B. Burke (Philadelphia, 1928), pp. 130-1, 138. Bacon was writing of the “multiplication of species” or action of an agent on a patient, not of mixtion, but the former action differed in degree rather than in kind from the sort of change that took place in mixtion (see Aristotle, On the Soul hi 12) and formed part of the discussions concerning the roles of form and matter.

[96]

The Scientific Reinterpretation of Form

other hand, he spoke of the geometrical configurations of the forms and qualities as having a causal role and affecting the behav¬ ior of the subject: “In addition to the shape [figuratio] which these qualities possess from their subject, it is necessary that they be figured with a figuration which they possess from their inten¬ sity. . . . Furthermore, it is necessary that qualities of this sort have diverse powers and actions depending on the difference in figura¬ tions previously described.”24 In discussing the configurations of qualities, Oresme emphasized the pyramidal shape more than any other and even went so far as to speak of “pyramidal qualities.” He acknowledged the source of his inspiration by setting his discussion in the context of Aristotle’s arguments about geometrically shaped particles in On the Heavens hi

5: The Ancients, positing bodies to be composed of atoms, said that the atoms of fire were pyramidal in shape. . . . Bodies can penetrate more or less depending on the differences existing in the pyramids as a result of varying sharpness. . . . And since this is the case in regard to the shapes of bodies, it seems reasonable to speak in a conformable way concerning the previously described figurations of qualities. So, if there is a quality whose particles are proportional in intensity to small pyramids, it is accordingly more active . . . than another figure not so penetrating. Or, if there were two qualities and the particles of one were proportional to more acute pyramids than the particles of the other, the quality corresponding to the more acute pyramid would be more active.25

It is important to note that the primary connection between Oresme’s thought here and Aristotle’s is geometrical rather than corpuscular, in spite of his mention of particles. Like Roger Bacon, he was a minimist who argued against atomism; indeed, corpuscularianism seems to have played little part in his thinking. That his particles of quality were not material corpuscles of bodies is shown by his contrasting tin’s porous configuration in respect to heat absorption with its corporeal density, and wood’s corporeal 24. De configurationibus qualitatum et rnotuum 1.4, 24, trans. by Marshall Clagett, Nicole Oresme and the Medieval Geometry of Qualities and Motions (Madison, Wis., 1968), PP- *77> 233. 25. Ibid., p. 227.

Mixtion and Minima

[97]

porosity with its impermeability to heat. We must beware of seeing Oresme as a crypto-atomist in the light of this passage. In his opin¬ ion it was the forms and qualities rather than matter itself that possessed geometrical figuration, a point brought out by one of his followers: “It is to be noted that the proportion of form to form is the same as that of figure to figure, for since every form is to be imagined by some figure according as it is uniform or difform . . . it appears that the same proportion exists between two [form-] latitudes of any kind as between the two figures representative of them. ”26 Oresme’s contribution to the development of the form concept, then, is not so much that he was a precursor of the seventeenthcentury corpuscularians with their shaped particles, but that he encouraged a geometrical way of looking at forms and qualities and their changes. The words “form" and “figure" had always been closely connected, the latter implying the outward expression of the former; but now the form could be seen as having its own internal figuration as well as an external figure. Moreover, in place of the usual abstract discussion of intension and remission, Oresme approached the topic in a way that took account of the actual qualities of bodies and envisaged their intensity, distribution, and relation to the subject body in a geometrical manner. Even though this did not amount to a particle theory, it looked toward corpuscularianism for its fulfillment, and it can be seen as one of the factors that predisposed scholastic minimism to accept a geo¬ metrical approach to particle theory by suggesting that “every form is to be imagined by some figure." Oresme’s combination of form and figure found an echo in six¬ teenth-century minimism; there is no need to postulate any direct link, for which evidence is lacking, but the point I wish to make is that this was an association of ideas that could easily arise within the Peripatetic tradition. So we find that an emphasis on the geometry of form, whether drawn directly from Plato and Aristotle or indi¬ rectly through the association of ideas already familiarized by writ¬ ers such as Grosseteste, Bacon, and Oresme, began to make its contribution to sixteenth-century minimism. Eventually this ap-

26. De latitudinibus formarum secundum doctrinam magistri Nicolai Horem, pt. n, un¬ paginated edition of 1515, probably written in the mid-fourteenth century by Oresme’s pupil, Jacobus de Sancto Martino (Neapolitanus).

[98]

The Scientific Reinterpretation of Form

proach would produce a fully fledged theory of geometrical parti¬ cles, but it started from small beginnings. We First glimpse it in Nifo’s willingness to take account of shape as an aspect of form. He took his inspiration from some of Aristotle’s occasional reminders of the connection between shape and form, such as: “Of the bronze sphere or of the bronze cube both the bronze—i.e. the matter in which the form is—and the characteristic angle are parts”; “We describe the matter by saying that it is brass and the form by saying it is such and such a figure”; “The form [is] whatever we ought to call the shape present in the sensible thing.”27 Nifo translated this into particulate language: “The particle of a brass sphere and a brass cube is the same, for the matter is of the same kind; then it receives form, and the angle is also part of the form. ... If a brass cube be divided into brass and also into an angle, it is divided into matter and form, for the angle signifies the form.”28 With the geometrical aspect of form Nifo linked an idea that might superficially appear to come from atomism, but to which he gave a typically Aristotelian interpretation and setting. This was the notion of internal order or disposition, which had also been im¬ plicit in Oresme’s internal figuration and which would become important in the geometrical corpuscularianism of the seventeenth century. It had also occurred to Oresme’s contemporary, William of Ockham, who, from a different starting point, arrived at a sim¬ ilar link between the form and the internal disposition of bodies. His concern was not with the geometry of forms and qualities but with the nominalist requirement that particular things, not abstract universals, should be considered, and that extension and shape, as well as motion and change, should not be defined in distinction from permanent bodies; and this approach was capable of drawing the operations of matter and form closer together. Thus it was true that “the extension of matter depends on diversity of form; hence the same matter is more extended under the form of fire, less under the forms of air and water, less still under the form of earth,” but it was also true that “this condensation and rarefaction does not happen unless the parts of matter approach one another more or less closely by means of local motion alone”; similarly “figure and form are not really distinct from the natural thing,” for “a thing has first one shape and then another because of different 27. Metaphysics v 25, 1023b; vii 7, 8, 1033a,b. “Bronze” and “brass” both trans¬ late the Greek chalkos. 28. Expositiones in Aristotelis libras metaphysices (Venice, 1558), p. 333.

Mixtion and Minima

[99]

positions of the parts, which happens by means of local motion alone.”29 Ockham did not go so far as to interpret the form in terms of structure, but he helped to prepare for this to be possible. The idea of a regular arrangement of particles had received scant attention from either minimists or atomists. Aristotle re¬ corded the remark attributed to Leucippus and Democritus that “the differences [between atoms] are three—shape and order and position . . . for A differs from N in shape, AN from NA in order, and X from H in position.”30 This order, however, did not imply orderliness, a concept absent from atomism. To the notion of order and disposition suggested by Aristotle's quotation Nifo added Aris¬ totle’s own emphasis on orderliness and pattern, and he saw that it was relevant to minimism: “Disposition is said to be the order of that which has parts, either in place or potentiality or form. . . . Disposition does not occur in an indivisible thing, since it lacks parts; indeed, it lacks order, which must be understood in terms of parts . . . the disposition of the parts is to be understood in terms of the figure of the whole.”31 So the idea of disposition or arrange¬ ment was made to serve the Peripatetic belief that the form of the part was the form of the whole, and that the relation between part and whole was one of orderliness, which could be called the hall¬ mark of the form. External shape and orderly internal disposition of parts were both expressions of the form. Here we have the beginnings of a corpuscular reinterpretation of the form in terms of shape and structure, whose implications for matter theory and crystal studies would be recognized in the following century by Gassendi and Boyle. Since parts were disposed by their form in an ordered whole, it was clear that a body could not be defined in terms of the indi¬ vidual particle alone, as the atomists had tried to do. The relation of the part to the whole was fundamental to minimism, and it was based on the identity of form. In Aristotelian eyes, the lack of the concept of form was the gravest defect of atomism. Nifo grasped clearly that the real difference between minimism and atomism was not the more obvious question concerning the limits of divisibility, but rather the question of the form and its corollaries of specificity and the relation of the part to the whole. Nifo believed that atom29. Summulae in libros physicorum 1.19; 3.15—16 (Philosophia naturalis, pp. 24-5, 67-8). 30. Metaphysics 1 4, 985b. 31. Expositions . . . metaphysices, p. 328.

