English Logic and Semantics, from the End of the Twelfth Century to the Time of Ockham and Burleigh.: Acts of the 4th European Symposium on Mediaeval Logic and Semantics, Leiden-Nijmegen, 23-27 April 1979 9789070419028, 9782503563923

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ENGLI SH LOGIC AND SEMAN TICS

ARTIST ARIUM A Series of Texts on Mediaeval Logic, Grammar & Semantics EDITORS L. M. de RIJK &

H. A. G. BRAAKHUIS

E. P. BOS Leiden

C.H.KNEEPK ENS Nijmegen

&

Vol. I: L. M. de Rijk, Anonymi auctoris franciscani Logica ,,Ad rudium" (edited from the MS Vat'. lat. 946), Nijmegen 1981 in preparation: E. P. Bos, Johannes Hollandrinus, Logica: A Critical Edition of the Suppositiones, Fallacie, Obligationes, and Consequentie H. A. G. Braakhuis, Nicholas of Paris (?), Summe Metenses: A Complete Edition C. H. Kneepkens, Ralph of Beauvais, Opera grammaticalia L. M. de Rijk, Some 14th Century Tracts on the Probationes terminorum. An Edition of Four Current Textbooks with an Introduction and Indexes SUPPLEMENT A to ARTISTARIU M: Vol. I: English Logic and Semantics, from the End of the Twelfth Century to the Time of Ockham and Burleigh, Nijmegen 1981

ARTISTARIUM SUPPLEMENT A

I ENGLISH LOGIC AND SEMANTICS FROM THE END OF THE TWELFTH CENTURY TO THE TIME OF OCKHAM AND BURLEIGH ACTS OF THE 4TH EUROPEAN SYMPOSIUM ON MEDIAEVAL LOGIC AND SEMANTICS, LEIDEN-NIJMEGEN, 23-27 APRIL 1979

H. A. G. BRAAKHUIS,

EDITED BY C. H. KNEEPKENS,

Nijmegen lngenium Publishers 1981

L. M. de RIJK

ISBN 90 70419 02 5 Copyright 1981 by lngenium Publishers, P.O. BOX 1342, 6501 BH Nijmegen, The Netherlands. All rights reserved. No part of this book may be reproduced or translated in any form, by print, photoprint, microfilm, microfiche or any other means without written permission from the publisher. PRINTED by KRIPS REPRO MEPPEL, THE NETHERLANDS.

TABLE OF CONTENTS Pref ace List of Participants

VII VIII

L.M. de Rijk (Leiden): Abailard's Semantic Views in the Light of Later Developments

Notes

53

C.H. Kneepkens (Nijmegen): Robert Blund and the Theory of Evocation

59

Notes

82

Klaus Jacobi (Koln): Wilhelm von Shyreswood und die Dialectica

Monacensis Notes and Appendix H.A.G. Braakhuis (Nijmegen): English Tracts on Syncategorematic Terms from Robert Bacon to Walter Burley

Notes and Appendix

99 116 131 150

Karin Margareta Fredborg (K\'lbenhavn): Roger Bacon on "Impositio vocis ad significandum"

167

Notes and Appendix

180

Alain de Libera (Paris): Roger Bacon et le probleme de l'annellatio univoca.

193

Notes

222

Osmund Lewry (Oxford): The Oxford Condemnations of 1277 in Grammar and Logic

235

Notes

254

N.J. Green-Pedersen (K\'lbenhavn): Walter Burley, De Consequentiis and the Origin of the Theory of Consequence

Notes J. Pinborg (K\'lbenhavn): Walter Burley on Exclusives

Notes and Appendices

279 298 305 321

Sten Ebbesen (K\'lbenhavn): Suprasegmental Phonemes in Ancient and Mediaeval Logic

331

Notes and Appendix

345

Paul Desmond Henry (Manchester): Suppositio and Significatio in English Logic

361

Notes

381

Elizabeth Karger (Paris): Would Ockham Have Shaved Wyman's Beard?

389

Notes H. Hubien (Liege): Buridan and

408 Le~niewski

on the Copula

Ria van der Lecq (Leiden): Buridan on Modal Propositions

Notes and

415

427 440

Graziella Federici Vescovini (Torino): A la recherche du mysterieux Buser

443

Notes

455

Indexes Index of Manuscripts

461

Index of Ancient and Mediaeval Names

465

PREFACE Twelfth century education was a., European affair and the Parisian schools of logic were its centre. Masters and students flocked together on the banks of the Seine and on the Montagne Ste. Genevieve and, after a long or short stay there, returned home to occupy all kinds of intellectual positions. An entirely different picture is offered by the 14th and 15th centuries. English logicians, especially the Oxford masters, w~re

via their textbooks highly influential on the Art courses of

many Universities on the Continent. Their teaching was clearly felt, indeed, to belong to a tradition which was different from the continental approach. Modern scholarship generally acknowledges that this insular tradition of logic held sway in the late Middle Ages, but has good reasons so far to doubt whether this was the situation in the foregoing centuries. So the IVth European Symposium on Mediaeval Logic and Semantics was intended to clarify the early development of "English Logic". The present volume, which contains all the papers read, presents the results of such an attempt. The Editors strongly hope that these Acta will be a stimulus for further research in this field. The publication of this volume has been made possible through the generous financial help of the Leids Universiteitsfonds (LUF) and the Stichting Nijmeegs Universiteitsfonds (SNUF). Thanks are due to the Filosofisch Instituut of the Catholic University of Nijmegen and especially to Mrs. Ingeborg Hut-Scheepmaker and Alien Lim-Tan, who undertook the difficult typographical composition of the text with diligence and care.

Leiden - Nijmegen. March 1981.

The Editors

LIST OF PARTICIPANTS

E.P. Bos, Filosofisch Instituut, Witte Singel 71, 2311 BN

Leiden, Netherlands H.A.G. Braakhuis, Filosofisch Instituut, Thomas van Aquinostraat 3, P.O. Box 9108, 6500 HK Nijmegen, Netherlands S. Ebbesen, Institut for Graesk og Latinsk Middelalderfilologi, Njalsgade 90, DK 2300 K6benhavn S, Denmark K.M. Fredborg, Institut for Graesk og Latinsk Middelalderfilologi, Njalsgade 90, DK 2300 K6benhavn S, Denmark N.J. Green-Pedersen, Institut for Graesk og Latinsk Middelalderfilologi, Njalsgade 90, DK 2300 K6benhavn S, Denmark D.P. Henry, Department of Philosophy, The University, Manchester Ml3 9PL, England H. Hubien, Avenue des Tritons 28, B-1170 Bruxelles, Belgium K. Jacobi, Thomas-Institut, Universitatstrasse 22, 5 Koln 41, FR Germany E. Karger, 12, Rue Masseran, F 75007, Paris, France C.H. Kneepkens, Instituut Oude Letteren, Erasmusplein I, P.O. Box 9103, 6500 HD Nijmegen, Netherlands C. Kopp, Thomas-Institut, Universitatsstrasse 22, 5 Koln 41, FR Germany R. van der Lecq, Filosofisch Instituut, Witte Singel 71, 2311 BN Leiden, Netherlands O. Lewry, Blackfriars, Oxford Ox I 3LY, England A. de Libera, 34, Rue de Provence, F 75009 Paris, France A. Maieru, Viale Pinturicchio 45, I-00196 Roma, Italy G. Nuchelmans, Filosofisch Instituut, Witte Singel 71, 2311 BN Leiden, Netherlands J. Pinborg, Institut for Graesk og Latinsk Middelalderfilologi, Njalsgade 90, DK 2300 K6benhavn S, Denmark L.M. de Rijk, Filosofisch Instituut, Witte Singel 71, 2311 BN Leiden, Netherlands H. Schepers, Rothenburg 32, D 4400, Munster/i.W., FR Germany P.M.J.E. Twnmers, Filosofisch Instituut, Thomas van Aquinostraat 3, P.O. Box 9108, 6500 HK Nijmegen, Netherlands G. Federici Vescovini, Lungopo Antonelli II, Torino, Italy N.B.:

The Logic of John Buridan, Acts of the 3rd European Symposium on Medieval Logic and Semantics, Copenhagen 16 - 21 November 1975, ed. by Jan Pinborg, Museum Tusculanum, Copenhagen 1976 (= Opuscula Graecolatina, 9)

ABAILARD'S SEMANTIC VIEWS IN THE LIGHT OF LATER DEVELOPMENTS

L. M. de Rijk,

Leiden

Semantics in Abailard's solution of the problem of universals

1

Abailard's attempt at solving the problem of universals may be characterized as a remarkable achievement in the field of semantics. The procedure of this solution found in his most mature work, the Glosses

on Porphyry

2

can be divided into two stages: first, the extensive

discussion of the formal distinction between vox and sermo, then the semantic analysis of the intensional act of intellection. I.I

Vox and sermo formally distinguished

As is well-known Abailard makes an important distinction between vox (word) and sermo (significant word). Contrary to the Realists he considers vox and sermo materially identical, following in this respect his former master Roscelin of Compiegne. However, in order to solve the problem of universals he lays much stress upon their formal diversity (or: non-identity). To his mind, there is a formal distinction, indeed, between 'being predicable of many' and 'that which is predicable of many'. Well, it is predicability that must belong to a word (vox) for it to be a universal. He tries to elucidate this distinction in contraposing the following propositions: (I) Genus est vox

and (2) Vox est genus, the former of which is true, the latter false. In fact, (I) is equivalent to (I') Generale vocabulum est vox,

and this is true, no doubt. Abailard points to similar sets of prop-

ositions. I pick out two of them: (3) Haec materia Socratis est Socrates (true) (4) Utrumque istorum est aliquid (true) as contradistinguished with (5) Socrates est haec materia Socratis (false) and (6) Aliquid est utrumque istorum (false). How should we understand this? For (3) to be true the subject phrase

'haec materia Socratis' should_ be taken as 'this material thing Socrates' (where Socratis is an explicative genitive). Now, what about its converse (5) Socrates est haec materia Socratis? Nothing seems to prevent us from translating: 'Socrates is this material thing Socrates', except for Abailard's most explicit assertion that (5) is false (negamus omnino). So we have no other choice than rendering it by (5) Socrates is this matter belonging to Socrates, where the genitive case Socratis is a possessive one. However, is this not done quite arbitrarily? Before giving an answer we pass on to the second set: (4) Utrumque istorum est aliquid, as opposed to (6) Aliquid est utrumque istorum. No difficulty at all, this time. For whenever (4) is true, (6) is obviously false. What is, however, far more interesting is that the term 'aliquid' has changed its meaning together with its syntactic position. Indeed in (4) the distributive force of the subject term 'utrumque' obviously has its bearing on aliquid, whereas such influence is absent in (6). Now, it seems obvious that we should look for a similar change of syntax as effecting the falsity of (5): (5) Socrates est haec materia Socratis. I think we have to rephrase our original question this way: Is there

2

anything that prevents us from taking the genitive case Socratis as an explicative one as we did in (3)? I would propose this answer. In (5) the subject term 'Socrates' signifies a clearly complete whole, a subsistent entity, and that to the effect that when later on in the sentence the same noun occurs in the genitive case, the only consistent interpretation is obtained by taking it, again, as referring to the subsistent entity: Socrates; and this results in understanding the clausula as: 'this material part of Socrates' ('this matter belonging to Socrates'). On the other hand, in (3) Haec rnateria Socratis est Socrates it is the phrase haec materia Socratis occuring in first position, that has the task of signifying a subsistent entity and for this very

reason one is bound to take the genitive case Socratis as an explicative one, since taken as a possessive genitive ('belonging to Socrates') the phrase 'haec materia' cannot help but signifying itself a subsistent entity; and that would cause a false assertion, since a person's matter is just one component of a subsistent entity, not itself a subsistent entity. Well, returning to our propositions (1) Genus est vox (2) Vox est genus it will be clear that in (1) the subject term genus is to be taken in its 'completeness', that is, as signifying a subsistent entity, to the extent that it is equivalent to generale vocabulum, that is, the material sound that has a significative function; in other words: it does not mean, here, the formal quality as such of being a significant word. And so (1) is true. Its converse (2), however, asserts that an articulated sound, as such, is a genus and in doing this it neglects the important formal distinction of vox and genus, however identical they are in material respect. 1.2 Universals as the 'intrinsic object' of human understanding

3

The first part of Abailard's procedure aimed at showing that Roscelin of Compiegne was wrong in taking the universal (e.g. ANIMAL) as fully identical with the correspondi ng articulated sound (vox)

'animal'. In spite of their material identity they still differ formally, since the universal is a vox gifted with a significativ e function. However, recognizing this might plunge us into another pitfall of Realism. Indeed, what is the object of that significativ e function? Is it an extramental thing (such as the Platonic Ideas), or is there no referent at all? The question leads Abailard to a second manch of his procedure. It is found at the end of the introductory part of the Porphyry commentary (ad Boethiwn, 159, 7 ed. Brandt). In fact it contains a brilliant analysis of what is nowadays called the problem of the 'opaque or non-referen tial context' arising from the use of verbs involving mental attitudes. Abailard's view is substantial ly the following (see LNP 530, 38 - 533, 9). When we say (7) Homo intelligitu r (Man is understood or: 'intellecte d'), the sense is that somebody through an act of understandi ng (per intellectwn; rather than 'through an idea') conceives the form: hwnan

nature. It may be compared with a proposition like (8) Desidero cappam (I want a hood). For that matter, when Boethius says (De divis. 889 B) that when this word 'man' has been uttered, (9) Auditor non habet quad intelligat,

(The hearer has no thing to understand) , the assertion is an ambiguous one. It stands for either (9') Nulla res est de qua intellectum habet (true) (There is no thing of which the hearer has an intellection ) 3 or (9'') Nullum intellectum habet (false) (He has no intellectio n).

4

A similar case is found in

(IO) Quid vis? (What do you want?) which may stand for

(IO') Quae res est de qua voluntate m habes? (What thing is it of which you have a want?) or

(IO'') Quam voluntate m habes? (What want do you have?). So we may say that in proposit ions like (II) Aureum castrum volo (I want a golden castle) the object is a so-calle d 'intrins ic object' just as in 'to dream a dream'; an intrinsi c object having no other function than to determin e the act. Indeed (II) does not assert anything about some golden castle existing somewher e, it rather describe s my desire. Accordin gly, (II) could be rendered by: 'I am a golden-c astle-wa nter', that is: 'I am a day-drea mer' . 4 Likewise , proposit ions such as (7) Homo intellig itur should not be rendered by (7*) A MAN (or: man) is intellec ted, in the sense: there is a (species ) Man and there is some intellec t that directs itself towards it, but by (7') There is (some case of) man-int ellection . A universa l does not exist as some 'thing' in the outer world. Its existenc e, rather: its being given is merely due to some producti ve way of human thinking and, accordin gly, never exceeds the realm of . k.-ing. 5 t h-in 2

Predicat es being affected by their subjects ?

2.1 Abailard 's rule

5

As we have seen, the first stage of Abailard's semantic procedure shows that he was aware of the semantic impact of a word's syntactic position in the proposition. Since all his examples given there [our (1), (2), (3), (4), (5), (6)] contain a contraposition of the respective subject and predicate terms, it seems tempting to reduce the syntactic phenomenon at issue to just the subject affecting its predicate. Let us consider first our problem from this point of view. 6 . . In the so-cal led Intro ducti-ones Montane Mai-ores we are to ld b y the anonymous author (from the circle around Alberic of Paris, presumably) that Abailard used to see some difficulties where others did not see anything of the kind. So in the (supposed) inference from (12) Nullus lapis fit a Socrate (No stone is made by Socrates) to (13) Nulla statua lapidea fit a Socrate (No stone statue is made by Socrates). For that matter, the anonymous author did not have any trouble with this kind of 'difficulties', since they were not objections at all to the view of Abailard's opponents (Hee et huiusmodi non sunt oppo-

sitiones secundum sententiam quam tenemus, loc. cit., 15). Abailard, however, (who apparantly took the objection as a real one) always had much trouble in disposing of the objection by proving its falsity

(magister Petrus vero nimium in huiusmodi oppositionis solutione ut suam falsitatem defenderet, lciborabat, ibid.). He used to say, we are told, that that which is denied in (12) is not denied in (13). Indeed, when we say (12) Nullus lapis fit a Socrate (No stone is made by Socrates), the force of the subject term is carried over into the predicate term

(vis subiecti redundat in predicatum, ibid.), to the effect that its sense is (12') Nullus lapis operatione Socratis promovetur in esse lapidis

6

(No stone is brought into being a stone by an operation of S.), whereas the sense of (13) is: (13') Nulla statua operatione Sortis movetur in esse statue (No statue is brought into being a statue by an ope.ration of Socrates). Well, in (12) the verb fit('is made')means movetur.in esse lapidis ('is brought into being a stone'), and in (13) the same verb fit ('is made') means movetur in esse statue ('is brought into being a statue'), and that because of the different subjects of the respective proposition s (12) and (13). Thus, our anonymous author adds, in always relating the predicate term to the subject term Abailard used to say that no body is made by Socrates but a statue really is made by him (loc. cit., 15). Thus we find Abailard here pointing to the same distinction as is found in LNP, 522, 30ff. in order to elucidate the important distinction between the material identity of vox and genus and their formal diversity (see our discussion, above, pp. 1 - 3 ). There, too, he underlines the material identity of this stone and this stone statue and their formal non-identit y, to the extent that 'being a stone' (esse lapidis) is a different form (forma) from 'being a statue' (esse imaginis). To be sure, it is only the latter form that is brought into existence thanks to the sculptor's acting. Again, we have got a situation similar to the one we met with in the examples discussed in the previous section. Indeed, we may ask a similar question as we did in the preceding examples (l) - (6), viz. why (12) Nullus lapis fit a Socrate (No stone is made by Socrates) cannot be interpreted as meaning ( 12*) .No stone thing (image, statue and so on) is brought into existence by Socrates. The obvious reason is that the term lapis ('stone') has to signify something (either intensional ly or extensional ly) only under the form

7

of stone-ness, and, accordingly, it is not correct to attribute the production of that form to Socrates. On the other hand, in (13) Nulla statua lapidea fit a Socrate (No stone statue is made by Socrates) the subject term signifies something (either intensionally or extensionally) under the form of being a (stone) statue. Both times, accordingly, it is the specific form under which the act of signifying occurs, which is supposed to be carried over from the subject term into the predicate term. It is easy to see now the parallel with (3) Haec materia Socratis est Socrates, where, as we have discussed above, (p. 3 ), the subject term 'haec

materia Socratis' signifies a complete whole, or: subsistent entity, as such, capable of existence. 2.2 An interesting passage from Sherwood's Logic Tweedale's discussion of the problem at issue (AbaiZard on UniversaZs, 147ff.) is focused mainly on Abailard's rule that some predicates are being affected by their subjects. In fact, this precludes Tweedale from seeing the semantic point proper. Indeed, from the semantic point of view it seems not satisfactory at all to point to Abailard's syntactic rule, that some predicates have their meanings affected by their subjects. This rule leaves the semantic question why subject terms (sometimes) affect the meaning of the predicate terms unsolved. For that matter, when discussing (78, 4ff. ed. Grabmann) the question whether simple supposition is a property of predicates, William of Sherwood (d. after 1267) says that the subject term's meaning depends on what the predicate demands, in accordance with the principle: "subjects are of such sorts as the predicates may allow them to be" (ta-

Zia sunt subiecta quaZia peY'l'Triserint predicata). He adds that it should be pointe.d out, that the authoritative statement of Boethius runs as follows: "Predicates are of such sorts as their subjects may allow",

8

and not its converse; and that Boethius' example there (De Trinitate, 1252 A - B ed. Migne = p. 156, 4 - 5 ed. Peiper) is 'A man is just' vs. 'God is just', where the word 'just' is taken differently in the two cases, depending on what the subject demands.

