Logic as a Liberal Art [1 ed.] 7565137111, 9787565137112

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Preface to the Series

Semiotics AnotherWindowon the World Jie ZHANG and Hongbing YU (Eds.)

The intelligentsia nowadays is characterized by diversity in ways of knowing the world. Facing the vastness and complexity of society, nature and the universe, humankind has a deeply-felt sense of their tininess and powerlessness, but on the other hand, humans have always been actively exploring new ways of looking into the world. Since ancient times, there have been two major paths of human intellectual inquiry. One is constantly extending and deepening social studies; the other is using theoretical and logical reasoning to examine and even predict the laws of nature and the universe. It is precisely along these two paths that contemporary semiotics proceeds and progresses. The first five English monographs that are included in this book series of Select Works of Eminent Contemporary Semioticians, published by Nanjing Normal University Press, represent these two paths and thus reflect the latest trends in current semiotic inquiry. These books may afford not only revelations in the ways of knowing and the dimensions of thought, but also new perspectives for interpreting contemporary socio-cultural phenomena and their developments. We would first like to introduce Basics of Semiotics ( eighth edition), written by the late American master philosopher and semiotician John Deely. Since its first edition, this book has been a well-known classic in sem1ot1cs, and various editions have been published in different languages. However, the last edition in English was the fifth edition, which is no longer available, as it sold out in 2015. This up-to-date eighth English edition is long overdue. The book highlights two overarching issues concerning the entire enterprise of modern semiotics. One is the differences between semiology and semiotics; the other is the scope of semiotic inquiry. Deely points out that semiology, to wit the " minor tradition" traced back to Ferdinand de Saussure, confines sign studies to the limited fields of human cultures centering on language, whereas semiotics, namely the "major tradition" following Charles Sanders Peirce and upheld by Charles William Morris and Thomas Albert Sebeok among others, has enlarged the scope of semiotic inquiry to include not only linguistic signs, but also the biology of semiosis. Stressing the differences 00 I

between the two traditions, Deely is manifestly against equating semiotics with semiology. Moreover, in this most up-to-date edition of Basics of Semiotics, Deely grasps theoretically the full extent of the action of signs. Inheriting Peirce's formulation of semiosis that the essence of signs involves a _triadic relation between representamen, object and interpretant, none of which needs physical existence in the semiosic process, Deely further argues that physiosemiosis is an action of signs that precedes •and stays free from life. The action of signs features its involvement with nonbeing. In Deely's own words, the sign "must exist in order to convey an object signified to or for some third ( be it a person or not). But what is conveyed may not exist, and similarly the 'third' to which it is conveyed may not yet exist." In addition to the above two issues, Deely also distinguishes between source date and access date by means of what he calls "historical layering, " for which the raison d'etre is "No one writes after they die." According to Deely, the source date must and can only be a date from within the lifetime of the author of the given text, whereas the access date is the date of the translation, or edition, used to access the source. In both the scope and the quality of research, Basics of Semiotics has made considerable progress, which is why in 1990 the late American Paterfamilias Semioticorum Thomas Sebeok praised the first edition of the work as "the only successful modern English introduction to semiotics ... a clear, creative, and provocative synthesis of major trends, past and present." Although entitled "Basics of Semiotics, " the book is different from other general introductions to semiotics in that it not only introduces to its readers crucial masterpieces of semiotics and master semioticians, covering significant topics ranging from the historical development of semiotic thought to current institutionalization, subject matters and prospects of semiotics, but also showcases Deely's own theorizing and academic viewpoints. By comparison, Signs in Society and Culture, written by the renowned American media critic & theorist Arthur Asa Berger, has something significant in common with Deely's Basics of Semiotics ( eighth edition): adding the epistemological breadth and depth of semiotics. However, in terms of their writing styles, Signs in Society and Culture is somewhat different from Basics, in that the former highlights the connections between semiotics and modern ordinary life, whereas the latter focuses more on theoretical interpretations. In vivid and humorous language, Berger manages to apply semiotic concepts to the analytical and meaningful interpretations of socio-cultural phenomena and emphasizes theorypractice integration that is grounded in current social media and folk arts. The book can stimulate its readers to think deeply about socio-cultural phenomena and emphatically embodies the social value and effects of semiotics as a methodology. Perhaps this will be a cross-disciplinary tour de force that brings a novel reading experience to its readers. One of the 002