The Scientific Reinterpretation of Form

[ioo]

ism lacked a true concept of species because it lacked the concept of form, for a species is defined by its common form: Into water, earth, fire, and air, each of its own individual species, all compounds are divided according to form. But the elements are not divided into other things according to form; according to quantity they are divided into parts that are identical with respect to form. . . . [Empedocles and Aristotle] hold each element to be of a single spe¬ cies, but according to the atomists it is not so much a single species as a single size . . . for the atoms [of an element] are of one size rather than of one species.32

Minimists believed that the body and its minimum particles had the same form irrespective of their disparity of size, but for atom¬ ists who denied the form there was no such continuity between a body and its atoms. T he contrast was well brought out by Nifo’s comment, in the above passage, on Democritus’ comparison of atoms to the letters of which syllables and words were composed: “If the elements are divided, the parts are of the same nature, so that a part of water is water; whereas a part of a syllable is not a syllable . . . but a letter.” It was the whole, Nifo insisted, that alone gave meaning to the part—the finger as part of the hand, the semicircle as part of the circle, the minimum particle as part of the body. One aspect of corpuscular theory that had received little atten¬ tion in minimism, in contrast to atomism, was the motion of parti¬ cles. It was not until the sixteenth century that this dynamic aspect found a place in minimism, although the materials for it lay ready to hand in the Peripatetic tradition. Aristotle had classed all kinds of change as types of motion: locomotion was motion in respect of place; increase or decrease was motion in respect of quantity; al¬ teration was motion in respect of quality; generation or corruption was motion in respect of substance. The role of the form was less obvious in locomotion than in other sorts of change, but, as we saw in chapter 2, the schoolmen tried to define it in terms of a flowing form (forma fluens) or a flux of form (fluxus formae). The topics of generation and mixtion, too, were drawn into the debate as the result of the fondness of writers of all points of view for Averroes’ phrase that “motion is the generation of one part after another.” This phrase came to be used to represent the successive nature of substantial change in mixtion and generation. The discussion 32.

Ibid.,

p. 271.

Mixtion and Minima

[101]

about the extent to which change took place successively or in¬ stantaneously involved such Averroist views as the strengthening and weakening of elementary forms, stages or degrees in mixtion, and minimum parts. But it was left to Nifo to draw these threads together and to try to link the conceptions of motion and the suc¬ cessive generation of parts with the minimist interpretation of mix¬ tion as the successive interaction of minimum particles: By flux should be understood the reception by which the subject successively receives the form . . . and by the flowing form Averroes understands the form which is received by this successive recep¬ tion. . . . Flux is motion, and the flowing form which is its subject is also motion. . . . [Motions] involving the flowing form and the receiv¬ ing subject are sudden and take place by means of minima. . . . [Alteration and growth] concern the flowing form . . . and they take place by means of minima.33

Nifo’s connection of minimism with motion was only lightly touched upon and was couched in abstract and general terms with¬ out any application to the actual motions of particles. His contem¬ porary, Scaliger, carried it a stage further. He saw that the com¬ monly accepted definition of mixtion derived from Aristotle— “mixtion is the union of the altered miscibles” (mixtio est miscibilium alteratorum unio)—was no longer adequate in the light of increased understanding of the process. He proposed to substitute for it his own minimist definition of mixtion: “mixtion is the motion of the minimum bodies towards mutual contact so that union is achieved” (:mixtio est motus corporum minimorum ad mutuum contactum utfiat unio). Scaliger did not, of course, believe that contact alone sufficed for union; it was only the first step in mixtion and must be followed, as Zabarella later wrote, by “mutual alteration . . . and the production of the mixt by the eduction of forms; this is what is called union in the definition of mixtion."34 Scaliger was anxious that his defini¬ tion should not be understood in the light of the atomistic belief that union was no more than contact: Our corpuscles do not make contact with each other in the same way as the Epicurean atoms, but as a continous body, so that they make a unity. . . . Where there is one body, the ends of all its parts are one with each other, not only because of continuity . . . but also because of

33. Expositio . . . de physico, fols. g6v, 170V, 212V. 34. Liber primus de rnisti generatione et interim, De rebus naturalibus, cols. 547—8.

[102]

The Scientific Reinterpretation of Form

the act by whose force these parts become one. ... I say that the form is the act by which the parts, whose nature and aptitude make them capable of uniting, actually become one.35

Thus Scaliger combined with his exalted view of the form the Aristotelian conception of the form as act which enabled him to achieve a dynamic understanding of mixtion by envisaging the form as the act bringing the particles together into contact and then union. This was not Scaliger’s only contribution to minimism. An important new development was his use of minima to explain a far wider range of phenomena than mixtion and organic growth. Nearly all previous scholastic writers had confined themselves to these themes and had, moreover, usually discussed minimism in general philosophical terms without going into particulars. One of the few exceptions was John of Jandun, whose brief minimistic explanation of rarefaction and condensation may have suggested to Scaliger the possibility of further work along the same lines. It may be asked whether Scaliger borrowed from Lucretius’ atomistic explanations of natural phenomena. The answer must be that he did not, for not only was Scaliger’s particle theory unmistakably minimistic, but there was no resemblance at ail between his exam¬ ples and Lucretius’. The phenomena explained by Lucretius con¬ cerned solidity and liquidity, porosity, transparency, taste, and magnetism. Scaliger had a totally different list: rarefaction and condensation; fineness and coarseness; the difference between ice, hail, snow, and water, and between niter and saltpeter; heat phe¬ nomena such as combustion; the explosiveness of gunpowder; crystallization; water drops; and shadows.36 These were explained by the sizes, not the shapes, of particles, and sometimes their closeness together; Lucretius’ explanations were in terms of atomic shapes. Following some schoolmen, includ¬ ing William of Ockham, Scaliger proposed that rarefaction and condensation were caused by the “disposition of the parts by spatial motion,” and perhaps (his language was ambiguous here) also by a change in the size of minima as John of Jandun had suggested. He

35. Exotericarum exercitationum liber XV, ex. 101, pp. 143—4. The definition of mixtion occurs in the same passage. 36. Ibid., pp. 4, 20, 25, 27-8, 33, 35-6, 131, 164, 167, 181, 356. Contrast Lu¬ cretius, De rerum natura 11 102, 388—470; iv 623-6, 648—58; vi 1084-9.

Mixtion and Minima

[103]

held that combustion, brightness of burning, and explosiveness resulted from the minima being pressed together, but ease of com¬ bustion also depended on particle size: “Why does earth receive the form of fire so slowly? Is it because the minimum of earth is a hundred times bigger than the minimum of fire, so that it needs a hundred minima of fire [to ignite it]?’’37 These minimistic explanations were firmly rooted in Aristotelian doctrine and owed nothing to atomism; they were accompanied by arguments against the atomists. But one cannot help noticing that they introduced into minimism some notions that seemed likely to modify it in the direction of atomism. The emphasis on the sizes and motions of the particles tended to suggest that minima had a certain independent and perhaps permanent existence rather than existing temporarily and then merging back into the continuum. We see this clearly in the writings of Scaliger’s French contempo¬ rary, Jean Fernel, a minimist whose arguments against atomism were meant to be “cudgels to drive that turbulent concourse of atoms . . . into exile, out of Nature, and out of the world,” and who used to “laugh at the ancient atoms and marvel how anyone could persuade himself of them.”38 Yet his minimist account of mixtion, faithful as it was to Avicenna’s version of mixtion theory, seemed, like Scaliger’s, to point to a more permanent particle: The elements . . . divide themselves into tiny but not minimum por¬ tions and arrange themselves in order so that at length each one coheres more deeply to one of a different sort. ... In this generated simple body, tiny portions of the elements remain; they subsist whole by their forms, yet they are not free . . . but bound and as it were held fast by the battle of their qualities and the presence of an even nobler form. Hence their original and innate forces cannot be exerted . . . but exist only potentially. . . . The form [of the mixt] is every¬ where identical so that . . . the particles which consist of the tiny por¬ tions of the elements disappear from view.39

The same permanent and independent existence seemed to be required by Scaliger’s minimistic physical explanations, which had previously been the preserve of atomism or of Peripatetic nonpar37. Exotericarum exercitationum liber XV, pp. 25—6, 33. 38. Physiologia 11 4, p. 53; preface to De abditis rerum causis, p. 62. In the latter passage he admitted, however, that “Democritus might laugh even more loudly at what we believe about the elements.” 39. Physiologia 11 8, p. 58.