7

However, it seems

important for our purpose to take the whole context into consideration (p. 78, 7ff. ed. Grabmann): Every name signifies a form only, not taken separately (absolute), but insofar as it informs a substance bearing it and thus makes (us) in some way have an intellection of a substance. Therefore a name (used) in the predicate makes (us) have an intellection of a form, that is (dico), to the extent to which it is the form of the 8 And so, since that substance is

substance which is the subject.

(already) understood in the subject, it will not be understood a second time in the predicate. Therefore the predicate expresses 9· just the form, (not form and matter i.e. a substance) Thus the context rather suggests that the decisive point is not to be looked for in the subject-predicate relation as such, but in the semantic nature of names in general •. The mere occurrence of the two contrary rules ('sometimes the subject affects the predicate, sometimes the other way around') should cause us to be on the alert not to describe the syntactic phenomenon in terms of the subject-predicate relation taken as such. Besides, a term's meaning being changed presupposes its having some meaning whatsoever by itself. For that reason one had better start, it would appear, with an inquiry into the significative function of names in general. 3

Abailard's view of the significative function of a name (noun)

As early as in his Logica Ingredientibus Abailard links up the significative function of names (nouns; nomina) with the production of epistemological forms (formae) by the human mind. In this earlier work, it is true, he is rather explicit in distinguishing them from

9

the acts of understanding, which distinction is significantly absent in the parallel passage of the Tract. de intellectibus, 734:

L.I. 20, 28 - 32: Just as the sensing (sensus) is not the thing perceived to which it is directed, so neither is the understanding . ll ectus ) the form of the thing . . l 0 it . conceives, . ( ~nte which but t h e understanding is a certain action of the soul after which it is called intellect (intellectus), but the form to which it is directed is a certain imaginary and fictive thing, whi~h the mind constructs for itself when it wishes and as it wishes. Well, after a general examination of the nature of understanding our author goes on to distinguish between the understandings of universals and particulars. Again, forms are in the game:

L.I. 21, 32 - 22, 2: When I hear 'man', some equal (instar) arises in my mind which is so related to individual men that it is common to all proper to none. When, however, I hear 'Socrates', some form arises in my mind, which expresses the likeness of a definite particular (certae personae). So by this word 'Socrates', which generates in the mind (viz. of the hearer) the proper form of one particular, some thing is specified and determined, but as to 'man', the understanding of which - on the part of the hearer

(intelligentia ) - rests in the common form of all men, that very commonness leads to confusion lest we should not understand any one in particular. It should be noticed that as early as in L.I. a sharp distinction is drawn between sensing and understanding (intellectus). In his later glosses, too, Abailard makes understanding depend on specific, nonsensible forms:

LNP, 527, 23 - 27: Certain genera and species, but not all, have been given

(sunt posita) in sensibles, that is, they have to name

(nominare) sensibles, and are (also) put (ponuntur) outside sensibles, that is, they have to signify things, but not through

10

some form that is subject to sensing. For, if things would lose all forms that are subject to sensing, they could just as well be named by genera and species. It is true, and rather striking at the same time, that Abailard does not call the non-sensible forms formae; he contradistinguishes them with sensible forms only by saying that in the case of understanding there is no role for the 'forms subjacent to sensing'. Of course, he does speak elsewhere of 'essential forms' (e.g. Dial. III 2, 415, 35 - 416, 9), but obviously only in a ontological rather than an epistemological context. The text quoted above (p. 10 ) from L.I. 20, 28 - 32 is remarkable in that respect. Indeed there is made a sharp distinction between the (ontological) forma of a thing and the act of understanding, just as we have to distinguish between sensing and the thing perceived. Likewise, in the Dialectica (V, 595, 32) the author calls substantive nouns those which have been given to things insofar as they are (secundum hoc quad sunt), whereas adjective nouns are imposed after

thei~

having assumed some (substantial) form (alicuius

forme). Elsewhere (Dial. II, 181, 27 - 30) he calls the substantial form of man (taken as an epistemological entity) species hominis: quodsi ad speciem illam hominis quam fingunt puram per abstractionem accidentium ipsum nomen referat. His usual word for it is 'common conception' (communis conceptio; see L.I. 19, 17 ff). The only passage, as far as I know, where Abailard uses the word 'forma' in an epistemological context to designate also the common forms of intellec-

tion, is found in L.I. 24, 26 - 31; for that matter, the concluding sentence seems to point to a novelty on Abailard's part:

L.I. 24, 25 - 31: Reason, too, seems to agree with those authoritative statements which seem to confirm (astruere) the view that through universal names common conceived forms (conceptas communes

formas) are designated. For what else is it to conceive forms through names than that those forms are signified through them? No doubt, however, whenever we make out of forms something else

11

but understandings, then we have got besides 'thing' and 'understanding' the 'signification of names' as a third entity. Well, although this (latter consideration) is not found in the authoritative tradition, it is nevertheless not contrary to reason. One should notice the rather subtle ambiguity in the author's using here the word forma: it both stands for 'a thing's ontological form, which is conceived' and 'a thing's form conceived' = 'conception, or concept, of a thing'. Later on the substantial form is more often mentioned explicitly, e.g. Tractatus Anagnini (Log. Mod. II 1, 421, 32) where the common name is said to be imposed after a common form (which may be a substantial or an accidental one as well, to be sure). The Tractatus de proprietatibus sermonum (presumably from the School of Abailard) is more explicit in this score (see below, our section 7). Finally, in the thirteenth century the epistemological sense of forma (substantial form included) is commonly found. E.g. in William of Sherwood's well-known definition of signification: signification, then, is the presentation of some form to thought (est igitur signi-

ficatio presentatio alicuius forme ad intellectum). Peter of Spain is most explicit in this respect, in contradistinguishing the (ontological) forma materie with the (epistemological) forma predicabi-

lis: Tractatus XII, 213, 25 - 31: 'Form' can be taken in a twofold way, since one form is the form of matter, as my soul is the form of my body, and yours of your body; and that form is a part of, and is not predicated of, that of which it is the form. The other is the form which is a predicable form, and thus all the higher (predicables), such as genera, species and differentia, are said to be forms of the lower ones, such as man, horse and

animal, and the like. But the individuals covered by that predicable form are its matter. Returning, now, to Abailard it may be asked what exactly is the

12

semantic value of those forms, which~ usually calls communes conceptiones. Well, he answers the question concerning the nature of the common conceptions (forms) in connection with the question about universal names. So in the L.I. 19, 14 ff. Abailard asks, among other things (1) what is the intellective conception of the common likeness

(conceptio intellectus communis similitudinis) and, (2) ·whether a word (vocabulum) is called common because the things designated by it have something in common or because of a common conception or because of both taken together. After an extensive discussion of several aspects of the question Abailard expresses his view on the formation of such common conceptions by abstraction as follows:

L.I. 24, 38 - 25, 14: Likewise we must speak more definitely (definiendum est) about what we have said above (23, 7 ff,), viz. that the conceptions of universals are formed by abstraction and we must indicate how we can call them "alone, naked, pure but not empty" (solos, nudos, puros nee tamen cassos). And first concerning abstraction. In that respect it must be known that matter and form always subsist mixed together. Well, the rational mind (animi ratio) has this power that it may now consider matter by itself, now turn its attention to form alone, now, again, conceive both intermingled. The two first processes are by abstraction: they abstract some thing from things conjoined that they may consider its very nature. But the third process is by conjunction. For instance, the substance of this man is at once body and animal and man and vested in infinite forms; when I turn my attention to this in its material subsistence (in materiali essentia substan-

tiae) apart from all the forms, I have got a concept (intellectum) by the process of abstraction. Again, when I consider only corporeity in it, which I join to substance, that concept likewise (although it is by conjunction with respect to the first, which considered only the nature of substance) is formed also by abstrac-

tion with respect to other forms than corporeity, none of which I consider, such as 'animation', 'sensuality', 'rationality', 'white-

13

ness'.

11

Next he denies that such abstract conceptions are to be considered vain and empty, as they are concerned with matter by itself or form by itself, which, indeed, do not exist separately. Yet, this way of understanding is not empty. For when I consider, Abailard goes on, this man only in the nature of substance or of body, and not also of animal or of man, obviously I understand nothing except what is really in that nature, only I do not attend to everything it has. And when I say that I consider 'only this one' among the qualities the nature has, the word 'only' refers to my attention alone, not to 12 the thing's mode of subsisting, otherwise my understanding would be an empty one, indeed. It only is the mode of understanding that is different from the mode of subsisting. So matter is perceived purely and form simply, although the one does not exist purely and the other does not exist simply, so that obviously that purity or simplicity should be reduced to the understanding (intelligentiam), not to a thing's real state, to the effect, namely, that they are modes of understanding, not of subsisting (L.I. 25, 15 - 37). He goes on (27, 18 ff.): For that matter, the understanding of universals must always take place by the process of abstraction. For when I hear 'man' (homo) or 'whiteness' (albedo) or 'white' (album), I do not recall, by virtue of the meaning of the name, all the natures or properties which are in the things underlying ( these forms }

(in rebus subiectis) but by 'man' I only get a conception, although confused, not discrete, of animal and rational and mortal, but not of the additional accidents as well. (I say: not discrete} for the conceptions of individuals, too, are formed by abstraction, when, namely, it is said: 'this substance', 'this body', 'this animal', 'this man', 'this whiteness', 'this white'. For by 'this man' I

attend to the nature of man alone

(naturam tantum hominis), albeit

(sed) as related to a certain substrate

(circa certum subiectum),

whereas by 'man' I attend to that same nature simply [i.e. without the material substrate]

14

in itself, not as related to any individual

man (27, 18 - 29). Thus Abailard is able to explain why the understanding of universals is rightly spoken of as 'alone, naked and pure'. Indeed, it is alone from the senses, because it does not perceive the thing as sensual; it is naked in regard to the abstraction of all or of some forms; it is pure, finally, with respect to discreteness, since no thing, whether it be matter or form, is made particular (certificatur); and it is in this sense that Abailard calls such a conception 'confused' (ibid, 27, 29 - 34). Let us try to gather the substantial content of these important passages - the conceiving of universals is a process of abstraction - it rests on the basic condition of sensibles, that is, their being composed of form and matter the first type of abstraction is that by which the very nature

(ipsa natura) of matter is attended to - the second type of abstraction is that by which the very nature of form is attended to - the process of abstraction can be considered a process of conjunction, to the effect that conjunction is the considering of a thing's corporeity alone, not, however, in formal abstraction but as it is joined to (coniunctum) substance; thus the process of abstraction ('corporeity alone') is combined with that of conjunction ('corporeity joined to its substance'). We can also inventorize some pivotal points by starting from the sensible things in the outside world: I this particular man may be considered

in his material subsistence alone, quite apart from all .his forms (L.I. 25, 6 - 9). The product of such a logical procedure (abstraction) is (the conception of) man taken in its materiality as such. E.g. an individual man taken as just a material entity in the outside world (cfr. 25, 6 - 9)

15

2 this particular man's form alone may be considered, quite apart from its matter (resp. materiality as such, and from its other forms as well, to be sure), to the effect that this form is perceived simply (L.I. 25, 12 - 14 and 34). The product of such a logical procedure (abstraction) is the (conception of) pure form. E.g. Man (see 27, 27 - 29), 'Rationality', 'Whiteness' (see L.I. 25, 14). 3 this particular man may be considered in his formal nature, which

is taken, however (unlike in (2)) together with ('joined to', 'con-

iunctum') underlying matter. The result of such a logical procedure is either 3. I (the conception of) man (and so on) taken in its completeness (as 'a subsistent entity', see above p. 3), which, unlike the product of (I) is performed by conjunction (per coniunctionem; L.I. 25, IO - 12) .For instance, 'man', 'white'; (see L.I. 27,

20) ; 'this man' , 'this animal' , 'this whiteness', 'this white' (see 27, 26 - 27); or 3.2 the same conception of man (and so on) taken in its completeness, which, unlike the product of (3.1), is performed by abstraction, that is, putting apart all other forms (L.I. 25, 12 - 14). For instance, 'man'

'whiteness', 'white' (see L.I. 27, 20).

All this should be put together with Abailards doctrine of the adjectival names. For that matter, in L.I., he defines them (calling them there nomina sumpta) as names which have been invented in order to signify an accidental form (formam adiacentem), such as 'rational', or 'white'. They do not signify a subsistent thing affected by that form, but just the form itself (122, 34 - 123, 4). In the

Dialectica (V, 595, 32 - 36) their counterparts, the substantival names are defined as names which have been given to things according to their being presently (secundum quod sunt), whereas the adjectival names are imposed according to a thing's having some form. The full impact of the distinction becomes clear when Abailard deals with the problem of the definition of the adjectival names (Dial. V, 596- 598).

16

First, the adjectival names (nomina swrpta) are said to have a double meaning, a primary one, which concerns the foY'111, the other a secondary one, which concerns the thing informed by that form (foY'matum). So 'white' (album) primarily signifies the whiteness, which it designates in the underlying body (quam circa corpus subiectum deter-

minat), and secondarily that underlying body itself by naming it (quod nominat). Therefore the question can be raised whether such names refer to subjects (=substrates) or to forms (foY'mae). For instance, when 'white' (album) is defined as 'informed by whiteness' (formatum albe-

dine), is, then,'informed by whiteness' the definition of white or of whiteness? The latter is impossible since whiteness itself is not informed by whiteness. However, if the definition holds good for 'white', it may be asked whether it is applicable to all white things taken distributively or collectively. Neither is true. Abailard gives the following solution of the problem (Ibid., 596, 27 ff.): (1) the definition also holds good for the form, but only for the form which is assumed as an adjacent one (forma secundum adiacentiam accepta); so it can be said: every white thing is informed by whiteness; (2) whenever the definition 'informed by whiteness'

(formatum albedine) is used for 'white' (album), then it is attributed to the (white) thing according to some form inhering in it (secundum

quandam foY'mam sui), not according to what it substantially is (secundum id quod ipsa est; see 596, 38 - 597, 1). Next Abailard presents an alternate, semantic formulation:

Dial. V, 597, 7 - 14: One may also assert the definition ['informed by whiteness'] to hold good for the word 'white', too, not however according to the latter's being a particular word (secundum essentiam suam) but according to its signification; accordingly, it will not be predicated of 'white' taken in the latter's subsistence (as a word), to the effect, namely, that we should say that the word 'white' is 'informed by whiteness'; no, it is predicated of 'white' according to that word's signification, as if we

17

would say: 'a thing which is called white (res quae alba nominatur) is informed by whiteness'. And in fact to define a word is to reveal its signification by way of definition; to define a thing, on the other hand, is to designate it (ipsam demonstrare). These important passages taken from the Dialectica clearly show that, as far as the semantic value of the adjectival names is concerned, Abailard makes a sharp distinction between two significations; the word 'white' (album), for example, may signify either (a) whiteness

(albedo), not in itself however, but as inhering in a subject (substrate) or (b) 'white thing' (album), that is, a subsistent thing which is 'named' according to its being 'informed by whiteness'. The first signification presents whiteness to the hearer's mind in its particularness, that is, as inhering in a subsistent entity (i.e. 13 . . . . 1 substrate; per con~unc . t ~onem, ' Joined to its materia as Abai·1 ar d says in the Log. Ingred.; see above, p. 13

; here he says: albedinem

quam circa corpus subiectum determinat, 596, 7 - 8 and 596, 28 - 30: dicatur itaque illa definitio albedinis esse non secundum essentiam suam, sed secundum adiacentiam). The second signification, on the other hand, presents a particular, subsistent thing itself to the hearer's mind, but 'named' in an abstractive way, since the name used to designate the thing does not

as such point to a particular entity, and singles out just one form of the thing concerned. The most striking in this semantic picture seems to be that the two significations, also the primary one, concern entities in their

particularness: album= a subsistent thing itself, and albedo= particular whiteness as inhering in a subsistent entity, not whiteness taken by itself. The contradistinction of 'whiteness by itself' and 'whiteness inhering' is expressed by our author as that of 'whiteness

secundum essentiam suam' and 'whiteness secundum adiacentiam' (596, 28 - 30). For that matter, elsewhere (Dial. I, 124, 33 - 35) Abailard calls adjectival names adjacent names, and, thus betrays his semantic approach. The passage is also interesting in that it

18

opposes adiacentia to essentia: bee (sc. nomina) sunt essentie, que substantiva dicimus, alia vero adiacentia, que sumpta nominamus. The use of the word 'essentia' needs some further discussion.