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main reasons that this book is included in the series is that we want to make it clear that semiotics, as a methodology of research, is not merely something exclusive to metapbysics. It can also be a potent way to understand and interpret daily life situations, appreciate folk arts, and shed light on communication media, etc. Apparently, it is from the perspective of semiotics that both Deely and Berger set out on their quests for new approaches to the world, each with their own new mythologies, new interpretations, and new routes, in theory (Basics) and in practice ( Signs in Society and Culture) . Logic as a Liberal Art, another Deely book in the series, and The Way of Logic, written by Canadian philosopher Christopher S. Morrissey, a managing editor of The American Journal of Semiotics, mainly use theoretical and logical reasoning to examine and interpret the mystery of the universe and the complexity of human societies. In the inadequacies of our human capacity to exhaust the subjects of the vast universe and our capricious human societies, logic often seems to be an ideal route to theoretically construct and interpret them. A major contribution of Deely's Logic as a Liberal Art is that it lays the theoretical foundations for logical analyses in contemporary semiotic research and thus restates the fundamental value of· logic in liberal education. Using the theoretical framework constructed in his Basics of Semiotics, Deely manages to reinterpret the philosophical root of logic in the entire field of semiotics and provides the foundation for the logical reasoning of semiotics. His theoretical treatment of the subjective world is quite unique and •affords a contemporary interpretation of classical ontology and epistemology. Deely proposes that the mission of logic is to use clear and workable rules to turn invalid arguments into •valid arguments, so as to interpret the world from the viewpoint of semiotics. The logic Deely has built is extraordinarily constructive and it is a new development of term logic and propositional logic. Moreover, Deely also associates logical analysis with liberal education, arguing that the purpose of a liberal education is to enable the freedom and liberation of thought, in which process logic plays a critical role. Deely had encountered this in the Greek and Latin philosophical traditions, which he strongly advocates reviving. Therefore, whether we consult it to know the world from the perspective of philosophy and logic, or whether it is used to improve liberal education, this book can come as a great source of revelations to its readers. It is doubtlessly a cross-disciplinary classic. Morrissey's The Way of Logic starts with the problem of existential import, a fundamental philosophical topic in philosophy, to strive for an ideal path of logical analysis within the frameworks of philosophy and semiotics, and to provide an effective " way of logic " for human understanding. The author proposes adopting term functor logic, which he developed from Aristotelian term logic. He also points out that mainstream 003

first-order logic, namely predicate logic, is limited by the existential condition -imported and encoded in the syntax and therefore unable to show traditional logic in its entirety. While following the classical logic system, the author introduces two basic functors, + and - , and the. only rule of calculation, DON. On the one hand, this has returned logic to pure propositional reasoning; on the other hand, it gives logical reasoning more concise mathematical forms. This book provides an in-depth analysis of the problem of existential import and proposes a third solution between term logic and first-order logic. It is a classic that integrates tradition and innovation. It can be said that Deely's Logic as a Liberal Art paves the way for logical research in contemporary semiotics, whereas Morrissey's The Way of Logic affords an effective research method for concrete logical analysis. The common feature between the two books is the present-day adaptation of ancient knowledge, coalescing Hellenic and Latin heritages with contemporary semiotics and opening another window on today's world. Among the five academic monographs in the series, Marshall McLuhan: The Unwitting Semiotician, written by another North American master semiotician Marcel Danesi, seems to feature little theorizing concerning semiotics per se. Nor does it use many daunting and abstruse terms. Indeed, this book is intended mainly to be a pertinent and semiotically based close reading of the author's former teacher, Marshall McLuhan, an internationally famous scholar who was not a declared specialist in semiotics but actually an "unwitting" semiotician, as is shown in the book title. However, unlike many other books on semiotics, despite its seemingly un-academic interpretation, Danesi's portrait of McLuhan the semiotician is profoundly significant: Semiotics exists in everyday real-life situations as a way to perceive and understand everyday life. The term "semiotician" can even extend to the ordinary living people around us. With his usual liveliness and wit, Danesi narrates the dynamic ideas of a visionary theorist, in a way akin to a tireless spinning of a soothing yarn .. This quasi-orality writing style can bring the readers a unique experience of reading, lighthearted yet of depth and insight. In fact, Marshall McLuhan: The Unwitting Semiotician is not only an excellent case study concerning semiotic interpretation, but also a wonderful source book for many areas, including communication, media studies, cultural semiotics, and so on. To the readers who take a particular interest in the evolution of human communication, this book will prove an especially great revelation. The value of this series extends beyond semiotics itself in that it also provides methodological guidance for studies in the fields of the humanities and social .sciences, opening a semiotic window on the world, that is, using semiotic approaches in our attempts to explore and know the world. As we recall, Kalevi Kull emphasized at the 33rd Annual Meeting 004