[104]

The Scientif ic Reinterpretation of Form

ticulate explanations. Scaliger never explicitly admitted this, but we can see it as the start of a trend that would bring minimism and atomism closer together. A similar trend can be discerned in the work of Scaliger’s and Fernefs contemporary, the physician Girolamo Fracastoro (1483— 1553), who was one of the first modem writers to make use of atomistic explanations. However, his use of atomism was very slight; it was confined to explaining magnetism by Lucretius’ atom¬ ic effluvia, and it was accompanied by the Peripatetic definitions of magnetism as a “simple form” and as a “spiritual species like light.” His other explanations showed a similar mingling of particles and forms. To explain the absorbence of sponges he spoke of water and air particles entering and leaving pores in a way that owed as much to Aristotle in Meteorology iv as to Lucretius, and at the same time he suggested that it could be explained in terms of mutual attrac¬ tion by “the form with all its virtues.” When considering mixtion, he used the conventional minimistic mixtion theory, but with a suggestion of permanency for particles: “[In mixtion] the parts have the least possible distance between them, especially if it hap¬ pens that they become continuous with one another; but if this does not happen because the forms are not one, yet the parts will wish and seek to be as close and as well united as possible.”40 Here too he used the mechanism of pores and also the mutual attraction of like forms. Except when recounting Lucretian theory, he always used the language of minimism. Like Scaliger and Fernel, Fra¬ castoro occupied a basically Aristotelian position but he was moving in the direction of electicism, and he moved further than they did. Nevertheless, he insisted that “it must be granted that form exists throughout the whole of Nature.”41 In the mid-sixteenth century, then, minimism began to develop beyond the limited scope envisaged for it by Aristotle and the schoolmen and to occupy a more independent position within Peri¬ patetic physics. It had benefited from various insights that had arisen within scholasticism and that had been able to throw light on 40. De sympathia et antipathia rerum (Leiden, 1550), p. 100. See also pp. 41—57, 68— 9, 75 (magnetism); 83-90 (porosity); 84-91, 98-100, 104 (mixtion); 56 (form). Fracastoro is well known for his mention of seeds of disease (seminaria morbis) in De contagione (Leiden, 1550), a work which also contains minimism and form theory. It is often assumed that these seeds were copied from Lucretius’ disease seeds (De rerum natura vi 679, 825-9, K)75~7)’ although Fracastoro did not use Lucretius’ word semina, and the notion was not unknown elsewhere. 41. De sympathia et antipathia rerum, p. 56.

Mixtion and Minima

[105]

the process of mixtion and the relation between matter and form. But while these developments were preparing minimism for a more important role in natural philosophy and were making possi¬ ble a convergence of minimism and atomism, the concepts and language of minimism still testified to its continuing close connec¬ tion with the form theory of mixtion. It was essentially a part of Aristotelian philosophy, from which it drew its basic assumptions and to which it made its contribution. The form theory of mixtion, its original matrix, was still the context within which it was chiefly to be understood and would be the source of much that was of value in seventeenth-century corpuscularianism.

CHAPTER

FOUR

Minima and Atoms: The Corpuscular Reinterpretation of Form I will use great Plato’s shield and Empedocles’ sword, which I found rusty in Democritus’ well. Etienne de Clave, Paradoxes Our age has brought to light three kinds of philosophizing. Some are addicted to a certain author, by whose words they are bound as by an adamantine chain . . . such are the Peripatetics ... or those who admire Paracelsus. . . . Others are the champions of intellectual freedom and weigh the reasonings of all . . . such are Basso, Paracelsus . . . many of the chemists . . . Kepler, Ga¬ lileo. . . . The third sort of philosophers . . . Copernicus . . . Marsilio Ficino . . . and ourselves . . . adore one sole truth. Jean Magnenus, Democritus reviviscens

result of the sixteenth-century development of minimism was not that it began to borrow from atomism, but that the new atomists of the early'seventeenth century, who were turn¬ ing toward Democritus in an attempt to escape from scholasticism, began to borrow from minimism. Andreas van Melsen points out that “it is not correct to attribute ideas such as those of van Goorle . . . exclusively to his atomism, for those ideas can already be found in earlier supporters of the minima theory. . . . Van Goorle took over Scaliger’s elaboration of the minima theory without its philo¬ sophical background.”1 Thus the atomist David van Goorle ex¬ plained evaporation and condensation in terms of receding and approaching particles, as Scaliger had done; and Sebastian Basso he first

i. Andreas van Melsen, From Atomos to Atom (New York, i960), p. 90. [106]

Minima and Atoms

[107]

explained tastes not by Lucretius’ sharp atoms pricking the tongue but by the Aristotelian notion of the tongue’s humidity attracting the substance of fire bound by humidity.2 If early seventeenth-century atomists were content to borrow from minimism in a physical context, they were wholly indebted to minimism in a chemical context. In atomism there was nothing corresponding to mixtion theory. A fact that cannot be emphasized too much, and that is often ignored by historians, is that minimism usually arose in the context of mixtion, whereas atomism, whether classical or seventeenth-century, was never related to that context but always to a physical context. Minimism was indeed sometimes used for physical explanations, as it was by John of Jandun and Scaliger, but it was in the domain of mixtion theory that it really came into its own; in fact it had the monopoly of particulate chem¬ ical explanations. There were several reasons for this. First, the precedent of Aristotle’s and the schoolmen’s use of particles in mixtion counted for a good deal, and the sixteenth-century devel¬ opment of minimism increased its effectiveness. Then the Paracelsian chemists were largely untouched by corpuscular thinking, so the field was wide open here. Finally, on the subject of mixtion atomism was at its weakest. Democritus and Epicurus gave no rea¬ son for combination except the cohesion of atoms by contact alone; Lucretius’ ingenious explanations were confined to physical properties. So for these reasons minimism was unchallenged in the early seventeenth century in its role of providing a particulate explana¬ tion of mixtion. Lacking a precedent for an atomic theory of mix¬ tion in the doctrines of Democritus, Epicurus, and Lucretius, even self-confessed atomists left their atomism and turned to minimism as soon as they were confronted with a chemical question. Mini¬ mism was the only corpuscular explanation of mixtion that was available to them, and Aristotelians and atomists alike, with the occasional chemist, took advantage of it without hesitation. We will briefly consider a few examples of this. An opponent of scholasticism such as Basso considered himself duty bound to offer objections to minimism. But his refutation scarcely progressed beyond bare denials of certain scholastic posi¬ tions and did not replace them by a genuine atomistic understand-

2. David van Goorle (Gorlaeus), Exercitationes philosophicae (Leiden, 1620), pp. 248—9; Sebastian Basso, Philosophiae naturalis adversus Aristotelem libri XII (Geneva, 1621), p. 107.

[io8]

The Scientific Reinterpretation of Form

ing of mixtion. Just as Basso’s opposition to Scaliger did not stop him from borrowing the latter’s physical explanations, and his ar¬ guments against the substantial form did not stand in the way of his own form theory, so his arguments against minimism did not hinder his use of it and even elaboration of it to explain mixtion. We will look later at the important insights he gained from mini¬ mism; at present it suffices to note that his corpuscles, which he described in the traditional way not as atoms but as subtle mini¬ mum parts and particles, took nothing from atomism except their inability to suffer substantial change. He made no attempt to bring into his treatment of mixtion the essential atomistic doctrines of shaped and indivisible atoms moving in a void. Basso was interested in chemical phenomena without being a Paracelsian chemist. Although few chemists in the early seven¬ teenth century took any interest in particle theory, corpuscularian chemists were not altogether unknown. The most important was Anselm Boetius de Boot, a minimist whose position was similar to that of Scaliger. Division into subtle minimum parts followed by merging into union was his explanation not only for mixtion but also for physical properties such as transparency; he occasionally spoke of atoms (sometimes in the popular sense of dust motes) but his usual words were “parts,” “particles,” “corpuscles,” and “mini¬ ma.” De Boot published his Gevimarum et lapidum historia in 1609. It is significant, and it illustrates the atomists’ dilemma, that when Jean Bachou translated the book into French a generation later (Le parfaict joaillier ou histoire des pierreries, 1644) and wanted to bring it up to date, he used the word “atom” throughout but left the minimist doctrine unchanged. There was still no atomistic theory of mixtion available for him to use. The chemist Etienne de Clave combined an antischolastic Democritan atomism like Basso’s with de Boot’s chemical doctrine. He was one of the three supporters of the anti-Aristotelian theses that were condemned at Paris in 1624, °f which thesis 12 defended atomism.3 Yet in his Paradoxes he found no place for atomism in the context of mineral chemistry; for this purpose he had no alter¬ native to minimism. Like Basso, he found it necessary to retain the concept of form; his minima or parts (he did not use the word “atom”) were susceptible of alteration and were characterized only 3. Omnia esse in omnibus et omnia componi ex atomis seu indivisibilibus. Thesis 2 opposed the substantial form, yet this too appeared in de Clave's system. See Lynn Thorndike, “Censorship by the Sorbonne of Science and Superstition in the First Half of the Seventeenth Century,” journal of the History of Ideas 16 (1955): 120—2.