4

Abailard's use of 'essentia'

4. l 'essentia' as 'substantial' (subsistent) appearance Since in the two passages discussed essentia is clearly opposed to

adiacentia, it cannot possibly be translated with 'essence'; it can only stand for '(what is) of a non-adjacent nature', '(what is a) substance'. Therefore the primary notion of 'essentia' must be that of subsistence or rather: 'substantialness'. We need not wonder, indeed, that elsewhere the opposition of secundum substantiam to secundum adiacentiam is found (595, 36 - 38). 14 Well, given its deriving from esse, the notion of 'substantialness' as found in 'essentia' is bound to refer to a substance's being settled in some particular being. As a matter of fact we found (Dial. 595, 32 - 33) substantival names defined as names which are given to things according to their

being (see above, p. 16 ). Thus several meanings of 'essentia' as used by Abailard, may be distinguished. A

'appearance' (that is, the phenomenal aspect of existence)

Al said of one particular thing:

Dial. I, 84, I - 4: non dico quidem quin substantia patris absque substantia filii vel essentia filii absque essentia patris subsistere queat in sue proprietate persone vel in natura substantie (ut Anchises absque Enea vel econverso).

Dial. III, 408, 33 - 34: neque enim eadem res est diverse substantie neque diverse substantie (sc. sunt) eadem essentia; cfr. L.I. 529, 39: nulla essentia est universalis.

19

Dial. II, 160, 28 - 29: esse autem rem aliquam, vel non esse, nulla est omnino rerum essentia ('does not belong to really existing things'); cfr. L.I. 275, 5 - 6; 287, 8 - 9; 293, 21 - 22, etc.

Dial. II, 186, 6 - 7: s ignum particulare discreti vum esse particularis essentie ('of a particular appearance'). Dial. III, 335, 12 - 14: si vero magis essentiam rei quam vocum proprietatem insistamus magisque identitatem essentie (= material coincidence) quam vim verborum attendamus, profecto consequentiam 15 ( recipimus} ; see below, p. 25; cfr. ibid. 409, 29 - 30: non itaque rerum essentia simplicem impedit conversionem, sed eadem transpositarum vocum acceptio; see also below, p. 27 . A2 of things in general= 'state of affairs':

Dial. II, 155, 25 - 29: ex his itaque manifestum est in consequentiis per propositiones de earum intellectibus agendum non esse, sed magis de essentia rerum, hoc modo scilicet ut si ita est in re quad omnis homo est animal, ita est in re quad omnis homo est corpus, et quecumque eiusdem sunt consequentia, necesse est in re

esse, sed non intelligi. Dial. III, 330, 36: non ad rerum essentias, sed ad enuntiationum constitutionem; cfr. ibid. 409, 13 - 14: non quantum ad rerum essentiam, sed quantum ad eamdem vocum transpositionem; 409, 19: secundum rerum essentiam; 409, 29 quoted above, sub I.I.

Nata: The singular is also found, e.g. L.I. 25, 36: subsistentia rei (opp. intelligentia) = 'a thing's real state'; see above, p. 14 . B

thing(s} as conceived in its (their) particularness

Bl said of one particular thing:

Dial. III, 334, 35 - 36: Licet enim essentia illa que per 'coloratum' attribuitur, eadem cum illa sit que per 'corpus' ponitur •.•

20

Dial. II, 159: non itaque per verbum interposit um inherentia copulatur, cum etiam illa sit proprieta s, sed sola hominis substantia attribuitu r, cum dicitur 'Socrates est homo'; cfr. III, 329, 32. Dial. III, 394, 12 - 14: Sunt autem que opposita sunt in essentia, secundum existentia m quoque opposite, ut nox et dies, que simul existere non possunt. Since here in essentia is opposed to secundum existentia m the former phrase must refer to particula r being as conceived . B2 mode of being particula r B2 I particula r generic (or: specific) mode of being:

Dial. III, 420, 32 -' 35: neque enim forme mutatio diversitat em specierum aut generum facit, sed substantie creatio (the creation of a concrete substance ). Quocumque enim modo varientur forme, si identitas manserit (if the substance remains the same), nichil ad essentiam generalem vel specialem agitur.

Dial. III, 267, 30 - 37: non itaque vel 'genus' vel 'species' vel 'oppositum ' vel cetera habitudinu m nomina (names of relationsh ips) in maximis propositio nibus posita aliquarum proprietat um designativa sunt, immo ipsarum substantia rum. Ut cum dicitur: 'de quocumque predicatu r species, et genus', hie est sensus ut, si aliquid sit ea res que est species, idest vel homo vel equus et cetera, sit quelibet res que eorum genus est, veluti animal aut corpus, aut substantia ; per genus itaque ac species substanti e ipse, non alique earum proprieta tes, attribuun tur.

Dial. III, 409, 36 - 410; 2: cum dicitur 'homo est animal', 'asinus est anirral' ( ...... }est itaque identitas tantum, non secundum rerum essentiam , sed secundum vocum denotation em (see also below, pp. 27 - 28). B2 2 particula r adjacent mode of being:

Dial. III, 370, 13 - 18: in essentia vero opposite sunt quelibet

21

diverse rerum essentie, ut albedo et nigredo ('all different particular modes of being are opposed one to the other taken in their particularness (in essentia), such as 'whiteness', 'blackness'). Sed horum alia in essentia tantum opposita, ut albedo et duritia, alia etiam in adiacentia, ut albedo et nigredo. Sicut enim in eadem re non potest simul esse albedo et nigredo, ita nee simul ( potest} ea( s) participare, idest simul alba esse et nigra. So whiteness and hardness are only opposed as two different particular modes of being which might belong to one and the same thing, whereas whiteness and blackness are two particular modes of being which cannot exist at the same time, unless they are found in two separate things.

Dial. III, 430, 37 - 431, 3: cum autem ipsorum essentia accidentium augeri vel imminui dicatur vel ipsum accidens in sUbstantia

sua maius alio vel minus dicatur, queri solet cur non etiam in essentia comparentur, ut videlicet hec albedo que maior est, magis albedo quam illa que minor est, dicatur. ('since the particular mode of being of accidents is said to increase or decrease and the accident itself in its particularness is said to be greater or smaller then another, one often asks why they are not also compared in their particularness, to the effect that this white-

ness, which is more intense, is more entitled to be called whiteness than that whiteness, which is less intense'). B3 'state of affairs' as conceived:

Dial. III, 372, 7 - 9: non enim essentia rei ut a propositione designata prior est veritate propositionis, immo simul cum ea, cum sine ea nullatenus possit consistere. C

the entity-aspect of particularness

+

'state of being', 'mode of

being' as such 'being-n~ss~:

Dial. III, 408, 32 - 33: sicut enim de eodem diverse non predi-

22

cantur essenti e, ita nee idem de diversi s: 'for just like differe nt modes of being are not predica ted of one and the same thing, so one and the same is not predica ted of differe nt modes of being either' . Before drawing a general conclus ion from these texts it seems to be useful to add a few words about the word 'substa ntia'. In L.I., 140, 3ff. Abailar d calls attentio n to Boethiu s' differe nt uses of 'substa ntia': (a) pro omni essenti a (iuxta illud Priscia ni: 'signifi cans substan tiarn cum qualita te') (b) 'pure form' (pro illis tanturn essenti is quae per se subsist unt,

nulli scilice t subiect ae materia e adhaere ntes ut forrnae eorurn). In this sense the word refers to the genus generali ssirnurn , which is defined as: substan tia est id quod per se subsist it, or: est

id quod neque est quantit as neque qualita s etc. (cfr. Dial. III, 339, 33 - 35: general is enirn substan tia tota sirnul et eadern in omnibus suis specieb us existit , veluti animal in hornine et equo, aut homo in Socrate vel in Platone ). Abailar d himself does not use the word in this sense (c) the general , specifi c and particu lar names designa ting particu lar subsist ent things: accipit ur quoque hoc nornen 'substa ntia' in designa tione norninurn tarn generali urn quarn speciali urn quarn singula riurn, quae scilice t ipsas substan tias in essenti a signific ant ( 140, 13 - 16) . The third meaning is the usual one with Abailar d. It contain s both the generic and specifi c substan ces (as taken in their particu larness ) which are constit utive of the outside things [for that matter, it should be noticed that Abailar d (Dial. 339, 33 ff.) the use found sub (b) ascribe s to Boethiu s] and the outside things themsel ves (so LNP, 517, 10 ff.; Dial. 84, I - 5; 87, 27 (specia lis substan tia); 91, 8; 425, 15 - 16: ornnis species individ uis suis, sicut et genus specieb us, in substan tia materia liter inest). From these texts the conclus ion may be drawn, now, that 'essent ia'

23

always refers to being in its particularness, mostly the substantial (=subsistent) thing taken as a whole (a 'substance'), sometimes an adjacent quality as existing in a substance. As to 'substantia', Abailard himself seems to use it preferably with the connotation of 'particularnees'. This specific feature of particularness should be further elucidated, now. 4.2 Naming and Particularness The aim of this section is to show that to Abailard's mind every name preferably means a particular entity, rather than an abstract one. When discussing (Dial. III, 332, 2 ff.) the locus a diffinitione Abailard points out the material equivalence of 'animal rationale mortale' and 'homo'. This does not amount, however, to saying that the following implication is true: 'si est animal rationale mortale,

est homo'. Rather, if one attends to the virtue of speech, the inference is not allowed. Only if we attend to the state of affairs (in

casu, the material coincidence of animal rationale mortale and homo), rather than to the virtue of speech proper, we can accept the inference. I give some relevant passages from the text:

Dial. III, 334, 31 - 335, 16: Although the same thing is expressed (predicetur) by 'mortal and rational animal' and 'man' , yet the inference from the former to the latter is not correct, since they designate that same thing in different ways. As is not this inference either: 'if it is a body, it is a coloured thing'. For although that particular mode of being which is attributed (to some thing) by 'coloured' is one and the same as that which is attributed by

'body', yet this inference is decidedly deprived of all stringency, since that thing once is 'named' after its being coloured, once after its being a body. ( •••.•• ) I t does not follow that if something is a rational and mortal animal, then it is a man, that is,

24

if we attend to the property of speech. If, however, we dwell on the state of affairs rather than on the property of speech and pay attention to the material coincidence (identitatem essentie) (of 'rational and mortal animal' and 'man'), then we can undoubtedly accept the inference, to the effect, namely, that either we understand by 'rational and mortal animal' as many beings as we do by 'man' or by 'man' as much as by 'rational and mortal

animal'. Abailard obviously tries to make two points here. First, seen from the formal viewpoint the inference from 'rational and mortal man' to 'man' is not allowed. Some lines before he explicitly said: it is true, the particular man (hominis quidem suhstantiam) is informed by all his substantial forms taken together with that general form (i.e.

animal) and for him to exist the forms gressibile, bipes and perceptibile discipline and many others are equally indispensable ( •....• ) So when animal is formed in man, it is necessary that it is vested with all the forms of man. However, he who says: animal rationale mortale, posits animal only invested with these (two) forms, which, when invested with these alone, cannot be man. Therefore it is not necessary that, if some thing is a rational and mortal animal, that is, an animal invested with (just) these two forms, it be a man (332, 9 - 20). Secondly, from the material point of view that inference is a correct one since there is a natural guarantee for the material coincidence of the two (in fact, nothing can possible be a rational and mortal animal without being a man). Accepting this inference amounts to equating the extension of 'rational and mortal animal' to that of 'man' (tot .... quot) or to giving the same intension to 'man' as

'rational and mortal animal' has (tantum .... quantum). The full impact of Abailard's view becomes clear from his own explanation, given in the next lines (335, 26 - 38), which may be put together with the one he gave before (332, 9 - 20; see above p. 25):

25

Dial. III, 335, 26 - 28: When we give the definition 'rational and mortal animal', we predicate that concrete entity that is man ( sc. of (a) man). Nevertheless, that entity as designated by the name 'man' does not necessarily follow from itself as assigned16 by the definition, provided that we correctly attend to the property of speech. So it is clear what power the property of speech has in 17 sentences. Most of all the primary signification of the words should be attended to, that is, the one which is . d 18 in . t h e wor d itse . lf an d accor d"ing to wh"ic h t h e wor d d esignate itself is imposed, r·ather than to the thing signified 19 which the primary signification is imposed upon. For although the definition and the definitum point to quite the same subsistent entity both by imposition and in the assertion, yet many times they do not point to quite the same 'thing' (feature) in that entity. Indeed,

'rational (and) mortal animal' is attributed to the subsistent entity of man (hominis substantie) in that respect only that the latter is an animal informed by rationality and mortality; 'man' on the contrary, according to its being informed by the other forms, too, which differentiate man. Thus from the formal point of view 'man' (homo) designates, apart from the forms animality, rationality and mortality, also all other forms which, together with the three already mentioned, differentiate man as a specific being. In other words: the formal semantic value of

'man' (homo) is that of '(specific) particular substance', '(specific) complete whole' or '(specific) subsistent entity', a being that is able to exist (c.q. actually exists) as an independent, selfcontained thing. The semantic value of 'rational and mortal animal', on the contrary, is that of an incomplete being as such. It is only the fact that such an incomplete being is always found in the particularness of the complete being man which guarantees that the farmer's occurrence is always accompanied with the being of man. Thus the following points may be stated: (I) from the formal point of view: the intension of MAN is different

26

from that of RATIONAL AND MORTAL ANIMAL (see 335, 11 - 12, 27 - 32 and 34 - 38) (2) from the material point of view: the extension of MAN is quite the same as that of RATIONAL AND MORTAL ANIMAL (see 335, 15 - 16 and 32 - 34). (3) from the material point of view, again: the intension of RATIONAL AND MORTAL ANIMAL as being necessarily joined to that of MAN can be taken for the latter; see 335, 35 - 37: "for 'rational, mortal

animal' is attributed to the particular entity of man (hominis sUbstantie) in this respect only that the latter is an animal informed by rationality and mortality". We should notice, now, the positive statement rather than restriction made by Abailard ('in this respect only etc.'). Next another passage from the Dialectica that will turn out to give similar information . It is found in Abailard's discussion of the locus

a relativis (Dial. III, 406, 31 ff.). When dealing with proposition s such as 'si pater est, filius est' and their possible inferences, he comes to speak about simple conversion and transpositio n of propositional terms in general. He defends the view that, from the material point of view conversion need not be impossible in some cases where it is bound to fail as a result of linguistic circumstanc es (409, 10 ff.). He adds:

Dial. III, 409, 29 - 30; 409, 35- 410, 2: So it is not the state of affairs which impedes simple conversion but again (eadem) the acceptance of the terms transposed ( ...... ) . Therefore it is asserted on account of the same demonstrati on carried out by a word

(ex eadem vocis demonstrati one) that the same is predicated of different things (such as in: 'man is an animal', 'donkey is an animal') or that different things are predicated of one and the same (such as in: 'some animal is a man', 'some animal is a donkey'), and that since 'animal' and 'some animal' both times say (dicant) the same, although neither materially the same (idem in re) inheres in different things nor different things are in what is materially

27

the same. So there is only an identity in signification (secundum vocum denotationem), not according to the particular modes of being. Again, a sharp distinction is drawn between the intension of animal as found in man and as found in donkey, in spite of their significative equivalence. So the following additional points can be made (for (I), (2), and (3), see above, pp. 26 - 27): (4) from the formal point of view: the intension of ANIMAL in 'man

is an animal' is quite the same as in 'donkey is an animal' (5) from the material point of view: the intension of ANIMAL as inhering in MAN is quite different from that inhering in DONKEY. A third illustrative passage is found in the opening part of the same book of the Dialectica (III, 267, 21 ff.), where the author discusses the nature of the maxima propositio, which is basic of certain implications e.g. 'if it is a man, it is an animal' and 'if it is a man, it is not a stone'. He is of the opinion that in such cases no statement is made about the relationship of the things signified, rather such an implication deals with the particular entities

(de essentiis agit). The text runs as follows: Dial. III, 267, 22 - 27: So who says: 'if it is a man, it is an animal', 'if it is a man, it is not a stone', deals with particular entities (viz. man, stone), definitely not with their formal relationships, to the effect, namely, that, if something be a particular man (essentia hominis), it is conceded that he 1:s also a particular animal and denied that he is a particular stone (lapidis.

suhstantia). Likewise, the words 'genus', species', 'oppositum' and so on, as found in the topical maxims, are not designative of certain properties of the things, but of the particular entities concerned themselves

(designativa .... ipsarum suhstantiarum). So the maxim: 'of which the species is predicated, the genus is also predicated', has the following sense: if something be an entity that is a species, such as man or horse etc., then it is also every entity that is their genus, such

28

as anirral, body or substance.

20

So the (corresponding) particular

entities themselves (substantie ipse) are attributed (to the subjects), not some of their formal properties (Ibid. 267, 30 - 37). Here, again, the particularness (that is, the particular inherence in an substantial entity) of specific and generic intensions is stressed: So we can add a sixth point: (6) whenever something is predicated of some other thing, it is particular intension (that is, intension as inhering in a particular subsistent entity) that is designated by the terms involved, not an intensional form taken as such. 5

Does Abailard's notion of 'essentia' include existence?