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of SSA in 2008 that we study semiotics to make the world pluralistic. It is for the same purpose that we publish this book series, using an intrinsically pluralistic method of academic inquiry to understand our pluralistic world. As a matter of fact, . natural sciences aim chiefly to search for regularity in the bewildering complexity of the world, that is, to simplify what is complex, whereas the humanities and social sciences, in addition to their own necessary search for regularity, can "complicate" what seems simple. It is in the latter that the genuine significance of semiotic inquiry as a methodology lies. Since late 2015 when it was first prepared, the final publication of this book series has taken more than two years. In this process, many have offered their kindhearted help. Besides the authors of the books in the series, the book editors, and the authors of Chinese guides to reading for the five books, we would like to express our heartfelt gratitude to the president of IASS-AIS Professor Paul Cobley for his professi~nal suggestions and constant support, and to the director at Nanjing Normal University Press . Ms. Chun Zhang for her devotion to the series. Very special thanks go to our dear old friend· John Deely, who had spared no effort to support Chinese semiotics in the international arena since we made our first acquaintance. Alas, John passed away on January 7th 2017. To this international master semiotician, we dedicate his two posthumous swansongs Basics of Semiotics ( eighth edition) and Logic as a Liberal Art. Each book in the series is complemented by a Chinese guide to reading. The authors of the guides are prime scholars in the semiotics team at the School . of Foreign Languages and Cultures of· Nanjing Normal University. They have thorough training in semiotics and relevant fields and long-term involveme.nt in research. Their efforts will better prepare the series for Chinese readers, paving the way for a more comprehensive engagement with the content. Their devotion to the project has made the series more reader-friendly. Society, nature and · the universe are vast and boundless in that society is temporally inexhaustible while nature and the universe are spatially bottomless, so to speak. Human intellectual inquiry is similar to a small boat sailing on the sea, and semiotics is merely ..another window opened on this boat.

Suiyuan, NNU October 2017

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Figure 17.2 The Existence of "Things" Within Experience

In this figure, the full nature of indirect conversion as a process symmetrically inverse to the direct process stands in clear relief. While this process may have been devised historically merely as a way around the roadblock preventing an O from being converted at all and preventing an A from being converted without restriction, as Poinsot claims ( 1631: 47a44-bl), it is nonetheless actually a much more fundamental operation than the incidental circumstances of that original devising would indicate. Indirect conversion reveals considerably more about the nature of the

274

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dicisign than would ever be guessed from its usual presentation as a practical remedy, providing "the only way in which a restricted negative can be converted at all" or "the only way in which an unrestricted affirmative dicisign can be simply converted". Following each step in the Table, note that in the process of indirectly converting the original basic varieties of minimals, the first step is to transfer the impossibility of conversion from the original O to what was asserted in the original I, and to transfer the restriction on simple conversion from the original' A to what was asserted in the original E. Of course, this transfer of the obstacles to conversion is precisely achieved by using negation to make the original O take the form of an I and the original A take the form of an E, so that the basic determination resulting from the dicisignificative syntax in its fundamental opposition as affirmative or negative continues to be the ruling immediate consequence in both procedures. But, having thus transferred the locus of the conversion impediments, obversion also inverts the results of the final outcome, so that, where in direct conversion it was the original A that was restricted in its convertibility, in indirect conversion it is the original E that is restricted in its counterposability to I, and hence in its final indirect conversion to 0. Similarly inversely, where the original E is not only unrestricted in its convertibility but is also convertible by restriction ( or "accidentally") , in counterposability and finally in indirect conversion it is the original A that has this inclusive luxury. And where the original I was simply convertible and the original O insusceptible of conversion, for purposes of counterposition and indirect conversion it is the original I that become insusceptible. Finally, in all three cases-in direct conversion, in counterposition, and in indirect conversion-the original variety of four dicisigns is winnowed down to three; but, whereas in direct conversion it is the original A that collapses into the final I and the original E that expands into O as well as E, in indirect conversion or counterposition it is the original E that collapses into a restricted form and the original A that expands to occupy both a restricted and an unrestricted form of minimal dicisign. Thus the original S > c < P syntax realized in A, I, E, 0 forms becomes the directly converted P > c < S I, E, 0, with the original 0 suppressed entirely and replaced by the accidentally converted version of the original E; while the same S > c < P original syntax in its original realizations becomes the indirectly converted S > c < A, I, 0, with the original I suppressed entirely and replaced by the accidentally converted version of the original A, the whole procedure mediated by the double negation required to complete the symmetry of the interchange ( that is to say, the maintenance of the original dicisignificative quality) on the indirect side. 275