Minima and Atoms

[109]

by smallness, subtlety, and chemical activity. De Clave gave the Aristotelian definition of mixtion as “the union of the elements diversely altered with one another,” and a passage typical of many in his book shows how he blended form theory, minimism, and chemical doctrines: “The spirit, joining with earth by minimum parts, attenuates, agitates and ferments it in such a way that it engenders a more precious stone according to the specific form which it has received by its mixtion.”4 De Clave did not use this language for love of Aristotle, but because it was the only cor¬ puscular language available for chemical use. Like Basso, he was an involuntary witness to the fact that the Democritan atomists of the early seventeenth century turned naturally to minimism and not to atomism for their particle theory of mixtion. However, in the early seventeenth century a few writers were starting to extend atomism; Isaac Beeckman, followed by Rene Descartes, used Lucretius's physical explanations, and Pierre Gas¬ sendi adopted Epicurean atomism. Did these more developed ver¬ sions of atomism embrace chemistry? Leaving aside until later the Cartesian particle theory, which was not strictly atomism, we find that Lucretius and Epicurus did not help Beeckman and Gassendi to achieve a chemical atomism. Isaac Beeckman, a significant figure because of his strong influence on Descartes and Gassendi, was one of the earliest adherents of the revived atomism, which he began to discuss in his journal for 1613; and it seems that the initial stimulus to his interest in atomism was Lucretius' De rerum natura. However, his support for atomism coexisted with a use of minimism, which was reflected in his phraseology. In chemical or biological contexts, the traditional matrix of minimism, he used minimistic terms, and in the context of matter theory and physical explanations he used the language of minima when following Aristotle's or Scaligef s views and the language of atoms when following Lucretius.5 Like Basso, he adopted some of Scaliger's physical explanations, and his frequent use of mechanisms involving pores owed as much to Aris¬ totle's Meteorology as to Lucretius. We shall see later how presup¬ positions about minima and the form modified his atomism; here we merely note that he turned to minimism for all his chemical and some of his physical explanations. 4. Paradoxes, pp. 385, 271. 5. References to Beeckman's journal are to Journal tenu par Isaac Beeckman de 1604 & I&34, ed. Cornells de Waard (The Hague, 1939). Beeckman used the mini¬ mistic words particulae, partes, minima, corpuscula, minutiae, homogenea nearly three times as often as atomi and Lucretius’ word primordia.

[i io]

The Scientific Reinterpretation of Form

Gassendi’s elaborate Epicurean system represented the peak of seventeenth-century atomism in the strict sense of the word, as opposed to the eclectic systems of Descartes, Boyle, and others; but even he was not capable of applying atomism to chemistry. The contrast is striking between his account of matter theory in terms of Epicurean atomism and his treatment of the chemical elements or principles where, apart from the minimist statement that “salt can¬ not take part in mixtion unless divided into very tenuous particles,” he relinquished particulate language and admitted: “I am silent about what can be added concerning the resolution of the five [chemical] principles into their seeds and afterwards into atoms.”6 His section on mixtion was not only named “On Generation and Corruption,” but also largely consisted of Aristotelian arguments about form and the elements. In his treatment of minerals, too, he mentioned corpuscles (not usually atoms) in a physical but not in a chemical context. There was an especially marked contrast in his account of gold between his explanation of its physical properties in terms of Lucretius’ hooked atoms and of its chemical properties by means of the Aristotelian exhalations and the chemists’ princi¬ ples and seminal forces. Gassendi was aware that it ought to be possible to say something of a particulate nature about mixtion. For his mineral chemistry he was heavily dependent upon de Clave’s Paradoxes, and he would have liked to transfer to chemical seeds and their atoms the properties and actions that de Clave had allot¬ ted to seeds and spirits. Copying de Clave’s language about reac¬ tion mechanisms, he conceded: “I omit, like Epicurus, what might be said about the [metallic] principle, whether the seed is always made from the same atoms, which in a definite way make their own proper configurations, textures, and structure, and afterwards penetrate matter by means of their own innate mobility; they digest it and transpose it, i.e. disposing its atoms in a definite way so that it is formed into such a species of metal.”7 The materials were here for a chemical corpuscularianism, but Gassendi was not in a posi¬ tion to achieve the desired result. The atomists who used minimism for chemical explanations

6. Syntagma philosophicum, De opinionibus statuentium materiam affectam . . . qualitatibus secundis, Opera omnia, vol. i, pp. 244, 245. 7. Ibid., De metallis ac eorum transmutatione, vol. 11, p. 141 (compare de Clave’s Paradoxes, pp. 225, 384—5). The section on mixtion, De generatione et corruptione rerum, interrupts the Aristotelian account only once to say that “the con¬ crete is firstly and directly from atoms . . . the atoms entangle one another by the force ... of motion and their little hooks and handles” (vol. 1, pp. 474—5).

Minima and Atoms

[111]

while using atomism in a physical context could not keep these two systems in wholly watertight compartments, and the result was bound to be an eclectic particle theory with features of both atom¬ ism and minimism that could deal with both chemistry and physics and that could incorporate the form concept and interpret it in corpuscular terms. However, not all writers moved in this direc¬ tion, although the majority did. A physicist such as Galileo was satisfied with straighforward atomism because he did not concern himself with chemical questions, and many chemists seem to have been untouched by particle theories of any kind. It is in the writ¬ ings of those with a foot in both camps—Sennert, Basso, Beeckman, Descartes, and Boyle, for instance—that we find the mutual interaction of atomism and minimism which led to their final amal¬ gamation. It was facilitated by the common seventeenth-century tendency toward eclecticism, so that there seemed nothing strange in the combination of ideas from different and even opposed back¬ grounds. An accommodating outlook was favored not only by the widespread acceptance of Scaliger’s physical explanations as well as of minimistic mixtion theory, but also by Scaliger's trend toward assuming a more independent and permanent minimum particle. Another factor was the universal familiarity with Aristotle’s writ¬ ings, where Democritan atomism was described and was read through Aristotelian spectacles against an Aristotelian background that included minimism. The way was open for minimism to ac¬ quire more definite particles and greater precision from atomism, and for atomism to enrich itself by assimilating the concept of form with its associated notions of pattern and order. The amalgamation of atomism and minimism could not proceed without a certain disregard or blurring of their philosophical back¬ grounds. To allow for this, as Melsen does in the case of van Goorle, who “took over Scaliger’s . . . minima theory without its philosophical background [and] replaced the latter by another one,’’ has more to be said for it than Hooykaas's contention that “scientists themselves, without the help of philosophy, taught by physical and chemical experience, developed a corpuscular theo¬ ry.”8 Eclecticism was incompatible with strict philosophical con¬ sistency and would have been spurned by the rigorous scholastic thinkers. But the seventeenth-century eclectics were more con-

8. Melsen, From Atomos to Atom, p. 90; Reije Hooykaas, “The Experimental Origin of Chemical Atomic and Molecular Theory before Boyle,” Chymia 2 (1949):65~6-

[112]

The Scientific Reinterpretation of Form

cerned with the use of particle theories than with philosophical orthodoxy, and although they were aware of the different back¬ grounds of minimism and atomism, they were content to overlook inconvenient distinctions. This is exemplified by a blurring of lin¬ guistic differences; whereas de Boot, Beeckman, Basso, and de Clave earlier in the century usually avoided speaking of atoms in a minimist context, it soon became increasingly common to treat the words “atom,” “particle,” “minimum,” and so on as synonyms. Thus Digby, a minimist who was accepted in atomistic circles, wrote: “By which word Atome, nobody will imagine we intend to express a perfect indivisible, but only the least sort of natural bodies. . . . Aristotle expressly teaches that mixtion ... is done per minima, that is in our language and in one word, by atomes; and signifyeth that all the qualities . . . are made by the mingling of the least parts or atomes of the said Elements.”9 Similarly Sennert, likewise an eclectic minimist, slurred over the divergences between the two systems in a way that would have angered Scaliger, whose support he was claiming: “Without doubt, what we have proposed [minimism] is the opinion on mixtion of the most ancient philoso¬ phers, and amongst them Democritus, who constituted all things from atoms. . . . Doubtless Scaliger meant the same thing. . . . Yet natural things are not made by a fortuitous concourse of atoms (if indeed Democritus really did believe this) . . . but by the direction of a superior form.”10 The Dutch scientist Isaac Beeckman (1588—1637), a man of very wide interests, was one of the earliest eclectic corpuscularians and was also one of the most fertile in new insights, many of which were adopted by other writers, and which represented the mutual modi¬ fications of atomism and minimism. For instance, whereas the an¬ cient atomists postulated a very large or even infinite number of different types of atoms, Beeckman seems to have been the first modern to adopt Plato’s notion that there need be only four kinds of atoms corresponding to the four elements.11 But these funda¬ mental, unchangeable units of matter were not, he decided, the basic units of chemical and biological change; as early as 1613—14 9. Two Treatises (London, 1644), pp. 425 and 48. On Digby’s relations with the atomists, see Robert Kargon, Atomism in England from Hariot to Newton (Oxford, 1966), pp. 70-3. 10. Tractatus, Opera omnia, vol. in, p. 799. 11. Journal, vol. i, p. 153; vol. iii, p. 138. William of Conches held this view in the twelfth century; see his Glosae super Platonem, ed. Edouard Jeauneau (Paris, 1965), pp. 129-30.