The conclusion of our previous section was that on Abailard's view the notion of particularness is the central one in the semantic field of names. It may be asked, now, whether or not particularness should imply existence in the outside world. Let us consider some relevant passages. (a) Names, too, are designative of time:

Dial. I, 123, 9 - 15; 20 - 22: As to the fact, then, that verbs are designative of time, this suits also to names, since they are designative of the present time, no matter of whether they are substantival or adiectival nouns. For just as 'white' (album) is imposed on the ground of a present whiteness (ex presenti albedi21 so 'roan', too, is imposed on the ground of the present

ne),

existence of a rational and mortal animal (ex presenti substantia anirralis rationalis mortalis) 22 and when you call somebody man, you are pointing to him as a present rational and mortal animal and the word 'man' is equivalent to 'what is presently a rational and mortal animal' ( tantumd~m 'hominis' vocabulum sonat quantum

'quod presentialiter est animal rationale mortale' < •••••• >.A name, then, determines a thing as inhering ( in some thing) at

29

some time or other (aliquando), such as 'white' (album) signifies whiteness as adjacent and inhering (in some thing) (b) Our author often defines substantia as res per se existens (e.g. Dial. 331, 16; 334, 25; 594, 9; L.I. 140, II; L.N.P. 517, 7 - IO). Well, 'heri' (yesterday) is said (Dial. I, 77, 24 - 27) not to be designative of an existent thing. It may be concluded, accordingly, that the phrase res per se existens refers to existence in the present time. (c) When discussing (L.I. 348, IS ff.) the ambiguity of phrases such as 'erit arribulans', 'fuit arribulans', which can be taken, indeed, either as one dictio, (in vi unius partis) 23 viz. arribulabit ('will walk'), arribulavit ('has walked') or as two dictiones (in vi duarum

partium), Abailard points to a difficulty: L.I. 349, 9 - 17: For if 'will-be-walking' would be accepted as two dictiones (viz. will-be and walking), to the effect, namely, that 'will-be' (erit) should signify its own time which is the future, and 'walking' (arribulans) its own time which is the present, predicating the phrase 'will-be-walking' of that not-walking thing (see 349, 6) would be the same as if were said: 'this not-walking will be a walking-presently'. For 'walking' taken by itself, which is only designative of the present time, covers those who presently walk only. Well, this not-walking does not belong to those who presently walk. Therefore 'will-be-walking' ought to be taken as one verb, as if were said 'will walk' (arribulabit). For that matter, the same holds good for such propositions as 'this old man has been a boy' (hie senex fuit puer). Since 'boy' is a name of those who presently have boyhood (qui in praesenti

pueritiam habent) the proposition could be taken in this sense: 'this old man has been what is presently a boy', which would give a false proposition, of course. (See ibid. 349, 23 ff.; Dial. II, 249, I ff.). (d) A similar discussion is found in Dial. I, 134, 3 ff. where

30

Abailard deals with the meaning of the verb 'est' as a copula:

Dial. I, 139, 7 -

II: Just so it will be false to say of

Socrates who is an old man now, that he has been a boy, provided that 'boy' is taken by itself according to its own imposition which it has on the ground of a present boyhood; the proposition would have the sense: 'he has been one of those who have presently boyhood'; which is clearly false. (e) However, there is found one passage, at least, where our author appears to make a formal distinction between 'being particular' and 'existence' in contradistinguishing things that are opposed one to another in essentia with those that are mutually opposed not only in essentia but also (quoque) secundum existentiam:

Dial. III, 394, 12 - 19: Things that are opposed when taken as particular beings (in essentia), are also (mutually} opposed when taken as really existing (secundum existentiam), such as night and day which cannot exist at the same time. So we can infer about them when taken as really existing (secundum eorum .. i.

•

suus~s

t en t.~am 24 ) : ' i. f it . . d ay, it . is . not nig . h t ' ; accor d.ing to is

the following rule: being one of two opposites in existence, the other fails to be so (existente aliquo oppositorum in existentia,

o.lterum deficit). A similar consideration is put forward more hesitatingly by Abailard in his discussion of the word 'yesterday' (heri). It seems not to designate real (=present) existence. However, Abailard adds: perhaps those who pay more attention to the nature of things than to the imposition of the words when species are concerned, would pretend that by 'yesterday' (heri) a kind of present adjacence is designated which the thing itself possesses because it has existed on the day before, to the effect, namely, that it retains its preterite properties in the present, since it is vested in them. (Dial. I 77, 25 - 78, 1). It seems quite impossible to draw an entirely unambiguous conclusion from these texts. I think, we have to recognize that the opposition

31

between what I have termed 'particularnes s' and 'existence' was a rather vague one in Abailard's mind. In fact, it is rather sophisticated to distinguish between 'existent' = 'having subsistence in the outside world' (c.q. 'belonging (as a particular accidental form) to something in that world') and 'particular' = 'being materialized, whether or not found in the outside world, c.q. belonging (as a particular accidental form) to such an entity'. For that matter,

existence and particularness are not mutually exclusive, but, rather, existence presupposes particularness . The pivotal force of this distinction is that an entity (viz. a mental entity) may be taken as particular without existing in the outside world. 25 Finally, three remarks. First. It is the metaphysical speculation of the 13th century (and afterwards) that made a sharp distinction between 'being' (either pure form or particular form) and 'existence'. From those days. onwards 'essentia' acquired its specific meaning of 'essence', 'true substance', 'true nature'. Secondly. The distinction between what is particular or metaphysically complete (c.q. what belongs to something of that kind) and what really exists is less abstruse for an Ancient or Mediaeval mind as it might be perhaps for a modern one. 'Whatever is real, is an individual', runs the Ancient and Mediaeval adagium. However, as late as the second half of the 13th century philosophers began to take the individual so seriously, indeed, as to consider it no longer a byproduct of (non existent!) prime matter. Thirdly. Abailard's apparent failing to use the words 'essentia', 'sUbstantia' and 'existentia' ('sUbsistentia ') unambiguously corresponds with his hesitant view about the basic question of what exactly is designated by speech (nouns and verbs). 6

Like

Being as a sema.ntic problem in 12th century philosophy 26

his contemporaries Abailard used to distinguish between the copula 'est' (as in 'Petrus est homo') and 'est' secundo adiacens (as

32

in 'Petrus est') (e.g. L.I. 361, 12 - 18). Many historians of Mediaeval logic 27 are of the opinion that, in spite of the clear cut distinction, with some Mediaevals the copula, too, has existential import. Abailard is supposed to be one of them, in that he admits such an inference as 'Petrus est homo; ergo Petrus est' (Dial. I, 137). On the other hand, Abailard (like his fellow-logicia ns) is most explicit in stressing that the task of the copula is just to link up a predicate with a subject (Dial. I, 135, 2 - 17; II, 176, 20). This clearly precludes any existential import of the copula. I shall deal here with Abailard's original solution of the problems concerned. Twelfth century logicians used to link up the semantic problem of being with the verb 'be' (esse). Accordingly, their expositions focused on the copula taken by itself. They were all aware of the ambiguity of that verb when used as copula. Well, Abailard tried to solve the problem in attempting at a new analysis of predication. 6.1 The basic ambiguity of the verb 'est' In L.I. 359, 9 - 363, 24 Abailard discusses the predicative function of 'est' in an extensive way, as he also does in the Logica parvulorum 269, 36 - 276, 39, ed. Dal Pra. Every personal verb (verbum personale) has the double task of both predicating its own meaning or: semantic value: res Verbi and linking up the subject term with the predicate term. Two verbs only can connect something different from their own meaning with a subject, viz. 'est' and 'nuncupatur'; the former has, Abailard says, the unique property of connecting itself

ex ipsa essentia rei with a predicate (360, 9 - 15). This is explained in the next lines (360, 15 ff.). For instance, take the proposition

'Socrates is white'. Although the speaker has the intention of copulating and predicating nothing but 'whiteness', yet by the force of the substantive verb ('est') the substantive noun 'white' (album) is linked up with Socrates essentialiter, since by the very force of the substantive verb, which has the meaning of existence, Socrates is

33

said

28

to be. Two things, indeed, are linked up with Socrates by

the predicate 'white', viz. 'Whiteness' adjacently and 'the white', that is, the thing itself that is effected by Whiteness, taken in its subsistence (essentialiter). However, it is Whiteness alone that is predicated since it is the only thing the speaker intends to link up with the subject. Indeed, not whatever is linked up, is predicated, but only that which one intends to predicate. For he who makes the proposition 'Socrates is white', only argues that Whiteness inheres in Socrates; but if there were another verb to link up just Whiteness 29 with Socrates, to the effect that the speaker needed not touch anything of the subject Whiteness inheres in 30 , no doubt he would use it instead of 'est'. There is, however, - Abailard goes on - only the substantive verb, so that he has no choice. But this verb cannot help coming into play and asserting its own nature, that is, it must bring the fundamentu:m albedinis (i.e. the individual white thing itself) into the game. The result is somewhat astonishing: Whiteness, which is the only thing the speaker intends to for being predicated, is linked up only adjacently, whereas the supposititious child, the particular . th.~ng, is . pre d.icate d essen t.~a l ~"t er, 31 t h at is . as something . wh ite 32 subsistent.

From this passage it seems clear that the proper function of 'est' is to involve existential import, rather than designate some formal nature. In the passage quoted Abailard links up the function of 'est' with norrrinatio: the verb 'est' refers to existence in denoting (norrri-

nare) a form's suppositum (so album in the case of albedo). An important difference, however, between existential import and nominatio is, that the latter denotes a particular thing by presenting it as partaking in some universal nature, whereas the verb 'est' expresses the presence of the particular thing itself. In other words: the nomina-

tio presents to the hearer's mind a thing as being so and so, the verb 'est' as 'being' so and so. The difficulty, accordingly, consists in the unfortunate mixing up of predicating and composing (viz. the subject and the predicate).

34

Although predication is the only thing aimed at by the speaker, composition is an indispensable part of the package-deal. Well, the binding agent used in the act of composing, that is, the verb 'est', smuggles in, as it were, its own nature (viz. signifying existential import), which is, and this is to be stressed, quite incompatible with the universal nature (e.g. Whiteness) predicated (for the white

thing exists in the outside world, not Whiteness). It is true, the deal is not entirely abstruse in as much as the preponderant element, viz. the verb 'est' designating existential import reduces the formal nature intended to be predicated (e.g. Whiteness) to some nature partaken in (forma or natura participata), e.g. (a) white thing (al-

bum), i.e. a particular thing partaking in Whiteness (affectum albedine). The whole operation, however, still remains a misalliance in that predication proper is concerned with some formal nature alone (e.g. Whiteness), and copulation proper does imply existential import and particularness. For that matter, the verb 'est' itself cannot escape some degeneration either, as it has the improper task of copulating non-existent entities. 6.2 Abailard's solution based upon the imposition of names The problem of the copulation of non-existent entities is discussed by Abailard in the analysis of two famous propositions: 'Homerus est

poeta' and 'chimera est opinabilis' (cfr. Aristotle's De interpretatione) (21 a 25 ff.). In the Dialectica (I, 136, 19 - 36) the author tries to solve the problem by giving a depth-structure analysis of the propositions involved. Indeed, the terms in 'Homerus est poeta' are not to be taken in their proper meaning; an existing poem, not Homer as existent is referred to; as in 'chimera est opinabilis' somebody's thinking of a chimaera is meant, there is no question of the property 'being conceivable' (esse opinabile) which is attributed to something existent. Well, Abailard goes on (136, 36 ff.), all

35

predication brought about by means of the verb 'est' should be considered improper, since the verb 'est' unlike other verbs does not involve its own content (res verbi; i.e. existential import), but only exerts the function of copula. The proposition 'Petrus est homo, resp. albus' is instanced. It is true, we may infer: Peter is a man; therefore Peter exists, but, Abailard says, the conclusiveness probably (fortasse) rests on the existential import of the name 'man', not on any (supposed) existential import of 'est' when used as copula. So Abailard's attention is focused on the imposition of the names predicated. It leads him to a new interpretation of propositions such as 'Homer is a poet' and 'a chimaera is conceivable'. After a first attempt at a new interpretation of the propositions involvea, 33 our author puts them in a-somewhat larger perspective in comparing them with propositions concerning the past and the future. 6.3 The verb's tense linked up with the name's significate as one single sememe As we have seen above (pp. 33 - 35) the nucleus of our problem is the unfortunate combination of the two functions of the verb 'est'. Well, Abailard's definitive solution consists in a new interpretation of the composition of the verb with the name predicated. He proposes

(Dial. I, 138, 14 ff.) to take phrases such as 'is a man' (est homo), 'is a white thing' (est album) or 'is something conceivable' (est opinabile) as one single expression, that is, 'esse hominem', 'esse album', and 'esse opinabile' respectively. So when in explaining the proposition 'Homer is a poet' Aristotle says: "the verb 'is' is accidentally predicated of Homer, for it is because he is a poet, not in his own right, that the 'is' is predicated of him" (De interpr. 21 a 26 - 28), Abailard expounds: since 'being a poet' (esse poetam) . . . 1 e expression . h_ere, 34 t h ere is . no pre d.icat1on . is JUSt one sing proper, but 'esse' is part of the predicate. Likewise, every other copulative use of 'est' is not a predication in the proper sense, since esse

36

is not said, taken by itself but as linked up with the name predicated as one single sememe (e.g. 'being a poet'). The same applies to propositions with a preterite or future tense, Abailard adds (ibid. 138, 26 ff.; cf. L.I. 346, 25 - 350, 18). All propositions such as 'he will be sitting' (iste erit sedens) are obviously false as long as erit and sedens are taken in their proper senses, since, then, the proposition means: 'he will be something that is sitting presently'

(erit unum de his que presentiaZiter sessionem habent), which does not apply to somebody who does not sit now but will sit tomorrow. Abailard also gives an extensive discussion of the proposition 'senex fuit puer' which became a sophism of high repute later on. All propositions of this type are false unless the verb and the name predicated are taken together as one sememe. If so, they have the right sense: 'he is a future sitter', 'the old man is a former boy', and so on. Well, Abailard apparently intends to make it clear that this view of predication as well-suited to solve the previous problem of predication (see above, pp.34 -35) in that a formal nature (such as WHITENESS) and existence (existential import) are each taken as partial sememe and are melted together into one new sememe. 6.4 Abailard's view of the consignificatio temporis All this may be further clarified by taking the consignificatio temporis into consideration. Boethius had regarded the copulative verb

'est' as exempt of any designation of time, e.g. in propositions such as 'Deus fuit ante tempora', whereas when used of creatures it is designative of time (In Arist. Periherm. II, 51, 3 - 52, 9; cf. Abailard, L.I. 333, 17 ff.). The same author knows of another, cognate use of the same verb, viz. where the present tense is not taken strictly for ~e present time but also seems to cover other times (omnitemporal), or even seems to be exempt from any time designation (atemporal). It is termed praesens quad continuat praeteritum et futurum, and was to be called praesens continuum (or: confusum) from the 12th

37

century onwards. As to contemporaneous views we are told by Abailard (L.I. 346, - 24) that some people attributed designation of time to verbs when indicating an action or passion, but not when indicating a state of affairs. On their view a similar ambiguity was found in the verb 'est', since it either may be equivocally taken as meaning all kinds of action and passion as an equivalent to such verbs as 'amo',

'lego' and so on, or as the substantive verb (verbum substantivum) designating all things in existentia, that is, in their subsistence (or: particularity). Abailard, however, rejects this view and assigns designation of time (consignificatio temporis) to all verbs (and participles) whatsoever as their specific characteristic that marks them off as different from names. The time designation is explained by Abailard in the manner discussed above (n. 6.3). It should be remarked in this connection that in L.I. 350, 21 - 26 Abailard leaves open the possibility that such phrases like 'erit legens' are ambiguous, in that they may also be taken as consisting of two dictiones. So the proposition

'iste legens eras erit legens' may stand for: (I) this man who presently reads will be to-morrow

somebody who presently reads (false), or: (2) this man who presently reads will read to-morrow, which may be true. Just so, the proposition 'nullus puer erit senex' is to be considered true when the words 'erit senex' are taken as two dictiones and, accordingly, the name 'senex' stands for 'somebody who is presently an old man'; on the other hand, if one takes 'erit

senex' as one single expression, the proposition is obviously false (L.I. 350, 32 - 39). 6.5 'Actuality' ('Particularization') versus 'Facticity' ('Existence') To my mind the line of thought which underlines the semantic views discussed above can also be detected in the basic opposition made by

38

the Mediaevals between two distinct types of realization which I shall term 'Actuality' and 'Facticity'. I understand by 'Actuality' (or: 'Particulariza tion'; adjectivally: 'actual', 'particular') the realization of a formal nature in the present or preterite or future time ('omnitempora l'), or even taken quite exempt from any particular time ('atemporal'). 'Facticity' (or: 'Existence'; adjectivally: 'factual', 'existent') stands for a realisation of a formal nature at the speaker's time. From this point of view the praesens continuum (see above, p. 37) can be taken as covering all 'actual' being which is not 'factual' ('existent'). Likewise, the two distinct interpretation s of such propositions as 'Petrus est (erit, erat) homo' which are held by Abailard to be equally acceptable (see above, pp. 33 and 36 ) may be traced back to the distinction of actuality and facticity. As a matter of fact this proposition may be taken as a description expressing the formal relation between being 'actually' a man and being (a man named) Peter, and, then, the verb 'est' does not have existential import. On the other hand the proposition may express the 'factual' being a man as it is found in Peter and, in that case, existential import is implied, to the extent that the inference 'Peter is a man: therefore Peter

exists' is allowed. To my mind, Abailard's hesitation on this score in Dial. I, 137, 3 - 6 is to be explained in this light: "Nee quidem, quantum ad eius interpretatione m pertinet, ex eo quod dicitur· 'Petrus est homo' inferri potest 'Petrus est', sed fortasse (sic:) quantum ad predicationem 'hominis', quod existentis rei tantum nomen est". We may conclude, now, from the foregoing: (I) the following distinction seems to be of some use:

1 .1 'particularnes s of being' or 'particularisa tion' is the realisation of a form (forma, natura) at some particular time (either the present, or the past, or the future, that is, no matter whether or not it 1:s, was or will be existent), or even a

39

realisation only conceived of as possible 1.2 'existence' is the realisation of such a

particular nature

at the present time (that is, at the speaker's time). (2) In Abailard's (rather hesitant) view names seem to be endowed with two levels of meaning, at least (afterwards called modi sig-

ni ficandi) : 2.1 a name (noun) by its own nature (secundum propriam inventio-

nem or impositionem) refers to existent things alone 2.2 as a result of its occurrence in a syntactic formation (con-

structio), esp. in combination with a verb of a tense other than the present, a name's meaning is reduced to a more vague and confused level on which it only designates a certain form's particularisation, be it in the past or the future, or even a merely possible one. No doubt, the latter semantic level is an ambiguous one, varying according to different types of abstraction made by the speaker. A discussion of further details is dismissed, at present. It seems more useful to compare Abailard's views on the matter which those found in an utmost important tract composed in the same century, presumably in an Abaelardian circle, the Tractatus de proprietatibus sermonum. 7

The meaning of names in the "Tractatus de proprietatibus sermonum"

This important treatise on logic (henceforth TPS) which may be dated about 1200 35 contains a remarkable discussion of nomen. Its title containing the specific Abailardian word sermo, which is found nowhere else in this specific sense, clearly hints at the anonymous author's familiarity with the School of Abailard, presumably that of Melun. 7.1 The primary task of names

40

The most striking feature is its abundant use of labels pertaining to the psychology of knowledge. As a matter of fact sermo is defined as a kind of intermediar y between the outside world and our intellections (called intentiones ), and it is said to be determined by its relation to thought (as well as by its relation to the extramental world). The mental character of the act of meaning is stressed (nos exprimimus per sermones proprie quod concepimus intra; 707, 23 24). Universal names designating genera and species are said (709, 32 ff.) to be related with the intellect (significare intellectui ), that is, in as far as they are apprehended by the power of intellectio n

(virtute intelligibi li). Next, significatio n is divided into supposition and copulation. Supponere (to supposit) is defined as to designate some thing under some form (designare aliquid sub aliqua forma). He who first 'named' (nominavit) existing things named them according to their being given in the outside world, that is, according to either the substantial or the adiacent mode of being (711, 26 - 28). The substantiva l name signifies what is constituted in full being (constitutum in pleno esse; 711, 32); in other words: "what has a complete entity or self-contain edness" (habet esse perfectum; 711, 33); "that name is called suppositiva l properly and according to its primary invention, which is the name of a substrate, or substance, as it is given to it according to the perfect form of that particular entity" (secundum formam perfectam illius substantie; 711, 35 - 36). So it signifies a self-contain ed thing as self-contain ed (unum ut unum), for it signifies an existent thing under its own form, not under some form which is said to be related to that thing (signifi-

cat enim rem que est, sub sua forma, non que dicatur ad illam rem), but under the form which is proper to, and part of, that thing (712, - 3). A similar notion of unity and self-contain edness is already found in Abailard's discussion of what a name refers to properly: L.I. 48, 31 - 40: There are some people who ( •...•• ) call a concrete man (hominem vero compositum, viz. composed of matter and

4J

form) a multiple substance rather than a simple one, that is, they call him a plurality of substances (muUas pluraliter). ( ...... ) . On the contrary, we cal 1 a particular man a thing simple by nature, which, by the operation of nature alone, is united into an entirely simple person.

Ibid. 50, 19 - 21: So the whole substance of an individual is said to be found in its species (tota substantia individui sui species dicitur), since 'individuum' does not indicate any nature or form that is not covered by 'species'.

Dial. III, 332, 25 - 28: For if something is a man, it is informed by bipedality and all other substantial forms of man, which all are reasonably understood by the name 'man' according to Aristotle's saying: "genus and species mark off the qualification of substance". From these passages it is sufficiently clear that, from a metaphysical point of view, Abailard energetically rejects what is called later on the doctrine of the plurality of forms. But now we are more interested in his semantic views. Well, they amount to saying that by 'naming' one single form inhering in a thing one designates the whole thing, because of the material identity of substance and thing

informed by that substance's form. Well, since a name's primary task is to designate the substance of a thing, that is, to use the wording of TPS, a thing taken in its full entity (in pleno esse) or its self-contained ness (ut unum), its primary semantic value is the denotation of a subsistent entity. Well, accordingly it is this semantic value which applies as far as possible, that is, so far as it is not impeded one way of another by anything else. Thus a name's ambiguity (in signifying both substantial entity and formal nature: proprium est nominis significare substan-

tiam cum qualitate) is weakened to the extent that it preferably designates a thing in its particularness , in full entity (in pleno esse).

42

7.2 The semantic role of abstraction As is well-known

36

the Roman grammarians (following the Greek

Apollonios Dyskolos, 2nd cent. A.D.) looked upon the property of an appellative nomen (noun, name) as to signify 'substance and quality'. So Priscian, Inst. gramm. II 18 (55, 6 Hertz): proprium est nominis

significare substantiam et quaUtatem. The formula is commonly interpreted in twelfth century grammar as 'to designate an individual 37 thing and the universal nature (forma) which it partakes in'. Therefore, from the logical point of view there is a certain internal tension in the semantic field of an appellative noun (name): on the one hand it denotes an individual thing (substantia), this being the appellative function proper of the noun and, on the other, it also connotes some universal nature (forma or qualitas). Thus two foci are found in the twelfth century theory of meaning:

nominatio or appellatio ('denotation') and significatio ('connotation'). However, since the latter term is commonly used rather loosely for the designation of individual things as well, it is equivocally used in a broad and in a strict sense: appellatio (nominatio) ='denotation' significatio s.l. ('meaning')

-{ significatio s.s. = 'connotation'.

As has been already said above (p. 41) TPS pays much attention to the psychology of knowledge. 38 So before defining significatio the author discusses (709, 6 ff.) the question of what faculty of the soul (cui virtuti anime) significative words are concerned with. He clarifies the question by pointing out that the first name-giver, 'named' things after he had apprehended them and had thought about the things apprehended (postquam res apprehendit et cogitavit de

apprehensis). He continues: TPS 709, 9 - 19: So the question is whether (1) he named things

43

according to his apprehension of them taken by themselves (prout apprehendit res in se), or (2) according to his imagination, or (3) according to his intellection. ( .•..•. ) . Well, it seems that names were not imposed to things taken by themselves, that is, as things are apprehended as they are in themselves (simpliciter

in se). It is not necessary, indeed, to give names to things taken as they are by themselves and as long as this is the case (prout in se sunt et dum in se sunt). Indeed, as long as they are sensed (i.e. apprehended as they are), they are sufficiently known. Nominations, however, have been made for the sake of cognition and because of a thing's absense, not of its presence. Thus using names is clearly opposed to demonstrating things that are present, since the latter may take place together with our sensing things. Naming things and using the names is a means of dealing with things that are (taken as) not present; this happens when things are imagined or thought of. Then, the meaning of proper names is said to be concerned with imagination, that of appellative names with the intellect. Next, the author asserts that the primary task of the substantival names is to signify things as self-contained units (unum ut unum), or according to their being established in full entity (constitutum in pleno esse); see above p. 41 . The adjectival name, on the other hand, is to indicate what is an accident and that according to the mode of inherence, which is to be in a substrate. Therefore the adjectival name indicates an accident as being in a substrate, that is, as being adjacent to the substrate that is itself established in full entity (TPS, 711, 28 - 32). In the following passage, which seems to be of the utmost importance, our author discusses four different ways of thinking of things:

TPS 712, 24 - 713, 4: A name is primarily called substantival or . . . . . . . subpositival in t h at 39 it signifies a substance as a sub stance. 40 For a substance (sometimes) happens to be thought of not simply in

its self-containedness (non ut substantiam simpliciter) but accord-

44

ing to a certain dependence (quodammodo dependenter). In this way every name of a differentia signifies, such as 'rational', . . . 41 'sensible' and the like, according to the first mode of speaking. A name that signifies an accident as an accident (per modwn acci-

dentis) is called an adjectival name; so 'white', 'sane'. In this way, namely, an accident is thought of as being in that through which it is (as long as it is and is preserved in being). However, since it is not only possible to think of an accident as being in a subject, but also as to the accident itself (to consider) what it is, taken by itself and not related to its subject, therefore it is apprehended so to say through abstraction as a thing being by its own nature (per se) and in so far as it is signified (connoted) as an accident (prout significatur accidens). And when 42 it is thought of in this way, it is signified as standing by itself in the apprehension and not as related to something else occurring in that kind of thinking. So, after their similarity with substantival names it has been said that abstractive names, such as 'whiteness', 'blackness', or 'sanity' are substantival and suppositival. Indeed, something else can be related to it (viz. such an abstractive name); besides, such names can be made the subject term (of a proposition) so that they may be spoken of. However, such abstractive names are doctrinal names rather than given according to the real existence of the things (named). So they have been as it were 43 invented afterwards for the sake of learning. So our author knows of a fourfold abstractive knowledge: (a) that of the particular thing taken in its full entity:

substantia ut substantia (b) that of a substantial form informing a particular (individual):

substantia non ut substantia (c) that of an accidental form inhering in a particular (individual)

(accidens ut in subiecto) (d) that of an accidental form taken as if it were an independent

45

one (accidens ut per se stans); in this case abstractive substantival names are used ('whiteness ', 'blackness' and so on). By the way, this fourfold division runs entirely parallel with the fourfold classificati on of 'things there are' given by Aristotle in . the second chapter of his

~ . Gategor~ae.

44

When inserted into the semantical scala the above scheme comes out as follows: (a) what is signified by 'this man', 'this stone' etc. (b) what is signified by 'this sensible', 'this rational' etc. (c) what is signified by 'this white', 'this (particular) whiteness' etc. (d) what is signified by 'whiteness' . As is easily seen, (d) has a separate position, since the thing signified can in no way belong to the outside world. The other three, (a), (b), and (c), are all concerned with an individual in the outside world, but in rather different ways. The cases (a), (b), and (c) are all opposed to (d) in that they are concerned with (substantiv al or adjacent) forms taken together with the substrates they inhere in. In that connection it should be noted that most Mediaeval authors were inclined to take a form together with its substrate (that is, as

forma participata ) rather than in its own right. I give two examples from quite different contexts. As is well-known, Mediaeval metaphysics , substantial ly influenced by Aristotle's anti-Platoni sm, preferably took the forms (eide, formae, naturae) as forms invested in matter (formae materiae), the forms being primarily actualisatio ns (actus essendi) of particular beings. See e.g. Thomas Aquinas: - unumquodque (sit) id quad est per suam formam (S.Th. I, q. 5, 5 c). - forma, inquantum forrna, est actus (ibid. q. 75, 5 c). - materia secundum hoc acquirit esse in actu quad acquirit formam (ibid. q. 75, 6 c). - forma autem per seipsam facit rem esse in actu, cum per essentiam

46

suam sit actus, nee dat esse per aliquod medium; unde unitas rei compositae ex materia et forma est per ipsam formam, quae secundum seipsam unitur materiae ut actus eius (ibid. q. 76, 7 c). - forma nihil aliud est quam actus materiae (ibid. q. 105, I c). - forma est qua aliquid est; est enim actus (Contra Gentiles II, 43). Our chief witness

is Aquinas in his discussion of the proposition

'Deus genuit Dewn' (S.Th. I, q. 39, 4). He says that in virtue of speech not only the 'thing signified' (res significata, here for 'the significate', or form) is to be attended to but also the mode of signifying. Well 'homo' properly signifies the form as invested in the substance, that is the particular entity:

S.Th. I, q. 39, 4 c: Sed in proprietatibus locutionum non tantum attendenda est res significata sed etiam modus significandi. Et idea, quia hoc nomen 'Deus' significat divinam essentiam ut in ha-

bente ipsam (sicut hoc nomen 'homo' humanitatem significat in supposito), alii melius dixerunt quod hoc nomen 'Deus' ex modo significandi habet ut proprie possit supponere pro persona, sicut et hoc nomen 'homo'. As to such nouns as 'man' (as opposed to 'God') Aquinas adds (ibid. ad 3) that they primarily designate particular entities: Ad tertium dicendum quod aliter se habet hoc nomen 'Deus' ad supponendum pro persona et hoc nomen 'homo'. Quia enim forma significata per hoc nomen 'homo', idest humanitas, realiter dividitur in(= is distributed over) diversis suppositis, per se supponit pro persona, etiamsi nihil addatur quad determinet ipsam ad personam. Unitas autem sive communitas humanae naturae non est secundum rem, sed solum secundum considerationem. Unde iste terminus 'homo' non supponit pro natura communi nisi propter exigentiam alicuius additi; ut cum dicitur: 'homo est species'. In this connection one should remember Thomas' statement that being in its substrate is an essential notion in the concept of 'forma': ....

47

cum de ratione formae sit quod sit in eo cuius est forma (S.Th. I, q. 40, I c). Here William of Sherwood's remarks about the proper meaning of names also deserve our attention (Introd. 78, 7 ff. ed. Grabmann; discussed above, p. 9). Every name, he says, signifies a form only, not taken separate.ly, but insofar as it informs a substance bearing it. For this reason it makes us in some way have an intellection of a particular, concrete entity. A name used in the predicate also makes us have an intellection of the form of the particular entity that is the subject. 8

The semantic stratification of appellative names in Mediaeval Logic

As early as in Abailard's days the appellative name apparently was considered having a two-level stratification (see above, p. 40 ) : (a) a name by its own nature (sec. propriam inventionem or imposi-

tionem) refers to existent things alone; in this case its basic level is concerned (b) as a result of its occurrence in a syntactic formation (constructio), the name's meaning, however, is reduced to a more vague and confused level on which it only designates a certain form's (forma, natura) particularisat ion covering any concretisation in any time or even in mere imagination. This picture runs parallel with the distinction between two kinds of semantic particularness as conceived of by human thinking, viz. (c) existence = the factual occurrence ('realisation' ) of a thing in the outside world (d) particularness = the 'reification' of a form as thought to

exist as a complete whole (or: a self-contained unity) in the outside world. Well it is remarkable that whereas (a) precedes (b), the relationship between their respective counterparts is reserved; indeed (c) presup-

48

poses (d). The sphere in which the semantic operations take place is the grarmnatico-log ical syntax, called constructio by the Mediaevals; the main rule governing every constru.ctio is - at least in the view of the greater part of the Mediaeval logicians - that a term's actual meaning is determined by its occurrence in a proposition ('contextual approach'). Thus the semantic pattern can be compared with a tissue of which the warp is the intrinsic semantic stratification of the names, and the woof is formed by their syntactic (or more generally: contextual) position. Now, the whole semantic operation seems to be governed by this fundamental rule: (FR): A name's basic semantic level (that is, its existential .import, c.q. its . . 1arness ) 45 is . maintaine . . d most so l i'd k.ind o f particu

as far as possible, that is, as long as the name's occurrence in some syntactic (contextual) position does not affect its semantic value proper. To be sure, there are quite different types of syntactic pattern: (I) that which is characterized mainly by the subject-predic ate relationship. Supposition theories are substantially based on that relationship (i.e. the P S relationship) 46 (2) that which is determined by the use of special verbs (c. q. special

terms)

2. I that which is determined by the use of Verba quae positionem existentiae faciunt (to mark them with the label found in the . . ., . 47 . Trac. t de Un~vocat~one monacens~s ); here the famous rule applies: presens confusum non tenet presentis usum 2.2 that which is determined by the use of Verba quae ad enuntia-

bilia pertinent (verbs of intensional attitudes), e.g. 'scio', 'desidero' etc. 2.3 that which is determined by the use of modi (termini qui modi appellantur), e.g. 'verum', 'falsum', 'possibile', 'necessarium' etc.

49

It would be very useful, indeed, to undertake a close analysis of the Tractatus de Univocatione Monacensis on this score. Finally, I will briefly sum up some of the important items of Mediiaeval semantics which may be fitted into the frame-work of what I have labeled the 'semantic stratification of appellative names'. First. There is the distinction of esse actuale and esse habituale as adhered to by many 13th century authors but energetically rejected by Roger Bacon, whereas William of Sherwood turns out to stand some. . 48 . . where half-way between Roger and the maJority. The point at issue is the significative force of an appellative noun. Whereas others commonly accepted a name's referring to an esse habituale (that is, being common to pre"sent, preterite and future being and even to what actually is and what actually is not), Roger most strictly held that even in such metaphysical propositions as 'orrmis homo de necessitate est animal' the subject term can only refer to actually existing things (therefore they are all false on Roger's view). William, though admitting the distinction between esse actuale and esse habituale, regarded such propositions as equivocal. This reminds us of William's view that a name's meaning is determined by the language users rather than by speech itself (Syncat., 52, 25 - 26). 49 The pivotal point of this controversy seems to be the different application of our F.R. On Roger's view, for instance, the determination 'de ne-

cessitate' in propositions such as 'orrmis homo de necessitate est animal' is unable to strip an appellative noun of its primary function of signifying only existing things, whereas his opponents are apparently of the opinion that that phrase compels the noun to withdraw to its second semantic level of designating just an esse habituale, with the result that the proposition is true. 50 Secondly, the problems concerning verbs expressing a mental attitude may be looked at from the same point of view. To quote Abailard (L.N.P. 531, 9 -

13; cfr. also above, pp.