Some authors, notably Parker and Veatch (1959: 198-200), have applied truth,.functional analysis to "this operation of ' turning the obversion-conversion crank' ", arriving at the following rule: "If the original is true all the derivatives are true; but if the original is false only those derivatives are false which are the same in quantity as the original, the others being undetermined." The reason why this rule holds will become clear upon the analysis of the opposition of minimal dicisigns, which will be taken up in a later section of this chapter. Just as the purpose of colligation within logic is ultimately to arrive at true inferences, so the purpose of direct and indirect conversion is to get around formulations of minimal dicisigns that are blocking the determination of valid forms of inference or the formation of colligations that . could lead to valid inferential forms, as we will see especially in the chapter on validation. Direct and indirect conversions, we may say, mark boundaries within which the parts inferior to the minimal syntax of dicisigns can be rearranged compatible with the integrity of the original assertion as represented. But once the underlying steps necessary to exhibit the validity of indirect conversion as a genuine implication or consequence of the minimally dicisignificative form have been traversed, it becomes possible to adopt a short-cut both to the contrapositive outcome and to the ultimate outcome of indirect converses. To reach the contrapositives, simply negate directly the predicate terms and the copulas of the three minimals which are susceptible of contraposition ( the A, the E, and the 0) and interchange the S and P terms, in the case of the E to be counterposed restricting its quantity at the same time so it counterposes to I, in the case of the 0 to be counterposed simply counterposing it to I, in the case of the A to be counterposed simply counterposing it to E and by restriction to 0. To reach the indirect converses, simply negate directly both the subject and predicate terms of the three minimals susceptible of indirect conversion ( again, the A, the E, and the 0) and reverse their position respecting the copula, leaving the quality of the copula unchanged, in the case of the E to be counterposed necessarily restricting the extension so that it indirectly converts to 0, in the case of the 0 to be indirectly converted proceeding simply to I, in the case of the A to be indirectly converted expanding it into two indirectly converted forms, once simply as an A and once by restriction as an I. In this shortcut to the indirect converse, the quality of the dicisign and its determination are unaffected, exactly as in direct conversion, but the indexical function played by the term under its properly symbolic constitution ( which, as we have observed, always includes as symbol indexical and iconic dimensions as well) is reversed, exactly as occurs when the full steps demonstrating the validity of the process are carried out in sequence. 276

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Hence the rules for indirect conversion: 1. The "A" variety of minimal dicisign indirectly converts either with or without restriction; 2. The "I" variety indirectly converts impossibly, i. e., it cannot be indirectly converted fully or even partially by any means; 3. The "E" variety converts only by restriction; 4. The "O" variety converts without restriction.

Similarly, the rules for contraposition: 1. The "A" variety of minimal dicisign counterposes simply to E and by restriction to O; 2. The "I" variety can't be counterposed; 3. The "E" variety counterposes by restriction to I; 4. The "O" variety counterposes simply to I.

The steps for contraposition may be summarized thus: 1. After reducing the dicisign to strict logical form, negate the copula and the predicate term of the A, E, and the O (leaving the subject term unchanged) ; 2. Interchange the S and P, restricting the A to I if desired, the E to O of necessity.

The steps for indirect conversion may be summarized thus: 1. Negate both the S and P terms of the A, E and the O (leaving the quality of the copula unchanged); 2. Interchange the S and P, restricting the A to I if desired, the E to O of necessity.

The inverse parallelism of direct and indirect conversion may be expressed in the following schema ( Figure 17. 3) : CONVERSION

INDIRECT

DIRECT

Simple Only: I to I

By Restriction Only: A to I (A drops out)

Either Way: E toEorO

Simple Only: OtoO

By Restriction Only: EtoO (E drops out)

Either Way: A to A or I

Figure 17.3 The Existence of "Things" Within Experience

Thus, if the subject and predicate terms of an A or an O are each negated and transposed, A becomes "Each nonP is nonS" and/or "Some 277