Minima and Atoms

[113]

he asserted that “silver is not broken up into its atoms (primordia) by nitric acid.”12 Combining this belief with his acceptance of minima as chemical particles, Beeckman drew the important inference that minima, the units of chemical change, must be compound particles formed of stable groups of small numbers of atoms: “The union of four or five atoms constitutes such a minimum substance . . . the minimum particle. . . . The minimum particle of fire is composed of many atoms of fire joined together. . . . The minimum of earth seems to consist of two or three or at any rate far fewer [than fire]. . . . One minimum can be divided into others and these again into others, down to the humours, elements, and atoms.”13 At a single step this bold idea unified atomism and minimism, while retaining for both atoms and minima their traditional ex¬ planatory contexts in physical matter theory and chemistry, respec¬ tively, and it became one of the universally accepted foundations of eclectic chemical corpuscularianism; whether derivatively or inde¬ pendently, it was put forward by Basso and Sennert, and was then adopted by others after them. Epicurus and Lucretius had postu¬ lated aggregates of atoms, although these were, according to Cyril Bailey, “endowed with no special characteristics or powers, nor constituted by any particular atomic formation.”14 The new com¬ pound minima, with their context of mixtion, owed as much if not more to scholastic beliefs about degrees of mixtion, hierarchies of matter and form, and decomposition down to a partly formed level above prime matter. Such an amalgamation of the two systems called into question what place could be found in it for the form concept. Some of Beeckman’s contemporaries, like Basso, were attracted to the Pla¬ tonic universal form, but Beeckman considered it unworthy of a philosopher; he preferred to emphasize the involvement of form with matter. Although the concept of form did not play a large part in Beeckman’s thinking, his thoughts about its nature and function developed some tendencies that were already present within scho¬ lasticism and that could be linked to atomic theory. He held that “even if everything is bodies and space, yet these are distinguished by us on account of their varied dispositions. . . . The form is the 12. Journal, vol. 1, p. 24. 13. Ibid., vol. 1, p. 280; vol. 11, pp. 96-7, 117-18. See also vol. 1, pp. 133-4, 216, 278; vol. 11, pp. 74, 92. 14. The Greek Atomists and Epicurus (Oxford, 1921), p. 578; see also pp. 342-8,

579-

[114]

The Scientific Reinterpretation of Form

disposition of the particles.”15 This view was close to Nifo’s, for Beeckman held that the atomic dispositions were not random but followed a God-given order: We believe that the concourse of atoms is not fortuitous, since they were made by God. For once all things were legitimately disposed at the beginning of creation . . . the atoms had to be congregated in no other than the right manner ... so that they cannot concur otherwise than well. . . . The atoms are not hindered by anything from follow¬ ing a certain disposition. . . . Indeed, a definite number of forms prescribes definite compounds.16

Thus for Beeckman, as for Nifo, the significance of the form with respect to particles was that it bestowed orderliness so that the dispositions were “the right manner.” Beeckman’s interpretation of form as disposition was expressed in a similar way to Oresme’s method of form latitudes. He wrote that a thing’s “base is not abstract, but its matter is the body; howev¬ er, the form is the figure by which it is called a base. Yet if from the body is abstracted the figure of the base, the matter will be solid, surfaces and lines, but the form will be as it were their combination (3°]

The Scientific Reinterpretation of Form

and the shapes of salts and acids were used to explain their physical rather than their chemical properties. But in Principia philosophiae (1644) Descartes introduced a new criterion, giving particle shape a chemical significance:

The particles of the third element can be reduced into three principal types. The first includes all those which have very awkward shapes . . . like the branches of trees. . . . The second sort includes all those whose shape makes them more massive and solid . . . like uncut stones. . . . The third sort includes all those that are long and thin like reeds and sticks. . . . The particles with plain smooth shapes . . . com¬ pose mercury. . . . The particles of salt are like little sticks. . . . The particles . . . divided into flexible branches . . . compose sulfur. . . . Thus I have here explained three sorts of bodies, which seem to me to be closely related to those that the Chemists are accustomed to take as their three principles and which they call salt, sulfur, and mercury.8

Descartes’s particle shapes have often been deemed arbitrary. But I suggest they were inspired by the important land drainage schemes that he saw in Holland, in which a framework of sticks filled in with interlacing branches was laid down and covered with stones to create an artificial terra firma—a technique employed since classical times (it was described by Vitruvius) and still in use today. It may well have suggested to Descartes that the natural creation of terra firma took place from particles shaped like sticks, branches, and stones. How did Descartes utilize his system of figured particles? In all his writings, their chief use was to differentiate between the ele¬ ments or principles. Their second use, derived from Lucretius, was to explain the physical properties of bodies. Their third use was to explain heat phenomena by particles entering and leaving pores; the dependence of this mechanism on Aristotle’s Meteorology iv is shown by the fact that Descartes, like other writers such as Boyle and Becher, copied Aristotle’s examples and explanations. Fourth, they were used to explain the relationships of acidic, sulfurous, and saline minerals, by postulating changes of shape resulting from passage through pores in the earth. For instance, salt particles might be “so pressed and agitated that they become flat . . . cutting and pointed,” thus forming acids, or they might “lose the shape of common salt and take that of saltpeter, sal ammoniac, or some 8. Principia philosophiae iv 33, 58, 61—3.

Atoms and Crystals

[131]

other kind of salt”; and sulfur particles might be “split up into many separate branches . . . attached to [earth] particles,” forming bitumens and oils.9 The final use of figured particles could be to explain mixtion, but this was less common than appears at first sight. The entry of particles into the pores of the earth or of saltpeter particles into the pores of carbon really explained the hardness of minerals and the explosiveness of gunpowder rather than the chemical processes involved. Unlike his mentor, Isaac Beeckman, whose main chem¬ ical mechanism was points and pores, Descartes preferred to en¬ visage mixtion in terms of the entanglement of branched parti¬ cles.10 But since he also made the branched shape specific to sulfur, this might seem to overrate the importance of sulfur in mixtion. Perhaps this was why the Cartesian chemists did not favor this mechanism, or perhaps because it was torn from its original Lucretian context of explaining hardness and thus was not supported by precedent, for, as we have seen, precedent and the correct context counted for a great deal in the seventeenth-century use of explana¬ tory concepts. Perhaps, as we shall suggest later, it was because it corresponded to nothing in the traditional form or nature of active chemical substances, a consideration to which most contemporary writers attached much more importance than Descartes did. Be that as it may, most Cartesian and other chemists abandoned the branched particle and, like Beeckman, preferred to explain mix¬ tion by pointed acid or salt particles fitting into pores. It remains to say something of Descartes’s accounts of crystalliza¬ tion. In Les Meteores, discours 3 (Du sel) and discours 6 (De la neige, etc.), he aimed to explain in purely mechanical terms the formation of common salt crystals and snowflakes, respectively. He did not explain snow crystals in particulate or structural terms but as the result of meteorological conditions and mutual contact, and his interest in the geometry of snowflakes was limited to pointing out the mathematical necessity of one sphere’s being surrounded by six others in a plane—an argument that met with criticism from Gas¬ sendi and Dortous de Mairan, as we saw in chapter 1. Salt crystalli¬ zation, however, he explained differently, in terms of the rodlike salt particles that he himself invented. The little rods took up posi¬ tions parallel to one another, or at right angles, to form a square raft floating on the water; subsequent layers piled up, forming a 9. Ibid., 61, 69, 62. 10. Ibid., 71, 112—15 (pores); 62—3, 72, 76, 93, 109 (branches).

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# #1 S & 259- 269; center of, 185, 187, 191, 193, 201—6, 217, 221; chemists’ prin¬ ciple of, log, 151, 177, 179, 184, 211, 21 g; Descartes’s principle of, 129, 131; eighteenth-century element of, 228—32, 2350; as material cause of minerals, 23—4, 28, 41, 209, 211—2; as matrix, 187, 189, 203—6, 239, 262; virgin, 219, 229 Eclecticism: in chemistry, 119, 173—4, 182, 194, 219; in form theory, 39, 64-5, 69, 118—9, j56- 174; in mineral theory, 28—9; in particle theory, 72, 88—9, 104—5, 110— 53, 220; in Platonism, 156—62, 164—5, 171, 176-7 Efficient cause, 22-g, 36-9, 54, 62, 185 Effluvia, 104, 115, 170, 183, 193, 207, 221 Electricity, 170, 183 Elementary forms: intensible and remissible, 79—81, 101; in matter theory, 51, 58—9, 161; in mixtion, 55, 79—85, 91, 103, 184 Elements: in chemistry, 174, 182, 200-1, 204, 267, 269—70; in eighteenth century, 197, 225, 228, 235n, 269; as matter and form, 23, 26, 3g, 100, 182; and mixtion, 64, 103, 109, 115; and particles, 112, 120, 255; in Platonism, 40, 42, 94, 112, 159— 61; and tria prima, 120—1, 182, 200, 228 Eller, J„ 225, 249 Empedocles, 49, 106, 140, 168 Entelechy, 71, 174, 194 Epicurus, 88, 101, 107, 109-10, 113, 116, 136, 160 Ercker, Lazarus, 28 Ether, 40, 57, 166, 187, 2650 Euclid, 89. 264 Exhalations: Aristotelian, 23, 110, 129, 191, 206, 209; chemical, 135, 179, 184, 186, 191 Extension, 51, g8, 128