4 -

5 ):

When it is said: "I want a hood (desidero cappam); well, every

50

hood is this or that hood", yet it does not follow that I want this or that hood. If, however, one would say as follows: "I want a hood; well, every one who wants a hood is wanting this or that hood; ( therefore I am wanting this or that hood ) ", then, indeed, the argument would go on correctly. However, the assumption would be false,then. 51 This much· is certain, Abailard rejects that in 'I want a hood' and 'every hood is this hood

or that hood' the term 'hood' has the same signification. As a matter of fact the term 'hood' in the former proposition, unlike that in the latter proposition, does not designate a hood actually existing, (except in case, I have some particular hood in mind, of course). So we have to conclude that the verb 'desidero' governing the object

'cappam' precludes us from taking it for an actually existing hood and compels us to understand it in the second-level-meanin g of 'a concrete, particular, hood', whether or not actually existing. 52 At a later stage, as is well-known, the word-order was regarded as significant in this respect. For example, 'promitto tibi equum' 'I promise you a horse', whereas 'equum tibi promitto' ='there is a horse and I promise you that particular horse'. Thus the word 'e-

quum' preceding a verb expressing a mental attitude maintains its own existential force, which, however, is bound to be reduced to the second level meaning (that is, a 'particular' horse, whether or not actually existing) whenever it is preceded by such a verb. Thirdly, there is the well-known controversy about 'cuiuslibet

hominis asinus currit' as opposed to 'asinus cuiuslibet hominis cur>rit'. In 1277 Robert Kilwardby condemned the view that both propositions had the same meaning. It is precisely the infraction of our FR (see above, p. 49 ) that is condemned: quod non est suppositio in

propositione magis pro supposito quam pro significato. As late as the 15th century the issue was still eagerly discussed by Peter of Mantua and Paul of Venice. 53 Finally. The general rules

given in the tracts De probatione pro-

positionum (of which Richard Billingham' s Speculum puerorum is the most

51

famous) as to the modus exponendi (especially the correct order of the exposition) seems to be basically concerned with the same matter. Billingham's example is 'tu differs ah hoc; et hoc est homo; ergo

differs ab homine'. This argument is to be rejected; the conclusion however, 'ergo ah homine differs' is correct, we are told. The fallacy occurs whenever the general rule is neglected: quandocurnque

sunt duo officialia vel exponibilia, vel unurn officiale et aliud exponibile, positurn in aliqua propositione, primum debet primo ordine exponi vel resolvi .vel probari per suurn officiurn. See Billingham, Speculum puerorurn ed. Maieru, pp. 373 - 4. One can imagine, indeed, that Paul of Venice speaks of 'the most noble rule of all logic•. 54 No doubt, it is Abailard who initiated many developments in Mediaeval semantics. So I have considered it useful to draw the attention to the achievements of this great master in the field of logic, since 'the logic before Ockham' cannot be properly understood unless Abailard is recognized as the man who stood, in many respects, at the craddle of fourteenth century logic.

52

A more extensive discussion of this matter can be found in L.M.de Rijk, The Semantic Impact of Peter Ahailard's Solution of the

Problem of Universals, in: Petrus Abaelardus in der Forschung des XX. Jahrhunderts (Acts of the Internationale Studientage - Petrus Ahailardus Trier v. 16 - 20 April 1979, forthcoming). Logica nostrorum petitioni, ed. Geyer, (Munster 19·33), pp. 505 - 533, henceforth quoted as LNP. 2

3

'intellection' = 'act of understanding '. See also Peter T.Geach, Logic Matters, Oxford 1972, 137. 5 It should be noticed, that in Abailard's view it does exceed the area of an individual's thinking, since its 'being there' is 4

founded on the human institution of common usage. See e.g. LNP, 524, 22 - 23, and the paper quoted (above, n. I). 6

See L.M.de Rijk, Some new Evidence on twelfth century Logic:

Alberic and the School of Mont Ste Genevieve (Montani), in VIVARIUM, 4 (1966), [I - 57), 12 - 22. 7

Cfr. Roger Bacon, Sumule dialectices ed. Steele, 281, 19 282, 3 (in 281, 21 one should read predicata instead of Steele's

predicamenta). 8

I take subiecti as an explicative genitive.

9 Cfr. Summe Metenses (in my Log. Mod. II I, 467): Sed quia predicatum forma est, ideo non est in eo ponere per indifferentiam quad est(= suppositum, substance) and quo est(= form), sicut in subiecto. IO II

which (quam) refers to thing (rei), not to form (forma). Cfr. the Tract. de intellectibus, pp. 745 - 7 ed. Cousin

(=pp. 117 - 120 ed. Urbani Ulivi).To

my mind the arguments brought forward recently in favour of the authorship of Abailard himself

are conclusive, indeed; see L.Urbani Ulivi, La psicologia di Abe-

lardo e il "Tractatus de inteUectibus'; Roma 1976, esp. pp. 95 - 100. 12 Cfr. L.I. 331, 6 - II: Illud etiam sciendum quod non est idem intellectus dividens qui (quod Geyer) abstrahens. Nam dividens dicitur qui plura sic attendit ut alterum ab altero separet, sicut

53

facit intellectus negationis. Abstrahens vero dicitur qui unum sic attendit quad alterum non capit. Ille utrumque accipit vel attendit sed abinvicem dividit, iste alterum tantum accipit nee ullomodo alterum at tendi t. 13

and per ahstraetionem, of course, in as far as this whiteness

is abstracted from other forms informing the same thing; see above, pp. 14 - JS. 14

For substantia = essentia, see Dial. 84, I - 2 (quoted below,

p. 19), 87, 27; 91, 8; 194, 4; 408, 33 - 34 (quoted below, p. 19); 425, 12 ff. For the definition of substance, see ibid. 331, 15 - 16; substantiam dicimus rem per se existentem (cfr. 594, 9); 334, 25: res per se existens, idest nullo egens subieeto. 15

one should supply isibilis', 'cr>eati-

vus', 'calefactivus', translatable (perhaps) as 'apt-to-laugh', 'apt-to-create' and 'apt-to-heat', similarly connote entities, conceived of as real "passiones" or as so-called "r>espectus aptitudina-

les vel potentiales 11 • 23 There must exist, for example, instances of risibility (sic) inherent in things apt-to-laugh. But among the terms expressive of possibility is to be counted the word 'possible' ('possibile') itself. Consider the sentence: (B) Creature x is possible.

396

Assume that one referent is unambiguously designated and that the sentence is true. According to the Assumption of inherence, sentence (B) is true because of some dependent entity, namely the possible being of creature x. Such a possible being is of course very different from what, 24 Ockham presents us with. In the first under the same appellation, place, we have here a species of dependent being. To see that it will naturally be conceived of as actual, one need only add the plausible assumption that dependent entities may inhere only in actually existent things, and are therefore themselves actual. As evidence that such a concept of possible being was indeed abroad, we may cite Walter Burleigh. On a page contained in the De

Puritate,

25

we discover that 'possible being' is equated with 'being

in its causes'. But what exists in a cause exists, and is therefore actual. Such is the concept of possible being which seemed prima facie so perplexing but is perhaps less so now that we have traced it back to its origin, namely the Assumption of inherence. But we can also recognize that it is an entire body of doctrine that Ockham opposes when he both eliminates' as unwarranted the Assumption of inherence and rejects its natural offspring, namely the 26 supposedly connoted by terms expressive of numerous "parva res" relations or of possibility; all are denounced as "false imaginations1127 with possible being - conceived of as a species of dependent being - among them. It remains to be seen by what analyses Ockham replaces those which are dependent upon the Assumption of inherence. Accordingly, we shall examine the accounts Ockham provides of the truth-conditions of those sentences which contain as predicates terms expressive of relations or of possibility. (i) Terms expressive of relations can always be replaced by their expansion (i.e. their "definition quid nominis") whereby it becomes

397

apparent that, if some objects are denoted by the term, others yet, which however equally possess autonomous being, are connoted by it. For example, 'father', or its expansion, e.g. 'animal having a son', denotes, say, John (among other individuals) and connotes Peter, who is John's son. 28 But John and Peter are of course "substances" existing independently from each other and from any other (created) substance. Now consider the sentence: (C) John is a father. which we assume to be true. Ockham accounts for the truth of (C) as follows: 'father' truly applies to John because John is indeed so related to someone else (Peter) that he is his father. 29 But this account involves no entity such as paternity, nor in general any "internal relation". In fact, Ockham may be regarded as ingenuously exploiting the notion that terms of this category have an expanded form (a definition quid nominis) to the purpose of putting monadic predicates to a truly relational use, thus allowing syntactical form and ontology to part company. If any principle replaces here the Assumption of inherence, it is only a very general version of the Principle of Correspondance according to which true sentences must assert things to be as they are. 30 (ii) Terms expressive of possibility are subjected to a yet different type of analysis. Sentences in which they appear are to be systematically reformulated (in a "better" language) so that the function of expressing possibility is shifted entirely from the term unto a mode (as present in the verb 'can'). 31 Consider for example the following sentence: (D) The somber man in the corner is apt-to-laugh. (D) is a sentence of an "inferior" language, misleadingly suggestive of some entity to be connoted by the predicate term. The counterpart of (D) in the "better" language is: (D') The somber man in the corner can laugh.

398

The misleading suggestion has disappeared. No particular entity at all is required by the immediate truth-conditions of (DI)' since 32 that the truth-conditions of (D') is a modal sentence and we know modal sentences are given by Ockham in terms of the possible truth of other sentences, namely contained non-modal ones. Let us call the principle which requires the rephrasing in a "better" language of sentences containing terins expressive of possibility the "Principle

of modal expansion". The same Principle enjoins to reformulate (B) as (B') : (B') Creature x can exist. But the reformulation of (B) as (B') is sufficient to reveal the 33 vanity of positing an entity such as a thing's possible being. On the other hand it does yield the "purely modal" concept of pass-

ib le being as a thing which though it does not exist yet can exist. The following sequence is now clear: the "purely modal" definition of possible being is an elementary application of the Principle of modal expansion; but that Principle is defeated as long as the Assumption of inherence rules; in short the "purely modal" concept of the possible is subordinated to the rejection of the Assumption of inherence; but since the latter required entirely new principles of logical analysis, one may regard the notion of a possible -though non-actual -- entity as an outcome of the revolution in logical analysis brought about by Ockham. Among the finer products of logical analysis, undertaken in this new mode, must be cited Ockham' s treatment of some of the more stubborn theological puzzles. We shall find that non-actuals prove to be theologically indispensable, a fact which seems to have escaped even Mac Ay's notice. One puzzle bears on the possible being (esse

possibile) of creatures, the other on their intelligible being (esse intelligibile). Consider again sentence (B) and also the following sentence: (E) God is capable of creating creature x.

399

Just as (B) suggested as an entity the possible being of creature x, so (E) suggests as an entity the capacity-of -God-to-cre ate-creature-x. Both entities (conceived of as dependent realities) are fictitious and indeed all temptation of positing such things disappears when one substitutes (B') for Band for (E), (E'): (E') God can create creature x. 34 In fact two perplexitie s regarding possible being arise, according to Ockham, from incorrect logical analyses based on (B) and on (E). The first consists in inquiring about the production of a thing's possible being. If there were such an entity, a causal account of it would indeed be required, as it would for any actual thing dependent or autonomous. But, of course, there is no such thing. The second perplexity pertains to the order of subordinati on between a thing's possible being and God's capacity to create the thing. Evidently that problem also disappears when the correspondi ng entities are made to dissolve as originating in misguided logical analysis. However if an analysis based on (B') and (E') is ontological ly economical with respect to actual entities, (B') requires the acknowledgmen t of merely possible entities, since creature x, which we assume not to exist at the time of utterance, is the object which the sentence refers to. But we need have no fear that the eliminated puzzles reappear under a new guise: possibilia are, so to speak, theological ly innocuous. It would be absurd to demand a causal account of entities which do not actually exist or to inquire after the order of subordinati on between the existence (!) of such entities and indeed anything else. Just as there is no such entity as the possible being of a thing, distinct from the thing itself, similarly there is no such entity as a thing's intelligibl e being. Entities bearing the latter denomination were sometimes posited for the purpose of providing adequate, hence eternal, objects to God's omniscience . Creatures were rejected offhand for this role, in view of their fleeting existence. But, as Ockham saw, there is an alternative to positing entities with "dim-

400

inutive existence" 35 One may challenge the implicit assumption that objects must coexist to be in any manner related - whereby coexistence is required in particular of a knower and the object Rnown. If that . . e l'iminate . d , 36 a sentence sue h as: assumption is (F) Creature x is known, can be regarded as true, though creature x hase no actual existence at all, not even of a diminutive sort. But that option remained unavailable as long as the basic assumption, namely the Assumption of inherence, was not first discarded. Otherwise the truth of (F) was thought to require some dependent entity, inherent perhaps in the creature - or perhaps in God 37 - and the intelligible being of a creature could not be avoided. Freed of both assumptions, Ockham saw no objection to considering that, despite their temporary (or merely possible) existence, the creatures themselves are objects of God's knowledge; (F) must be regarded as referring simply to creature x itself, regardless of whether it exists or not. Theology in this new mode has of course no need of divine ideas; nevertheless Ockham finds a "charitable" use for the expression: 'divine ideas' denote the creatures themselves, whether actual or merely possible, since God knows them al1. 38 Beyond any doubt, Ockham, qua logician and qua theologian, would not have shaved Wyman's beard! Nevertheless, as we may remember, Beaman still has objections in store against regarding Ockham as a mediaeval Wyman. In the first place, he will point out, Ockham does not use the language characteristic of Wyman. At any rate, he has searched Ockham's writings in vain for Latin equivalents of the Wyman favorite: (W) There are things which do not exist. But more conclusive is the presence of positive claims in Ockham's writings which, Beaman urges, are inconsistent with (W) and therefore with a Wyman-ontology.

401

"But," we may expect to hear Mac Ay protest, "this is no longer an issue; we have proven that Ockham is committed to such an ontology!" Mac Ay is right. Therefore, should Beaman succeed in providing sufficient evidence in favor of his thesis, he would thereby establish the existence of a major inconsistency within the philosophy of Ockham. But what is Beaman's evidence? It consists of the three following facts of Ockham lore: (a) Sentences which are likely candidates for translating the English: (W') A possible thing is something 39 are evaluated as false. (b) Mere possibles are neither self-identical things nor things dis. . . tinct from eac h ot h er and from other entities.

(c) An important text of the Summa logicae

41

40

contains the claim that

'thing' ('res') and 'actual existence' ('esse') signify the same. The obvious consequence, namely that the concept of a non-existent thing (non-ens) is contradictory is drawn by Ockham himself.

42

I shall argue that the claims contained in (a), (b) and (c), though indeed incompatible with Wyman's language are not incompatible with a possibilistic ontology. There lies no threat of inconsistency upon Ockham's doctrine. But this suggests that there are two languages: Wyman's and Ockham's. Wyman's language is of course a fragment of English, persumably intented however to adhere as closely as possible to a far better regulated language, namely a quantificational language, say a Cocchiarella-type language with distinct pairs of quantifiers 43 . . not with . ranging over actua 1s an d over possi'bl es. Our problem is that language, which can be precisely defined. But the same precision does not invest the fragment of Latin in which what we are calling

"Ockham's language" consists, even though it was highly systematized by the work of logicians, particularly of the 13 th and 14 th century - among them Ockham. Hence our immediate task is to partly fill the gap by providing.at least a description of that language - in the

402

respects relevant to our pursuit - sufficiently precise to authorize a comparison with a quantificational language, Since the differences between the two languages which we expect to be of import in the present issue pertain to the mechanisms by which reference to actuals and to non-actuals is achieved, it is the nature and functioning of these mechanisms within Ockham's language which we shall now describe. A succinct account will be followed by illustrative examples.