nonP is nonS", and O becomes "Some nonP is not nonS", which gives us at once the indirectly converted forms (i.e., the converts of obverses) of the originals. But to show exactly how these results are valid equivalents of the original varieties, 1t 1s necessary to go through the intervening steps of, first, obversion, and then contraposition (i.e., the converting of obverts). When these steps are in place, it is seen how each variation at each step follows as an immediate consequence of the directly preceding step, and how the whole sequence results in the inverse symmetry which suggests that direct and indirect conversions mark out positive and negative boundaries, as it were, within which internal redistribution can be made of the represignificative parts consistent with the syntax of a minimal dicisign. In particular, notice that in obversion, contraposition, and indirect conversion alike-that is to say, at each step in the process of indirect conversion-the negation the procedure relies upon is regulated and governed by the function of the copula within the syntax itself of the dicisign as a unity within its own order; for it is the copula that governs the determination and status of the predicate, as we have seen, and it is by reason of this governance of the determination of the predicate through the copula that negation (like modality and time) can be transferred back and forth between the represignificative iconicity of the predicate term as governed by the copula and the relating function of the copula itself governing the manner of application of the predicate to the subject. It is likewise this governance of the copula, as we have seen, that requires the avoidance of infinitation of the predicate term if the processes of obversion, contraposition, and indirect conversion alike are to retain formal validity, since in each of these processes, since a copula can only be negative and never infinite, as we have seen, the introduction of infinitation into one of the terms would violate the original extension and determination ( the proportion to the signified) of those terms as governed by the copula. Finally, the extended analysis above may make indirect conversion particularly, involving as it does so many steps, appear as an extremely artificial logical procedure, well removed from any context of discourse in natural language. Some consideration and a few examples suffice to obviate this impression. Consider, first of all, any; dicisign whatever may be regarded not as the starting point for an indirect conversion, but equally as the end product of such a conversion. The nature of immediate consequence equally justifies moving in either direction, since no example of a dicisign by its nature requires being regarded as representing either a terminal, seminal, or intermediate point in any of the formal processes that may be performed upon it. Any given dicisign may be regarded equally as a 278

Logic as a Liberal Art

contraponend or a contrapositive, or as any stage in between. We will see this further in our next section considering inversion. Some examples make the same point. Suppose you are travelling through Germany by train enroute to Geneva, and you awake from a lengthy nap as the train pulls into the station of a large city. Wondering if this city might already be Geneva, you ask a companion, "Are we in Switzerland?" and receive the answer "No". Then, assuming the truth of this answer, you are able to conclude directly, "Ah, I didn't think this could be Geneva already". ( For Geneva being in Switzerland, what is outside of Switzerland is outside of Geneva.) In the case of contraposition as a spontaneous phenomenon, in contrast to the process of indirect reduction as a critically controlled process of reflective analysis within logic, the individual understanding the represigns A and B as extremes united within a dicisign as subject and predicate, intuitively grasps that if A is B, whatever is interior to the extension of A is inside the extension of B, and therefore whatever is exterior to B is also outside A ( "Whatever is nonB is nonA") , which is to grasp something by counterposition. An excellent illustration of everyday reasoning using counterposition is given by Kelley ( 1988: 186): Suppose you wanted to argue that computers are not conscious-that they are not in the class of conscious things. You might try to do this by assuming that all conscious things (S) are living things (P), which means that all nonliving things ( including computers) are nonconscious. You just took the contrapositive.

Further illustrations of how the thought process involved in contraposition is a common one are given by Joseph ( 1916: 239-240) under the forms of conditional colligations; but here for the moment our attention is on the immediate consequences of dicisignifica~ive syntax as they bear on the internal arrangement of the represignificative parts of the minimal dicisign as they are subsumed within and regulated in their distribution by the form, that is to say, the syntax or relative unity of the dicisign itself as the minimal constituent of its own order. A.3. Inversion: The Consequent Limits in the Internal Transformation of Minimal Dicisigns The term " inversion" closest to the sense we will establish here was introduced in 1884 by John Neville Keynes in the 1st edition of his Studies and Exercises in Formal Logic (pp. 88-90 n. 2) to name the final steps needed in order to make the scheme of immediate consequences "scientifically complete". Prior to Keynes' work, the form of indirect consequence he labeled "inversion" had only been "more or less casually recognized by various logicians" and without receiving "any distinctive 2 79

name" (Keynes 1884: 88). Keynes systematized the notion, but in a context which included, along with dicisigns derived by immediate consequence, certain non-inferrible dicisignificative forms arrived at by more-or-less arbitrary placings of negations on various parts of the dicisign. ( see Keynes, Zoe. cit. , Maritain 1923: 146-14 7, etc.) . This context of discussion influenced Keynes' own discussion, marring his otherwise excellent terminological point. 1 Keynes arrived at his notion of inversion in this way ( 1884: 86): In what cases can we obtain by immediate inference from a given proposition a new. proposition having the contradictory of the original subject for its subject, and the original predicate for its predicate?

The answer to this question was A and E, the "inverse" of A being Some nonS is not P (Some s >cccC