[314] Fathers of the Church (patristic writers), 50, 53- 157> J99 Ferment, 142, 181, 187, 190, 195, 217, 2i8n Fernel, Jean: and form, 57—8, 61, 121, 173, 194—5, 200; and particles, 103, 140 Ficino, Marsilio, 65, 106, 162, 164-6, 170, 172, 179, 194 Final cause, 22, 59, 171 Fixed air, 227, 229, 2350. See also Carbon dioxide Fludd, Robert, 175, 199 Form, 19-20; accidental, 54, 58, 68, 75, 81, 173; as act, 54, 58, 67-9, 71, 75, 102, 117, 162; corporeal or material, 51-2, 82; de¬ grees of, 92-3, 113; elementary (see Ele¬ mentary forms); exalted (scholastic) view of, 54, 57—9, 167; exalted (sixteenth- and seventeenth-century) view of, 57-8, 62—5, 73, 102, 118, 173, 180, 194; as exemplar, 157, 159-62, 165, 170, 176; first, 51, 161; geometrical, 50-2, 94-8, 114, 135, 159— 60; hierarchy of, 59, 68—9, 71, 82, 113, 117; intension and remission of, 79-81, 92, 101; latent, 55, 59, 81, 158; as law, 66-70; low (scholastic) view of, 58-9, 167; low (sixteenth- and seventeenth-century) view of, 59-63, 66, 72, 75, 128, 173; of mixt, 79—85, 91, 103, 184. See also Specific form; Substantial form; Universal form Forma fluens and fluxus formae, 56, 100—1, H7

Formal cause, 54, 59, 62, 82, 128, 144—5, 171; of crystals, 30, 34, 36-40, 42, 45-6; of minerals, 22-9, 138, 173, 181, 187, 214 Form latitudes, 95-7, 114 Form theory: chemical, 172—232; corpuscularian, 106-53; crystallographic, 258-87; Hermetic, 163—8; of minerals and crystals, 22-47, 77-8, 135-9. 142-7, 233-43, 253—4; minimistic, 85—105; of mixtion, 76—85; of Platonists and Neoplatonists, 65, 155-63, 168-71; reconcilia¬ tion of Aristotelian and Platonic, 50—1, 53, 156, 160—2, 165, 174, 176 (see also Specific form); scholastic, 50-g, 79-105; seventeenth-century, 59—75. See also Aris¬ totle; Plato Fracastoro, Girolamo, 104 Freind, John, 254n Gahn, Johan, 272, 278 Galenism, 58, 172—3, 177, 180 Galileo, 72, 106, 111, 128—g Gallitzin, D. de, 248 Gas, 172, 181, 184, 195, 217 Gassendi, Pierre, 38, 42-3, 46-7, 183, 248; and chemistry, 109, 125; and form, 60—1, 135—6; and mineral seeds, 47, 138—9, 142, 196, 206; and particles in crystals, 43’ 135~9> 144-6, 254, 259, 261 Gaudin, M. A., 253 Geber, 27, 177

Index Gems, 21, 30—1, 185, 205; as earth princi¬ ple, 224, 230; and salt, 212-3, 242> shapes of, 30—2, 39—40, 43—5, 47, 136, 236, 260 Geoffroy, E., 225, 249 Geoffroy St. Hilaire, Etienne, 283n Geoffroy St. Hilaire, Isidore, 239 Gesner, Conrad, 32, 259, 274 Gilbert, William, 65, 133, 168—70, 172, 183 Giles of Rome, 83, 89 Giver of forms, 57-8, 6in, 161, 164, 168, 174 Glauber, Johann, 191-2, 197, 200, 205, 207, 2i7n, 229 Goniometer, 274 Goorle, David van, 106, 111 Greville, Charles, 248n Grew, Nehemiah, 45-6, 146-7, 213, 248, 274 Grignon, Pierre, 249, 253-4 Gronovius, 243-4 Grosseteste, Robert, 50-1, 53, 94, 97, 154, 161 Gulielmini, Domenico, 192, 226, 248, 253, 261, 264-8, 273-4 Gur, 191, 217-8 Guyton de Morveau, Louis, 227, 235, 249

Hall, J., 249 Hartman, George, 181 Hartsoeker, Nicholas, 1480 Haiiy, Rene-Just, 244, 248, 252; and chem¬ istry, 226, 253, 269—72; crystal laws of, 245, 277—84; and primitive form, 258—9, 271, 273, 278-80, 282, 284, 287 Helmont, Jan Baptista van: and alkahest, 217, 223; and form, 140, 172-3, 181, 195, 198-9, 217, 259; and mineral gener¬ ation, 175, 217—9, 290; and mineral seeds, 195, 198-9, 201, 203-4, 207, 217-8 Henckel, Johann, 218, 222-3, 225, 238, 248-9, 26gn Hermaphroditical salt. See Salt Hermes, 26, 164 Hermetic books, 27n, 163-5, 175, 199 Hermeticism: ancient, 163-4, 187, 194; meaning alchemy or chemistry, 164—5, 182, 196; in Renaissance, 66, 164—8, 170, 172, 179, 199-200 Hiarne, Urban, 225, 238—9, 247, 249, 261 Hill, J., 226, 248, 254m 260 Hippocrates, 70, 175 Hobbes, Thomas, 72, 128, 139, 183 Hoffmann, Friedrich, 193, 226, 249 Holbach, Paul d’, 228 Hollandus, Isaac, 228 Homberg, Wilhelm, 225, 231—2, 249, 256, 266 Hooke, Robert, 133, 148, 2040, 248-9, 251, 254n Huygens, Christian, 133, 148, 249, 264n

Index Hydrochloric acid. See Acid; Spirits of niter, salt, and sulfur or vitriol

[315] Logos, 156—7, 162—3, 17°’ x94 Logos spermatikos, 59, 129, 162, 170—2, 176, 194. See also Seminal reasons

Iamblichus, 163 Ice, 35, 45, 102, 115 Iceland spar, 133, 249, 260, 204n Ideas, 20, 53, 57, 61, 154-8, 168, 174; chemists’ use of, 142, 176-7, 187, 194, 198-9, 213, 217; criticism of, 35, 49, 6g, 154; as formative agent, 26, 35, 69, 169; in mind of God, 146, 154, 157, 159-64, 170, 199; as pattern of world, 52, 146, 157, 160-2, 165, 170 Iliad or iliastrum, 172, 175 Image: of God, 157, 174; of Ideas, 159-61,

Lucretius: and atomic shapes, 107, 114—6, 129, 145, 148, 1850; and compound atoms, 113, 138; explanations by, 102,

x76- x95> x98-9 Innate heat, 174, 180, 195 Integrant parts or molecules, 233, 255-7, 270-1, 277-80, 284, 287 Intelligences, 26, 58, 61, i68n, 169, 179 Islam, 52—3, 88, 156—7 Isomorphism, 271—2, 283

121—3, 12®’ 14° Magnetism, 65, 95, 102, 104, 169-70, 183 Mairan, Jacques Dortous de, 35, 131, 260 Mandeville, John, 30 Margraaf, A., 2qg Marx, Carl, 19, 21 Material cause, 22—9, 54, 59, 62, 69, 82, 144, 171 Matrix: as abyss, 175, 201-5, 220—1; as earth, 177, 187-9, 2°6, 219-21; as water and earth, 203—6, 239 Mayow, John, 118, 189—go, 196, 205, 211 Mechanical philosophy: and chemistry, 125, 183, 193, 2ig; and form, 61, 70, 73—4, 127, 170, 190; matter and motion in, 42,

Jacobus de Sancto Martino, g7n Jameson, Robert, 234 John of Jandun, 92, 102, 107 Jorden, Edward, 2gn, 36 Judaism, 52-3, 156-7 Juncker, Johann, 224, 253 Jungius, Joachim, 118, 121-2 Kaehler, Martin, 242—3, 268, 278 Kant, Immanuel, 20 Keill, John, 253 Kentman, Hans, 32 Kepler, Johannes: and crystals, 40—1, 154, i6g, 181, 259; Platonism of, 40—1, 65, 154, 168—9, x72; and stacking of spheres, 40, 133, 148, 249 Kircher, Athanasius, 204n Kirwan, R., 227, 248 Klaproth, M., 249 Landriani, M., 227 Lapidaries, 27, 32 Laurent, A., 253 Lavoisier, Antoine, 227, 235, 251, 270, 283n, 284 Le Blanc, N., 249 Leeuwenhoek, Anton van, 248 Le Fevre, Nicholas, 177, 186-8, 200, 207, 213-4, 219 Leibniz, Gottfried Wilhelm, 69—72, 149, 171, 236 Lemery, Nicholas, 150-1, 188-g, 205, 231, 261, 266 Le Mort, Jacob, 180, 189, 2ign, 2380 Leucippus, 87, gg Libavius, Andreas, 31—2, ig7n Linnaeus, Carl, 226—7, 229’ 237—45> 256. 258, 261, 267-70 Locke, John, 139