44

Characteristic of this language is that the denotation of the referential expressions cannot be determined independently of the

context of the sentence in which they are used. The referential expressions may thus be regarded as indeterminate outside of any propositional context; in other words, it is this context which provides a determinate unambiguous reading for all re·ferential expressions. Our terminology calls for explanation: what are "referential expressions" and how do we define "propositional contexts"? The property of being a referential expression is best construed as relative to sentence positions i.e. that of the subject or that of the predicate; we have chosen to take into account only referentiality with respect to the subject position. Our excuse is that this suffices to our present purpose. Referential expressions we shall consider are then any of the following: common terms or proper names (also demonstrative pronouns), provided they are used as subject in a sentence, or yet quantificational words ('all', 'some'), provided they are used as subject or as part thereof. We shall not define 'propositional contexts' in their full generality either; as sufficient for our purpose, we define a propositional context as either the verb 'is' ('est') in the role of the copula, or the verb 'can' ('potest') when it combines mode and copula (i.e.: when it is the main verb of the sentence). It is assumed that the language is of the expanded type where the copula is never • • • • implicit in a verb nor the verb

I

• • can 1 in the predicate term. 45 Hence

403

there are, for our purpose, two propositional contexts, which we shall refer to as 'the actuality context' and 'the possibility

context'. In order that the effects of a propositional context on referential expressions may be conspicuous, we introduce two "indicators", attachable to referential expressions. One is to be "the actuality indicator" (representable by an a which immediately adjoins a referential expression thus completing it), the other "the possibility indicator" (representable by a 11 used similarly). An obvious rule connects the indicators with the context. We shall observe on two examples -- one for actuality, one for possibility contexts -- how reference in this language obtains. Let the first example be the sentence (I) : (I) Some-a man-a is walking. The referential expressions are 'man' and 'some'; the indicators are actuality indicators since the context is df actuality. The denotation of 'man-a' is determinate: it consists in all actual men; however if here are no men, 'man-a' is vacuous. 'Some a' is here re. stricted to range over actual men (.if any ) . 45 In the case where 'man-a' is empty, (I) is false and its negation true. We may note that this truth-valuation requires that the language should include an external negation. The following sentence will serve to illustrate contexts of possibility: (II) Some-11 men-11 can be walking Indicators df possiblity have been appended to the referential expressions, since the context is of possibility. 'Man-11' denotes all possible men and cannot be vacuous. 'Some-11' is here restricted to . 1 e men. 47 range over possib We are now in a position to show that the claims contained in (a), (b) and (c) above are compatible with a commitment to possible entities. Let us examine each claim in turn:

404

(a) Ockham's language requires that the sentence (W') be evaluated as false. To see this, we need only make the referential mechanisms conspicuous by using indicators. Accordingly consider: (III) Some-a (merely possible thing)-a is something. (III) must be false, since the context requires that 'merely possible thing' be completed by the actuality indicator; but '(merely possible thing)-a'is necessarily vacuous for obvious reasons. However it is also apparent that (W') only denies that possibilia are actual entities: it is not a denial of Wyman's thesis. (b) We may consider as analytically true that only what is identifiable is a thing. But Ockham is not denying that possibles are identifiable, as can be readily seen. Consider the following: (IV) Caesar-a is not the same (person) as Anthony. (VI) must be false; the context is of actuality, consequently the indicator must be the actuality indicator. But 'Caesar-a' is vacuous, since Caesar no longer exists. But for the same reasons another sentence is assigned falsity as well, namely: (V) Caesar-a is the same (person) as Anthony. (IV) contains only an internal negation and therefore is not the negation of (V). Of course both the negation of (IV) and the negation of (V) are true. Ockham's claims regarding identity and non-identity of possibles are thus valid-within-his-language. But their content is harmless; it is indeed a trivial truth that possibilia are neither self-ident48 . 1 actua 1 t h.ings nor d.ist1nct . . ica actua 1 things. (c) The last claim seems to weigh heavily against ascribing possibilism to Ockham; but here, as in the preceding cases, the claim is not what it appears to be. In order to determine what the claim is however, we shall need to examine the relevant texts, mainly that of the Swnma logicae, Part III-2, Ch.27 in some detail, The thesis, on the "synonymy" of 'thing' ('res') and 'actual existence' ('esse') presupposes acquaintance with Ockham's definition of 'significatio'. We shall assume it, reminding only the reader that

405

the four acceptions of 'significatio' are presented in the Ch. 33, . . clear 49 . Part I, of the Summa "&Og~cae. It is that the four acceptions are relevant to the thesis at hand: Ockham intended "synonymy" in the strongest of the senses he

allow~d

for. Nevertheless, it does not

follow that nothing can be a non-actual entity; on the contrary, the thesis of synonymy is compatible with the fact that both terms can refer to the same non-actual entities; indeed they must refer to 50 . contexts o f poss1'b i· 1 ity. · non-actuals when used in

Thus Ockham' s claim of "synonymy" for these terms is not directed against the concept of a non-actual object: the view he is rejecting and which is indeed false if both terms are "strongly" synonymous, is that the existence of a thing and the thing itself ('entitas•) 51 should be two entities - both actual. The existence of a thing would, within that view, be conceived of as a dependent inherent entity of the kind we discussed earlier. Those who adopted such a view appar52 ently argued that a sentence such as: (An) A exists where A's are things of a certain kind of species -- such as men or angels --, could be now true, now false, only if a real change had affected the A's. Ockham rejects the argument on the basis that for the above sentence to be false it is only required that A should . . whic . h case even t h e fo 1 lowing . . fa 1 se: 53 d enote not h ing, in is

(An) A is (an) A. There is a concept of "entity" which Ockham indeed rejects; but it is not that of a possible though non-actual thing; it is rather the notion of a thing emptied of its existence as of a real inherent quality. Regarding the claim that 'non-existent thing' ('non-ens') is necessarily vacuous, it is clear that the claim is correct, though its import is more limited than Mac Ay imagined. A weaker and a stronger sense of 'necessarily vacuous' should be distinguished: in the weaker sense, it is sufficient that a term be neccesarily vacuous

in contexts of actuality; in the stronger sense in all contexts. Thus

406

'non-existent thing' can be seen to be vacuous in the weaker sense only - and a difference with the term 'chimera', vacuous in the stronger sense, appears. We now understand that Ockham sometimes asserts that 'non-existent thing' ('non-ens') can denote nothing but on other occasions uses the term referringly. We need only observe the difference between the following two sentences: (VI) Some-a (non-actual thing)-a is something and (VII) Some-rr (non-actual thing)-rr can be something. Whereas (VI) is necessarily false, (VII) is true. In fact we find a Latin equivalent of (VII) in the text concerning possible being which . 54 we commented on ear 1 ier. We have shown that a possibilistic ontology is not contradicted by claims which we might be tempted do give a sense to different from the one that Ockham, in virtue of peculiar features of his language, is committed to. It appears that the expressive pewer of Ockham's language is limited in a way that a quantificational language is not; but a benefit which Ockham derives therefrom is that he altogether avoids the more paradoxical expressions of possibilism, though espousing its ontology.

407

*

See Quine On what there is, in: From a logical point of view

(revised edition 1961, Harvard University Press). We are here using 'possible being' to translate both 'esse possibile' (Cf. Ordinatio d. 37 FF. [ Lugduni 1495]) and 'ens in potentia' (Cf. Summa logicae I c. 38 [ Franciscan Institute 1974 ] ) • 2 'Meaning' translates here 'significatio'. 3 Cf. SL (=Summa logicae) III - 1, c. 23, and passim. 4 Cf. Ord. (= Ordinatio) Prol. q. 1, [Franciscan Institute, 1967 ] , Reportatio II q. 14 - 15 [ P. Boehner, ed., in Traditio 1943],

Quodlibeta septem VI, q. 6 [ Paris iis 1488 ] . 5 In SL I c. 38 and in SL III - 2, c. 27, respectively. 6 SL I c. 38 1. 54 to 66 of which the first sentence reads: "Simi liter dividitur ens in ens in potentia et ens in actu". 7 The second sentence reads: "Quod non est intelligendum quod aliquid quod non est in rerum natura, sed potest esse, sit vere ens, et a liquid aliud quod est in rerum natura sit etiam ens". 8

The third sentence reads: "Sed Aristoteles dividendo 'ens' in

potentiam et in actum, V Metaphysicae, intendit quod hoc nomen 'ens' de aliquo praedicatur mediante hoc verbo 'est' in propositione mere de inesse, non aequivalenti propositione de possibili, sic dicendo 'Antichristus potest esse ens' sive 'Antichristus est ens in potentia' et sic de aliis." 9

We are interpreting: "Unde vult ibidem quod ens est dicibile

potestate et actu". In contexts such as these, 'dicitur' (and hence 'dicibile') is used by Ockham equivalently to 'verificatur' or 'praedicatur' (Cf. SL III - 1, c. 3, SL III - 1, c. 23, SL I, c. 64); it is therefore correct to read Ockham as claiming here that 'ens' can be predicated in two ways: "in potency" and "in act", or yet that 'ens' is true (of something) either actually or possibly. We have however adapted the relation of predication, which, according to Ockham, normally holds between terms, to its modern counterpart by making use of the property of suppositio on the part of the subject. Ockham himself sug-

408

gests such a reinterpretation of 'praedicatur', whereby a term is related to objects (See SL c. 63, I. 33 to 35). Anticipating the analysis to be given below, we may note that the reintroduction of

'in potentia' and 'in actu' (or nearly so) "in the metalanguage" as we would say - is a somewhat facetious way of saying that those terms are "modes of predication", i.e. that they modify the copula, rather than qualify the predicate term. 10

We are explicating: "sicut sciens et quiescens".

II

Such in the import of "et tamen nihil est sciens vel quies-

cens nisi actualiter sit sciens vel quiescens". 12

Cf. SL III - I, c. 5, I. 30 to 32.

13

This is somewhat reminiscent of "determinationes distrahentes

vel diminuentes" (Cf. Ord. d. 2 q. 7, pp. 244 - 45 [ed. FI t. I]), which may be regarded as forming new terms from old ones. 14

From the object language only, since the expression reappears

legitimately in the metalanguage -- or so Ockham's usage may be described. See footnote 9. 15

Modes are not only expressions which modify the copula; they

are also predicates of sentences (Cf. SL II, c. 9). However, in the present context, it is only as copula-modifiers that they need be considered. Ockham has a unifying account whereby all occurences of modes may be regarded as predicates of sentences; but we have no need for that theory here. 16

Cf. SL II, c. 10.

17

Cf. the same ch. 38, Part I of SL, a few lines above the

paragraph we are commenting on (I. 41 - 42). 18

Summulae in libros physicorum, c. 16, p. 19 [ Romae 1637 ] .

19

According to Ord. d. 43, q. 2 F [ ed. L. ] , predications may

be considered as true "because of something" (propter aliquid) which belongs (convenit) to the subject. 20

Ockham's insistence that be distinguished two senses of 'com-

petere' or 'convenire', such that real inherence be intended in one sense only, which is not the sense of 'true predication', suffi-

409

ciently testifies that the distinction was not usually made, in other words that true predication was considered either as meaning inherence or at least as requiring it. 21

A term may "connote" (signify indirectly) entities other than

those it applies to. Cf. SL I, c. 10. Cf. SL I, c. 51, I. 34 - 37 and Quod. VI, q. 7 and q. 12. For such entities conceived of as "passiones", see Ord. Prol., q. 3 (p. 138), [ed. F.I., t. I ] ; for the description as 'respectus 22

23

aptitudinales vel potentiales', see Quod VI, q. 18. 24 Cf. Ord. d. 36, q. I Y and FF ( ed. L]. 25

Walter Burleigh, De Puritate artis logicae tractatus longior edited by P. Boehner, Franciscan Institute Publications 1955], p. 59.

26

Cf. Quod VI, q. 8 to 25.

27

Cf. Ord. Prol. q. 3 (p. 139)

28

Cf. SL III - 3, c. 26 (p. 690).

[ ed. F. I. t. I ) .

29

For such an account of relations, see Quod VI, q. 25. In Quod VI, q. 25, Ockham claims in effect that, where a relational term is used as predicate, objects (signified directly 30

or indirectly) are said to be "disposed" in a certain way, in the way namely characteristic of that term ("esse tales quales denominantur

esse per talem relationem vel per tale relativum"). But for the ensuing sentence to be true obviously nothing further is required but that the objects referred to be so disposed. 31

Cf. Ord. Prol. q. 3 (p. 139)

[ed. F.I., t. I]; SL, c. 24

Quod VI , q. I 8 . Cf. SL II, c. 9 and c. IO.

( p. 80) ;

32

33 Such is the import of the paragraph with which Questio 2 Distinctio 43 of the Ordinatio ends. 34 In the Ord. d. 36, q. I FF [ ed. L; all subsequent references to the Or>d. are to this same 1495 edition ] , it is claimed that God creates though nothing in God need be posited on that account: the same holds, of course, of the fact that God can create. Regarding

410

"the possible being of a creature", the relevant text has already been referred to: it is Ord. d. 43, q. 2 F. 35

Cf. Ord. d. 36 q. 1 R.

36

As it is in Quod VI, q. 25, where a relational term is allowed

to apply to a non-existent thing.

37

Cf. Ord. d. 36, q.

38

Cf. Ord. d. 35, q. 5 D.

39

A close approximation to: A possible thing is something, we

find in the Ord. d. 36, q.

DD.

P, namely: Illud creabile fuit aliquid.

'Illud creabile' refers to an individual which did not exist in the past and which consequently was then a mere possible. But that sentence is false, its negation - 'illud creabile fuit nihil' - being, as Ockham argues, true. 40

Cf. Ord. d. 36, q.

41

Namely Part III - 2, c. 27, I. 22 to 43.

42

Cf. SL I, c. 26 (p. 88) and SL III - 3, c. 6 (p. 603).

43

Cf. Nino Cocchiarella: Existence entailing attributes, modes of

F.

copulation and modes of being in second order logic, in Nous 1969. 44

We are drawing from the chapters of the Summa logicae which

treat of modal syllogisms and other modal inferences (consequentiae). 45

A very limited number of predicate-terms generate a possibility

context, notably the terms 'known', 'signified' and 'supposited'. Cf.

SL III - 4, c. 13. Such terms are called 'ampliative' by many authors but rarely so by Ockham. 46

It may be suggested that since the range of the quantificat-

ional words is determined by the adjoining common term, indicators are in their case superfluous additions. Our reason for proceeding as we do is that quantificational words may be used "alone", i.e. without a subsequent common term (see the next footnote on this). Hence it is preferable to consider the range of quantificational words as determined in two stages, first by the propositional context, secondly and more restrictively by the adjoining common term if any.

411

47 There need to be two referential expressions in one sentence. However it is the referential function of the common term which is dispensable ; to be persuaded of this, consider that (I) can be read (I') :

(I') Some-a is a man and is walking. and (II) as (II'): (II') Some-rr man can be a man and can be walking. But Ockham gives of (II) an expanded form which is precisely (II'). For an example, see SL III - 3, c. 10, 1. 86 to 110. 48

Although possibles are neither really distinct (non distingUEbantur realiter) nor really identical (non fuerunt idem realiter), Ockham may yet have allowed for a sense of 'distinct', and consequently of 'identical' , which truly applies to possibilia. At any rate, he acknowledge in the Ord. d. 35 q. 5 G that things which may be created are distinct ('distincta e' without the qualificatio n 'rea-

liter'). In Quod II, q. 7, it is claimed that both terms signify and "consignify " entirely (omnino) the same. 49

50 Had we considered the case where an expression is referential with respect to the predicate position, we could have shown that 'exists' in a sentence of the form 'x can exist' refers to exactly the same objects as 'thing' does in a sentence of the form 'some thing can¢'. But we may achieve the same result by putting to use the fact that 'being' (esse) may be part of the subject, for instance in phrases such as 'the being of a creature' ('esse creaturae') . Cf.

Ord. d. 36, q.

G. We observe that 'being' in the sentence:'th e being of a sentence can be destroyed'a nd 'thing' in the sentence: I

'created thing can be destroyed' refer to exactly the same entities. 51 Cf. SL III - 2, c. 27,,1. 22: "Ideo dicendum est quod entitas

et exsisten tia non sunt duae res". 52

Same chapter as above, 1. 36 to 39: "Et ideo talia argumenta

'essentia potest esse et non esse, igitur esse distinguitu r ab essentia ', 'essentia potest esse sub opposito esse, igitur essentia dif-

412

fert db esse' 53

non valent".

Ibid. I. 39 to 41: "Sicut nee talia Valent 'essentia potest

non esse essentia et potest esse essentia, igitur essentia differt db essentia', 'essentia potest esse suh opposito essentiae, igitur essent-ia d-iffert ab essenlia'."

413

BURIDAN AND LESNIEWSKI ON THE COPULA

H. Hubien,

Liege

It has often been contended that Lesniewski's Ontology is the best system in which to formalize medieval logic. I submit that this is not the case and propose a new one, which, as I shall show, is both more faithful to one of the medieval logics (for there is more than one) and richer than Ontology, since it contains it but is not contained in it. First of all, let me introduce some symbolism. I shall use 'e' for the Buridanian copula, 'a', 'b', 'c', 'd' for common terms or names (teY'ITlini communes), 'x', 'y', 'z', 'w' for proper names (ter-

mini singulares siue discreti). For the time being the Lesniewskians are left in peaceful possession of the epsilon. That Ontology cannot represent adequately medieval logic is easy to show: some medieval theses turn false when their copulae are replaced by the epsilon and some Lesniewskian theses turn false when their epsilons are replaced by medieval copulae. I. aeb + bea

this is the principle of simple conversion for indefinite propositions. It is unanimously accepted in the medieval tradition, as are the special cases: 1.2

aey +yea

1.3

xeb + bex

1.4

xey

Now

'aEb

yex

+ +

bEa' is not a thesis of Ontology.

2. yea&yec. + cea this is the principle of the syUogismus expositorius in the third figure, which is found everywhere in the thirteenth and fourteenth centuries. Once again the Lesniewskian analogue, 'yEa&yEc.

+

cEa',

is not a thesis of Ontology. It has been suggested to me, by Professor Henry and Professor

415

Surma, that the principle of simple conversion may be accommoda ted by translatin g the copula not by the epsilon but by Professor Lejewski' s

(as I believe) delta. This is true, but the trick won't work with the principle of the expositor y syllogism , since it is plain that 'yAa&yAc.

~ cAa' is not a thesis. Conversely there are theses of Ontology which cannot be turned into medieval theses by changing the copulae. For instance the epsilon is transitive , but nobody has ever proposed this as a valid argument 'homo est animal et animal est asinus; ergo homo est asi-

nus'. What I said above is true of any medieval logic. However the system I am going to develop is adequate for only one of them, viz. terminist logic or, to name it from the man who perfected it, Buridanian logic. The fundament al difference between Ontology and Buridania n logic is that whereas the former has a threefold division of names wholly based on considera tions of extension , the latter distinguis hes five classes of names, using besides extension another principle of division. For example let us consider the following names: 'Socrates' (which we suppose to be the nickname of, let us say, Sir Karl Popper), 'Pegasus' (the winged horse of Quine an fame) , 'deus' , 'animal' and 'chimaera '. A Lesniewsk ian would classify these five names as follows:

empty names: 'Pegasus', 'chimaera '; 2. non-empty names: I.

2. I 2.2

unshared: 'Socrates ', 'deus', shared: 'animal'.