104, 107, 109, 114-6, 129—31, i85n

Macquart, L., 248 Macquer, Pierre, 22qn, 225, 228, 235, 254^ 255_6 Macrobius, 53, 160 Macrocosm, 160, 174-5, x95> *97 Magic, 163—6, 172, iggn Magnenus, Jean Chrysostom, 106, 118,

45- 72 Mercury: and earth, 219, 223, 228; and metals, 24, 120, 146; and spirit, 173, 17980, 186, 191, 193, 203. See also Sulfurmercury theory; Tria prima Metaphysic of light, 50—2, 94, 114 Meyer, J. F., 225, 229 Microcosm, 160, 174, 195, 197 Microscope, 43, 133, 137, 150, 248, 282 Miller, William, 2840 Mineral classification, 32, 180, 242, 244—5, 258, 270-1 Mineral generation, 23—9, 77—8, 234; from earth and acid, 219—32; by salt, 211-18, 239, 262; by seeds, 141-2, 181, 195-6, 200-8; by spirits, 181, 183-93 Mineral juices, 28, 33—4, 136, 211—2, 222, 262 Mineralogy, 24, 28, 225—6, 229—32, 234, 247-9 Minerals, 22-47, 77-8, 131> x42, 15°’ 181, 183-262; crystalline, 21, 30-47, 137-8, 22 1_5> 230-64 Minima: and atoms, 87, 89—90, 101, 112—3, 124; as compound particles, 113, 115, 117, 120, 123, 255; in matter theory, 97— 105; in mineral reactions, 108—g, 177, 184, 186; in mixtion, 85—7, 91—3, 119— 20, 143 Minimism: and atomism, 88—go, 106-25, 129, 255—6; in chemical context, 106—g, iig-21, 147m 177—8, 184-6, 250; in

[3l6l Minimism (cont.) mixtion theory, 85-94, 97—105; in phys¬ ical explanations, 92, 102—3, *°6 Mitscherlich, F., 271-2, 283 Mixtion: and chemistry, 140—2, 177-8, 184-6, 213; scholastic theories of, 76— 105; seventeenth-century theories of, 107-13, 117-25, 131, 143 Molecules, 140—1, 255; crystalline shape of, 250-4, 260, 270—1, 278—82; subtractive, 28on, 284. See also Integrant parts or molecules; Organic molecules Monad: of Bruno, 168; of Leibniz, 71 More, Henry, 70, 170—1 Motion, 55—6, 171, 178, 190; of particles, 98—102, 1 16—7, 142 Multiplication of species, 95n, 166 Muria, 239, 242—3. See also Common salt Napione, C., 248 Natron, 31, 239-42, 267 Natural history, 28, 32, 233-5, 237 Natura naturans, 63, 181 Neoplatonism, 53, 65, 157—8, 160—2; in Re¬ naissance, 165—8; and seminal reasons, 59, 74, 81, 162, 172-3, 194-5, 198; and world soul or spirit, 52, 166, 186 Neopythagoreanism, 156 Newton, Isaac, 35, 139, 148, 251, 254, 26411 Nicholas of Autrecourt, 89 Nicholas of Cusa, 167, i68n Nifo, Agostino, 68, 92-3, 98—101, 114—5, 117, 140, 154 Niter, 102; in air, 189-90, 192, 225 (see also Nitro-aerial particles or spirit); and gener¬ ation, igo, 211; as primary salt, 239—42, 266; in snow, 47n, i24n; and tria prima, 210, 214, 221 Nitric acid. See Acid; Spirits of niter, salt, and sulfur or vitriol Nitro-aerial particles or spirit, 189-90, 21 1 Nominalism, 53, 56, 98 Nous, 157, 162—3 Numenius, 157, 159 Olaus Magnus, 40 Oresme, Nicole, 68, 95-8, 114, 154 Organic molecules, 235—7, 240, 259 Oxygen, 227 Palissy, Bernard, 211-2 Paolini, Fabio, 166 Paracelsian and Helmontian chemistry, 29— 32, 36, 41-2, 65, 172-208; and corpuscularianism, 107, 118—9, 129> 138—^42, 250; and mineralogy, 234, 238-43, 259, 261-2 Paracelsus, 29, 106, 166, 172, 177, 19711; and crystals, 31, 33, 212; and mineral generation, 204—5, 214, 228; and spirits and seeds, 180, 197, 200, 203, 205—7, 211; and tria prima, 179, 200, 210 Parmenides, 166

Index Particles: compound, 113, 115, 117, 120, 123, 138—9, 143; elementary, 40, 94, 100, 112, 116, 120, 123; in mixtion, 85—93, 101 — 13, 119—25, 142> 178, 220, 255; mo¬ tions of, 38—9, 98—102, 1 16—7, 128, 142, 188; order or structure of, 97-9, 1 14—5, 136-50, 259-67, 278-83; sizes of, 92, 102-3, 124> >28, 147 Particle shapes, 96—8, 124, 128, 148—51, 236, 249—57; angular or geometrical, 43— 6, 114-5, 122> 135-51, 250, 254-67, 278—85; Cartesian, 129—35, 148, 150—1, 190; hooked, 107, 110, 114—5, 145, 148; irregular, 114, 135, 1850; Platonic, 40, 87, 94, 96, 114, 122, 159—60; pointed (acid), 115, 129—31, 146, 150-1, 185, 188, 231 — 2; porous (alkali), 151, 188, 266; round, 114, 122, 133, 148, 249-51 Pasteur, Louis, 253 Peiresc, N., 1330, 136 Peripatetics. See Aristotelians Petit, F. du, 249 Pfeiffer, Fhrenfried, 2130 Phillips, 2350 Philo of Alexandria, 156—7, 159, 164, 199 Philosopher’s stone, 210 Phlogiston, 221, 223, 227—g, 234, 235^ 268-9, 284 Plastic nature or principle, 39, 70, 73, 133,

44

!

,

171

Plato: form theory of, 20, 49—50, 61, 66, 84-5, 154—6; and geometry, 40, 50, 94, 114, 122, 136, 159; mentioned by Aristo¬ tle, 49, 57, 89, 94, 114, 122, 159; mineral theory of, 23, 3on. See also Creation; Ele¬ ments; Ideas; Particle shapes; World soul Platonism: classical eclectic, 156—60, 164; middle, 53, 156, 159—60, 162; medieval, 50—3, 81, 160—2, 164, 167; Renaissance, 65, 165-8, 170, 172; seventeenth-century, 40-1, 64-5, 168—76 Platte, G., 249 Pliny, 21, 24, 27, 30 Plotinus, 53, 157-8, 162-3, 165—6 Pneuma, 166, 194 Pneumatic chemistry, 227, 229, 268, 284 Pores, 104, 109, 116, 130—1, 183; in alkalis, 151, 188, 266; in earth, 130-1, 189; and points, 115, 125, 131, 143, 146, 148, 151, 188 Porphyry, 160 Potency or potentiality, 55—62, 78-81, 168. See also Active potency Pott, J. H., 225 Principles (five), 1 18, 179, 186, 203, 228 Proclus, 53, 162 Pseudo-Dionysius, 167 Ptolemy, 26 Pyrites, 340, 191, 218, 222-3 Pythagoreanism, 19, 26, 158—9, 172, 175 Quartz, 31, 219, 221-2, 224, 230—1, 234, 235n

Index Quellem, 204 Quintessence, 39-40, 42, 57, 64, 166, 173 Rarefaction, 92, 98, 102, 116 Reaumur, R. A. F. de, 249 Ripley, George, 177 Rock crystal: as earth principle, 219, 221, 224, 230-1; shape of, 26, 31, 33-4, 38-9, 41-2, 236, 240 Rome de l isle, Jean-Baptiste: and chem¬ istry, 226, 243, 268—9; and crystal studies, 244, 248, 274-7, 280; and primitive form, 245, 256-8, 273-7 Root (chemical), 174, 194, 198 Rouelle, G. F., 225, 249 Rupescissa, John of, 222 Sage, Balthasar, 225, 227, 235, 268 Sal ammoniac, 30m 131, 180, 198, 210, 214, 221, 264 Salt, 209—32; as agent of crystallization, 29, 33, 41-2, 147, 204, 212-3, 239-44; as agent of mineralization, 29, 41-2, 44, 150, 204, 211, 214-8; chemical activity of, 110, 119—20, 150, 185, 210, 221; crystals of, 31-2, 43-7, 232, 236, 262-7; geo¬ metrical particles of, 43—6, 147-51, 188, 231, 233, 256, 265—7; hermaphroditical, 177, 187-9, 214’ 218-9; primary species of, 147, 239-42, 266-7; as principle, 29, 151, 209-32, 238—44, 265; as seed, 150, 177, 207-12, 214, 239. See also entries for individual salts