But Buridan would give another classifica tion: I. termini communes: I. 2

pro nullo supponens : 'chimaera '; pro aliquo supponent es:

I. 21

pro uno solo: 'deus',

I. 22

pro pluribus: 'animal' ;

I. I

416

2. termini singulares seu discreti: 2.1 2.2

pro nullo supponens: 'Pegasus', pro aliquo supponens: 'Socrates'. Let us hear Buridan explain in his own words the rationale of

his division. This is found, of all places, in his questions on the

de Caelo et Mundo (I quote from Moody's edition, Cambridge, Mass., 1942). In an objection we read "iste terminus 'mundus' est terminus singularis, quia non est aptus natus praedicari de pluribus nisi false, cum in primo huius probet Aristotiles quod impossibile est esse plures mundos" (I, I, 3, 7 - JO). It is plain that 'singularis' means to the objector what 'unshared' does to the Le§niewskians. To which Buridan answers "iste terminus 'mundus' est terminus communis, quia secundum uerit.atem possent esse plures mundi. Et licet. non possent esse plures mundi, tamen adhuc esset terminus communis et, secundum grammaticam, appellatiuae qualitatis, sicut iste terminus 'deus', licet omnino impossibile sit esse plures deos; quia terminus non dicitur communis propter rem significatam, sed propter modum suae significationis, uel impositionis, scilicet /si/ non repugnat sibi ex modo

suae impositionis supponere pro pluribus. Vnde ponamus, siue per possibile siue per impossibile, quod esset unus alter mundus et unus alter deus, similes mundo nostro et deo qui est, isti termini 'mundus' et 'deus' supponerent pro illis sine noua impositione. Sed* sic non est de termino singulari: quia si singulariter impono quod iste uocetur 'Socrates', dato quod essent mille alii similes, tamen iste terminus 'Socrates' non supponeret pro eis nisi per nouam impositio-

nem." (I,

I, 5.41 - 6.15: the added 'si' is an emendation of mine,

as is the 'sed'* for 'et'; I have slightly modified the punctuation). It is clear from this passage that the Buridanian distinction between common and singular terms is not the same as the distinction drawn by Lesniewski between shared and unshared names; in medieval parlance, the former is founded on a difference in significatio, the latter on a difference in suppositio. Now the distinction of common from singular ternIB, according to Buridan (with whom I agree), is

417

formal, i.e. is concerned with the very form of propositions, whereas the Lesniewskian distinction is only material, or, to use modern jargon, the former is embodied in the very syntax of the object-language whereas the latter belongs to the metalinguistic semantics. By the way, if it is not too late to reform scholastic terminology, I would like to substitute 'communicabile' and 'incommunicabile' (Anglice 'shareable' and 'unshareable'), which seem to me to express the distinction rather nicely, for 'commune' and 'singulare', which, at least to my ear, have an unmistakable extensional ring. The Buridanian classification would then be expressed as follows: I. shareable names: I.I

empty,

I.2

non-empty:

1. 21

unshared,

1.22

shared;

2. unshareable names: 2.1

empty,

2.2

non-empty.

In Buridanian logic the distinction between shareable and unshareable terms or names is of the utmost importance. For the basic rule of this logic is that whatever is true for all shareable

names is true for all unshareable names, but not conversely. Or, to put it technically, the following rule of substitution holds: the result of uniformly substituting (with the customary restrictions when quantifiers are present) in a thesis any term, shareable or unshareable, for a shareable term is also a thesis, though only unshareable terms may be substituted for unshareable ones. For example, from the above-mentioned principle of simple conversion, we get successively the special cases 1.2, 1.3, and 1.4 by performing the substitutions (b/y), (a/x) and (a/x, b/y) respectively. In the same way we can get special cases of the principle of the expository syllogism by performing the substitutions (a/x), which gives 'yex&yec.

418

+

cex', (c/z), which results in 'yea&yez.

+

zea', or

(a/x, c/z), from which we get 'yex&yez.

+

zey'; but we are not allow-

ed to substitute 'b' for 'y', which would result in the plainly false expression 'bea&bec.

+

cea'.

I do not think that Buridan was conscious of this. In any case, I have not found it discussed in his works or in any of his disciples' (but of course I haven't read everything they wrote, far from it!). But their practice was in agreement with it, as can be amply shown. I shall now proceed to the formal development of the system. To a classical propositional calculus, with substitution and detachment and the four £ukasiewicz rules for the quantifiers, add the following rules: 1. if A and Bare terms, then AeB is a proposition; 2. if A is a shareable term and B any term, shareable or not, then if Tis a thesis, so is T(A/B), provided the customary restrictions for working with quantifiers have been observed; 3. if X and Y are unshareable terms, then if T is a thesis, so is T(X/Y), with the same proviso as in (2). There is but one proper axiom: Tl.

aeb

- aec

from T8 by T2 and PC

Tl I. yea&cey. ->- cea

from TIO by T2 and PC

Tl2. aey&yec. ->- aec

from T8 by T2 and PC

Tl3. aey&yec. ->- cea

from Tl2 by T2 and PC

Tl4. aey&cey. ->- aec

from Tl2 by T2 and PC

TIS. aey&cey. ->- cea

from Tl4 by 1'2 and PC

These are the principles of the expository syllogisms. I now introduce a new logical constant, the negative copula

'i',

corresponding to the medieval 'non est' in such expressions as 'homo non est asinus' or 'Socrates non est asinus'. It is a propositionforming functor of two nominal arguments. However, if I were to embed Buridanian logic in a more inclusive system, I would analyse the negative copula 'non est' into a predicate-forming functor on predicates, and the copula; but it is simpler for my present purpose to construe it as an unanalysed constant. In fact many medieval logicians (Buridan is one of them) hovered between the two categorizations, at times saying that in 'Socrates non est asinus' 'non est' is the copula, at times that 'est' is. The new constant is introduced by a unique axiom, which is in fact a definition in the style of Lesniewski. I shall derive but a handful of the most interesting theorems. Tl6. aib .: L:x.xea:v:L:x.xea&xeb Tl 7. aeb ->- a¢b i. aeb

hyp.

ii. L x.xea&xeb

Tl by PC

iii. nx.xea->- xeb

ii by FC

iv. L x. xea:v: L x.xea&xeb

iv by Tl6

v. a¢b TIS.

aea->:

iii by FC

aib

from TS and Tl 7 Tl9. beb ->- aib from T6 and Tl7

421

T20. xria -+ xea i. xria

hyp.

ii. L:y.yex:v: L:y.yex&yea iii. L:y.yex: -+ xex iv. xexv: l: y.yex&yea

T12 by PC

vi. L: y. yex&yea: -+ xea

v by FC

vii. xexvxea

iv, vi by PC xea

15 (a/x, b/a)

ix. xea T2 1. xea

by FC

ii, iii by PC

v. yex&yea. -+ xea

viii. xex-+

i by T16 Tl

vii, viii by PC

+> xi&.

i. xea -+ xria

T17(a/x, b/a)

u. q.e.d. i, T20 by PC This theorem is often found in the medieval authors; it is most often expressed as "in singularibus non refert praeponere vel postponere negationem".

We have now the means of expressing the four categorical propositions A, I, E, 0 in their medieval interpretation s. They are (A) arib, i.e. L:x.xea:&: fl x.xea -+ xeb, (I) aeb,

i.e.

L: x. xea&xeb,

(E) aeb,

i.e.

flx.xea-+ xeb,

(0) arib,

i.e. L: x.xea:v: L: x.xea&xeb.

We can now, if we wish, introduce the two quantity signs (signa quantitatis) 'I', for 'aliquid' and 'A' for 'omne' by the axioms: T22. Iaeb

aeb

T23. Iarib ,.. arib T24. Aaeb "" arib T25. Aarib

+>

aeb.

Notice that though no one of these axioms is a definition, T22 and T23 on the one hand, T24 and T25 on the other, jointly have the force of a definition of 'I' and 'A' respectively, since they enable us to eliminate them from any context whatsoever. Notice too that it would

422

be a problem to determine the syntactical category of these expressions. We could now enrich the system by definiLg sundry functors. For example, term negation, a functor well-known in medieval logic under the name of 'negatio infinitans', could be introduced by the thesis T26. aeb - ced vii. cea&dea. ->- ced viii. ced

i by T30

vi by FC iv, v, vii by PC

ix. ced&cEa

ii, viii by PC

x. cEd

ix by T33

T35. aEc&cEb. ->- aEb

i. aEc

hyp.

ii. cEb

hyp.

iii. nafld: aec&dec. ->- aed iv. aec&bec. ->- aeb v. aec

i by T29

vi. ceb

i i by T29

vii. bee

vi by T2

viii. aeb

iv, v, vii by PC

ix. aEb

T36. l: c. aEc&cEb:

i, viii by T33 -+ aEb

from T35 by FC. T37,

424

i i by T30

iii by FC

aEb ->-: I c. aEc&cEb

i. aEb

hyp.

ii. aEa

i by T32

iii. aEa&aEb

i, i i by PC

iv. I c.aEc&cEb

iv by FC

T38. aEb :I c.aEc&cEb This theorem, or its universalization, is Lesniewski's shortest axiom of Ontology. I have thus proved that Ontology is contained in the present system. I shall end this paper by proving, which seems to me rather illuminating, that with an unshareable subject Buridan's copula and Lesniewski's have the same force. T39. xea

-+

xEa

i. xea

hyp.

ii. n c n d: cex&dex.

-+

ced

iii. xEa T40. xea

- obligatione s".

444

Nous n'avons ni etudie, ni controle la veracite des indications concernant l'ensemble du contenu de ce codex. Nous savons seulement 6 que Hubien dans son edition du De consequentiis de Buridan a nie l'attribution de cette copie du De consequentiis a Buridan. Faute d'une enquete plus approfondie, nous ne sommes pas a meme de decider s'il s'agit ou' non d'une redaction abregee (brevis) du De consequen-

tiis. Mais nous savons que Buridan avait l'habitude de composer des redactions differentes completes (longae)

OU

abregees (breves) de

ses 'lectures'.

Le passe de notre codex nous est, en quelque sorte, eclaire par don Giovanni di Baldassarre qui, dans son carnet des livres donnes a lire a Florence, entre 1396 et 1400, donne pour l'annee 1396 le renseignement suivant: "Prestai a di 14 di marzo a frate Riccardo di Francia dell'Ordine de' frati Romitani le Consequentie di Bridano e l'Obbligationi di Pietro di Candia". Pour l'annee d'apres (1397) on trouve ceci: "Prestai a frate Riccardo di Francia dell'Ordine de' frati Romitani a di. .. di maggio, l'obbligationi di Pietro di Candia".

7

Nous supposons du fait que les Consequentiae attribuees a Buridan se trouvent dans le meme volume que le De obligationibus de Pierre de Candia et les Obligationes de Buser, qu'il s'agit du meme codex

miscellaneus qui est conserve a la Bibliotheque de Florence, c'est-a-dire notre codex Strozziano 120. D'ou l'hypothese que notre codex qui contient egalement le De obligationibus de Buser a circule a Florence dans les annees 1396 et 1397. En passant, le traite De obligationibus attribue ici a Petrus de Candia est une oeuvre differente de celle dont nous venons de . . . d'it: 8 par 1 er. En e f 'f et son 1nc1p1t f. I Ira: "Rogasti me carissime ut tuae in crucifixi latere caritati aliquas regulas artis obligatoriae in unum opusculum colligares, cum igitur fervor immensae dilectationis et fidei quern habui hactenus habeo et habebo me induci t grandiori animo tuum desiderium adimplere confisus tamen divinae bonitatis largitatem immensae (?) experiar .... unde cum multae species

445

obligationis a quibusdam modernis ponantur de quibus ad praesens non intendo nisi de duabus pertractare, scilicet positionem et depositionem, quia ut mihi videtur aliae ad istas possunt reduci, et ideo de singulis pertractare nimis foret longum vel superfluum videtur. Describitur namque obligatio communiter sic: obligatio est oratio mediante qua quis obligatus ad obligatum vel obligata affirmative vel negative respondere tenetur". Nous avons donne cet incipit parce qu'il est dans notre intention de montrer qu'il s'agit d'une exposition differente de celle de Buser qui propose six especes d'obligations, bien qu'il traite seulement de quatre d'entre elles, tandis que l'auteur appelle ici Petrus de Candia, parle seulement de deux types d'obligation, c'est-a-dire la position et la deposition (positio et depositio). ROME. Le ms. de Rome, Vat. Palat. lat. 994, XIVe siecle, contient notre traite De obligationibus en f. 153ra et suivants, en meme temps que les Swrmrulae de Buridan et que d'autres oeuvres de logique de cet auteur. Voici l'incipit qui succede a l'explicit du f. 152va (Expliciunt consequentiae magistri Johannis Buridani piae memoriae): 153ra: " < 0 > b rogatum quorumdam dilectorum sociorum et scientiae in se perutilem delectationem aliqua utiliora artis f.

obligatoriae ex dictis antiquorum necnon modernorum divina favente gratia, volo breviter compilare proponens tali ordine, procedam in futurum: quod primo terminos isti arti pertinentes describam, aliquas divisiones intermiscendo; secundo aliqua principia supponam quasdam regulas cuilibet speciei obligationis generales adiungendo. Tertio species magis consuetas pertranseam, easdem exemplis et sophismatibus declarando f. 159va, istius capi tuli" (a la fin l' explicit qui donne le nom de 1' auteur) : "Explicit tractatus artis obligatoriae per magistrum Wylhelmum Buserum compilatus".

446

L'autre copie que nous avons etudiee est celle de Turin, Bibliotheque Nationale, G, III. 12, Elle aussi appartient a un codex rrriscel-

laneus qui contient plusieurs oeuvres logiques de mattres differents: Buridan, surtout, Marsilius d'Inghen, le De insolubilibus de Pierre d'Ailly(?) et, enfin, notre Buser. Rappellons que nous avons signale l'existence de ce codex il ya, deja, quelques annees, 9 TURIN: f. 26 lva: "Incipiunt obligationes Busel, Obrogatum quorumdam

scolarium dilectorum in se et scientiae perutilem dilectationem aliqua utiliora artis obligatoriae ex dictis antiquorum necnon modernorum divina favente gratia breviter compilare proponens tali ordine procedam in agendis quia primo terminos isti arti pertinentes describam aliquas divisiones intermiscendo; secundo aliqua principia supponam aliquas regulas cuilibet speciei obligationis generales adiungendo. Tertio species magis consuetas pertranseam easdem exemplis et sophismatibus declarando". Le texte s'interrompt, vraisemblablement avant la fin de la quatrieme partie du troisieme chapitre, qui est aussi la derniere dans les autres copies. La copie de ce ms, de Turin est la moins correcte et son latin montre quelques traces de patois de l'Italie du Nord. II

Venons en maintenant au contenu du texte, qui nous semble fort interessant. Nous sommes en presence d'un traite De obligationibus (trac-

tatus comme on peut lire dans l'explicit), qui donne des references aux doctrines des anciens et des modernes, concernant les obligations et qui propose une classification en espece differente, par example,

de celle donne dans l'edition de l'oeuvre de Roger Swyneshed, preparee par Spade.

10

Pour Roger il y a trois especes d'obligations, c 1 est-a-

-dire: l'imposition, la position et la deposition. En revanche nous

447

lisons dans notre texte qu'il en a six: "sex sunt species obligationis, scilicet, positio, irnpositio , dubitatio , (ou 'dubie positio') sit (ou scit) verurn, depositio , petitio" (position, imposition , doute, etre vrai - ou savoir le vrai, variantes de la copie de Turin,f.21 9 va deposition et petition) . Nous avons done affaire a une articulati on assez cornplexe. 11 faut souligner ici que la copie de Rome donne le terrne suppositio n (suppositi o) au lieu de petitio (petition) et celle de Turin scit verum au lieu de sit verwn. Pour la premiere variante (suppositi o au lieu de·petitio ) il s'agit clairernen t d'une erreur du copiste: puisque, dans cette copie Vaticane la suite de l'expositi on ne parle pas de "supposit ion" rnais bien de "petition " cornrne dans les deux autres copies. Notre traite est divise en trois chapitres (capituZa ); dans le premier on trouve la descriptio n des terrnes relevant de cet art;

l'obligati o etant ainsi definie cornrne un 'ars', tout cornrne la dialectique (definitio n qui, en substance , figure egalernent chez Roger Swyneshed "huius autern artis ab Aristotel e traditae duae sunt partes . . quarurn una d e ob l'igationi spectante s a d .propositur . 'b us II •••• ) II n, in Dans sa descriptio n l'Auteur donne un resume des differente s definition s, proposees par les rnodernes, et i l en fait la critique. 11 soutient que l'obligati o est "multiple x, ut iuridica, realis et loycalis" , rnais annonce qu'il parlera seulernent de l'obligati on logique. Le ms. de Turin ajoute poetica. Notre Auteur refuse trois descriptio ns qui sont cheres aus modernes "plus novitati quam veritati intendent es", c'est-a-d ire: I) obligatio est oratio cornposita ex signis obligatio nis et posito vel deposito.r nediante qua una cum admisso tenetur obligatus infra, tempus ipsius obligatio nis concedere positurn et negare depos i turn. 2) Alii sic earn describun t: obligatio est quaedam ars rnediante qua opponens ligat respondent em ad suam voluntatem . 3) Alii autem sic describun t: obligatio est oratio composita

448

ex signis obligationis et obligate. 11 ajoute que ces trois definitions "deficiunt in hoc quod non dantur per genus proprium quia obligatio est de praedicamento actionis, cum sit actus obligantis". Puis il developpe sa critique (qui est tres interessante et qui meriterait une analyse en profondeur) pour enfin donner sa preference a la definition suivante: "obligatio est prefixio alicuius enunciabilis ad sustinendum aliquem statum", c'est-a-dire: l'obligation est le prefixe d'une enonciation capable de soutenir un certain status. Les obligations sont done etablies a cette fin,- qu' un homme quelconque, puisse souteni r une proposition quelconque, fut-elle fausse, au moyen de l'un des status et qu'il puisse, ainsi que le

repondre avec pertinance. Le but de l'obligation, tel