Saltpeter, 44, 102, 130—1, 198. See also Niter Scaliger, Julius Gaesar: and crystals, 33, 36; and form, 57-8, 62-5, 190, 200; and minimism, 92, 101-4, >°6> tit. 118; and mixtion, 82—3, 101 — 2 Scheele, G., 238, 249 Scheuchzer, Johann, 247, 254m 259-60 Scholasticism. See Aristotelians; Form; Form theory; Minimism; Mixtion; Seminal reasons Scopoli, G., 227 Scotists, 83—5 Scotus, John Duns, 54-6, 58, 79—81, 83 Seeds, 193-208; and crystals, 36, 38—9, 43, 47, 139, 142-3; and form, 29, 62, 142, 173-4, 178, 182, 194—5; and mineral gen¬ eration, 177, 191, 193—208; and particles, 43, 10411, 110, 138-43, 150, 196; and salt, *5°’ i77> 207-8, 211-2, 214, 239; and spirits, 181, 194-5, 205—8; and tria prima, 200, 203, 205, 207 Seminal reasons, 162; and chemists, 172-3, 176, 194-5, 198, 203; and creation, 74, 158; in Renaissance, 165-6, 170-1; and schoolmen, 55, 59, 81—2, 160 Seneca, 154, 156 Sennert, Daniel: and creation, 64, 198—200; and crystals, 39—40, 42, 213; and form, 64-5, 72-3, 174, 180-1, 194; and parti¬ cles, 73, 111-3, 118-21, 124-5

[317] Severinus, Petrus: and abyss, 175, 201, 203, 205; and form, 36, 173-4, 177—8, 180, 194; and seed, 36, 174, 194-5, 200, 205, 207 Shaw, Peter, 225m 230 Sherley, Thomas, 141-3, 196, 212 Smithson, J., 249 Snowflakes, 35, 40-2, 46-7, 1240, 131, 136, 169 Southwell, Robert, 2130 Specific form: and Ideas, 157, 159—61, 165, 170—1, 176; and minerals, 25—6, 36, 39, 44, 78; in mixtion, 64, 82, 184 Spirit, 179-93; ac*d or saline, 180, 184—5, 188- 93, 207-8, 210, 212-3; astral or planetary, 166, 180, 191, 201; and crystals, 38—41; and form, 140—1, 170, 181—2, 184—5, 192’ 194—5; mineral or lapidific, 38, 44, 73, 179-93, 205—8, 212; and particles, 109, 184—6, 206; as princi¬ ple, 118, 179-80, 186-8, 203-4, 207, 228-9; sulfurous, 191, 193, 229; univer¬ sal, 171, 175, 177, 186-93, 200> 214; world, 20, 65, 166, 179—80 Spirits of niter, salt, and sulfur or vitriol, 189— 91, 210, 221, 223—5, 227- $ee a^so Acid Stahl, Georg Ernest, 151; and earth princi¬ ple, 223, 228, 234, 259; influence of, 225-6, 232, 234-5, 261, 268-9; and un*' versal acid, 193, 218, 223-4, 226, 228, 259, 268 Stahlian chemists, 225, 227, 229; and phlo¬ giston, 221, 227, 234; and universal acid, 243’ 259 Star (chemical), 29, 174-5, 178, 194, 198, 200 Stars (in sky), 57, 164, 166, 187, 191, 200—1, 204, 206 Steno, Nicolaus, 35, 248, 259, 274 Stoicism: and eclecticism, 154, 156, 162, 165; and mixtion, 77, 780, 88; and semi¬ nal reasons, 59, 158, 162, 172, 194, 198; and spirit, 20, 166 Stones: and earth principle, 220* 224, 232; generated from earth, 23—4, 209; gener¬ ated by form, 39, 207; generated by salt, 211—3, 239; generated by seeds, 205, 207, 211; generated by spirits, 184—5, *87; shapes of, 32-3, 35, 38, 43, 240-3, 260 Substantial form: and accidental form, 54, 58, 68, 75, 81, 173; Leibniz and, 69-71; in mixtion, 79, 91; objections to, 36, 63, 108, 127, 135, 140; objections to explana¬ tory use of, 36, 43—4, 60, 70, 265 Subtle matter, 126, 183 Sulfur: and earth principle, 219, 221, 223; and form, 174; and inflammability, 204, 221; as masculine, 191-2; and metals, 24, 27—8, 33, 191, 209; and minerals, 29, 130, 191, 225, 249, 262; and seeds, 177, 207; and spirit, 180, 188, 191—3, 229; and vitriol, 217-8. See also Sulfur-mercury the¬ ory; Tria prima

[3 >8] Sulfuric acid. See Acid; Spirits of niter, salt, and sulfur or vitriol Sulfur-mercury theory, 24, 27—g, 33, 1 g 1 — 2, 196-7, 209, 217, 225 Summa philosophiae, author of, 26n, 77, 161, i7on

Swedenborg, Emmanuel, 248, 261-4 Tachenius, Otto, 192, 197, 207, 229 Terminists, Paris, 8g Themistius, 57 Themon Judaeus, 27, 40 Theophrastus, 23-4, 27, 29, 173, 205 Thomas Aquinas, 25, 27, 54, 59, 80, 82-3 Thomists, 83—4 Thomson, T., 25311 Townson, Robert, 2540 Transmutation, ig7n, 210 Tna pnma, 29, 42, 143, 182, 210; and Carte¬ sian principles, 130, 207; and elements, 118, 120-1, 182, 203, 228; and form, 174, 182; and minima, 120—1, 139; and seeds, 139, 177, 198, 200-3, 2°5> 207; and spirit, 179, 185-6 Tutton, Alfred, 2 1 Unity: of order, 52, 65; principle of, 20, 52, 65-6, 73, 154-5 Universal acid. See Acid Universal form, 63-4, 113, 116-8, 156, 168, 170—1, 179; and chemists, 175—6, 189, 192, 198; and crystals, 41; opposition to, 52, 64-5, 69-70 Universals, 53, 56, 98, 1560 Universal spirit. See Spirit Vacuum or void, go, 108, 129, 182 Valmont de Bomare, C., 226, 248 Vapor: and Aristotle’s mineral theory, 23, 183, 191, 206, 2og; and mineral seeds, 201, 204, 206; and mineral spirits, 179— 81, 184, 186, 193; and particles, 184—5 Vauquelin, L., 249

Index Venel, G., 225 Vincent of Beauvais, 27, 30-1, 230 Virgin earth. See Earth Vital principle, 173-4, 179, 198 Vital spirits, 179, 192 Vitriol: and mineral generation, 77, 214, 218, 222, 234, 262; and salt, 218, 221, 266-7; shape of, 31, 34, 40-2, 242-3, 2640, 266—7 Vitriolic acid. See Acid Vulcan, 172—3 Walker, J., 248 Wallerius, Johann, 226, 248—9, 256 Water: as abyss, 201—4, 219> 262; and acid, 223, 226, 228, 232; as matrix, 203—6, 239; and mineral generation, 23-4, 28, 211, 219, 222, 262; and mineral seeds, 142, 201, 206, 211, 217, 219—20; and mineral spirits, 187, 191, 206, 211; and mineral transport, 23, 28, 204-5 Watkins, F., 248 Watt, G., 249 Weiss, Christian, 284n Werner, Abraham, 244, 248, 255m 270; and crystallography, 245, 2540, 260, 264, 273-4 William of Conches, 89, ii2n, 160 William of Ockham, 56, 68, 98—9, 102 Willis, Thomas, 183 Wollaston, W., 251, 274n Woodward, John, 226, 230, 247 World soul: and chemists, 173, 176, 179—83, ig4—5, 198, 234; and corpuscularians, 63—5, 155; as formative agent, 35, 47, 70, 265; of Neoplatonists, 52, 162—3, *66, 179, 194; opposition to, 64—5, 70, 265; of Plato, 40, 53, 57, 61, 156; of Renaissance Neoplatonists, 166, 168—g, 175 World spirit. See Spirit Zabarella, Jacopo, 79, 92-3, 101 Zimmermann, C. F., 269

Library of Congress Cataloging in Publication Data Emerton, Norma E., 1932 — The scientific reinterpretation of form. (Cornell history of science series) Bibliography: p. Includes index. 1. Matter—Philosophy. (Philosophy)

I. Title.

QC173.3.E47

1984

ISBN 0-8014-1583-7

2. Hylomorphism.

II. Series. 530

84-45139

3. Science—History.

4. Form