The hypothesis of a theoretical unity between On Sophistical Refutations and Prior Analytics presents a major challenge to scholars attempting to unify the criteria of analysis. This paper examines this problem and proposes a middle ground between the perspectives of Woods and Boger to address this crucial question: If a unitary and coherent theory of deduction exists, why does not the technical apparatus of syllogistic modes for analyzing fallacies appear in SE? This paper makes useful contributions to the discussion on (...) the internal unity of Aristotle's logical writings on around categorical syllogistics and the doctrine of sophistical refutations. (shrink)

The hypothesis of a theoretical unity between On Sophistical Refutations and Prior Analytics presents a major challenge to scholars attempting to unify the criteria of analysis. This paper examines this problem and proposes a middle ground between the perspectives of Woods and Boger to address this crucial question: If a unitary and coherent theory of deduction exists, why does not the technical apparatus of syllogistic modes for analyzing fallacies appear in SE? This paper makes useful contributions to the discussion on (...) the internal unity of Aristotle's logical writings on around categorical syllogistics and the doctrine of sophistical refutations. (shrink)

ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for a hypothetical syllogistic which predates Stoic propositional logic. It emerges that Galen is one of our main witnesses for such a theory, whose authors are most likely Theophrastus and Eudemus. A reconstruction of this theory is offered which - among other things - allows to solve some apparent textual difficulties in the Institutio Logica.

Since McCall (1966), the heterodox principle of propositional logic that it is impossible for a proposition to be entailed by its own negation—in symbols, ¬(¬φ→φ)—has gone by the name of Aristotle’s thesis, since Aristotle apparently endorses it in Prior Analytics 2.4, 57b3–14. Scholars have contested whether Aristotle did endorse his eponymous thesis, whether he could do so consistently, and for what purpose he endorsed it if he did. In this article, I reconstruct Aristotle’s argument from this passage and show that (...) he accepts this thesis. Further, I show that the argument he gives is, making plausible assumptions, a correct proof in a consistent fragmentary nonclassical metalogic for a metatheorem he previously states concerning his assertoric syllogistic. In this way, Aristotle’s argument emerges as a fascinating case study in the use of a nonclassical metalogic to prove a result about a nonclassical object system. (shrink)

Aristotle studies syllogistic argumentation in Sophistical Refutations and Prior Analytics. In the latter he focuses on the formal and syntactic character of arguments and treats the sullogismoi and non-sullogismoi as argument patterns with valid or invalid instances. In the former Aristotle focuses on semantics and rhetoric to study apparent sullogismoi as object language arguments. Interpreters usually take Sophistical Refutations as considerably less mature than Prior Analytics. Our interpretation holds that the two works are more of a piece than previously (...) believed and, indeed, that Aristotle's treatment of fallacious reasoning presupposes the results of the formal theory. (shrink)

The large number of writers who have in recent years attacked the problem of the logical nature of commands appear generally in agreement in accepting the distinction of common grammar between imperative and declarative sentences as representing, albeit in no clear one-to-one manner, some real difference in the logical character of the two types of expression, and possibly in the psychological sign-functioning mechanism itself. The crucial logical difference adduced is that commands can apparently rot be classified as true or false. (...) One is then, however, confronted with the problem of interpreting arguments involving imperatives which appear syllogistic in form, such as:Keep your promises!You promised to pay on Wednesday.Pay on Wednesday! (shrink)

THE PROBLEM OF BEING IN PLATONISM FROM THE PERSPECTIVE OF THOMAS AQUINAS. A META-SYSTEMATIC ESSAY In spite of the apparent opposition to Plato, Aristotle accepted a lot from the thought of his master. The intuition, which plays the key role in the system of Plato, was understood by Aristotle in terms of how we grasp the middle term of syllogism. It is not, therefore, the intuition of being, but the reasoning, departing from the experience (nature’s “intention”), which is (...) the way of the cognition of the ultimate. The teleology of being, which Plato was so keen on finding, was found by Aristotle in the physical world as a counterpart of motion. Alas, Aristotle lost sight of what is most valuable in Plato: the sense of being that transgresses the categories. According to Thomas, being is what is the most perfect in things; so, consequently, what is the proper effect of the Ultimate Cause, and what is Its primary aim. It is better to be, i.e. to exist. Each thing craves for being. Being, however, is, in the Dionysius’ sense, a problem; it might guide us to God, but veil Him before us as well. It is a perfection, but not the Perfection itself, Plato was right at this point. Keywords: BEING, PLATO, ARISTOTLE, THOMAS AQUINAS. (shrink)

At Topics 8.11 161b19–33 Aristotle lists five criticisms () which may be leveled against a dialectical argument ‘in itself’ (). The five criticisms correspond in many respects to the familiar conditions Aristotle places on syllogism and refutation. However, begging the question —the violation of the condition that the conclusion of a syllogism be something different () from the premises—seems not to appear on the list of five criticisms. That this omission is only apparent becomes clear once it (...) is seen that the five criticisms are not independent but rather amount to five successive filters through which an argument may be passed before its non-genuineness is exposed. This result sheds light on Aristotle's curious insistence, in the face of the heterogeneity of his examples of BTQ in Topics 8.13, that every question-begging refutation contains a premise that is ‘the same’ as the conclusion. The fact that the five criticisms expose BTQ as a defect in syllogistic reasoni.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 34.3 (2001) 260-274 [Access article in PDF] Second Thoughts on the Critiques of Big Rhetoric Edward Schiappa This note is divided into three parts. First, I explore some answers to the question "How did Rhetoric get so Big?" Second, I review some of the more important criticisms of a "globalized" or "universalized" view of rhetorical studies. Finally, I contend that the critiques of Big Rhetoric do (...) not withstand scrutiny and ought to be dismissed for insufficient evidence. While there certainly are important issues for scholars of rhetorical studies to consider about how to enhance the quality and importance of our work, such issues should not include the concern that rhetoric has grown too "big."By "Big Rhetoric" I refer only to the theoretical position that everything, or virtually everything, can be described as "rhetorical." I refer to the growth of rhetorical scholarship in communication studies and other disciplines as the "popularization" of rhetorical studies. 1 Theories associated with Big Rhetoric are credited with popularizing or at least rationalizing what Herbert W. Simons (1990) calls the "rhetorical turn" in a variety of disciplines. Within the journals and conventions of members of the National Communication Association (NCA), popularization is often characterized by studies of the form "the rhetoric of X," where X could literally be anything. Outside of the NCA-defined parameters of communication studies, popularization is evidenced by the apparently ever-increasing ranks of scholars who use "rhetoric" as a relevant and important term of art within their scholarship. By either measure, it can be argued fairly convincingly that "rhetoric" has become a widely used construct in scholarship. What I wish to engage is the disputed desirability of broad definitions and the related popularization of rhetoric. [End Page 260] 1. Whence big rhetoric? There are a number of narratives on the rise of Big Rhetoric already in print in communication studies (Simons 1990; Gaonkar 1990), rhetoric and composition (Berlin 1987; Young and Goggin 1993), and interdisciplinary publications (Roberts and Good 1993; Mailloux 2000; Nelson, Megill, and McCloskey 1987). Many accounts identify the 1960s as a turning point. For better or for worse, there was a confluence of changing rhetorical practices, expanding rhetorical theories, and opportunities for rhetorical criticism. The cultural clashes of the 1960s were felt perhaps most acutely on college campuses. The sufficiency of deliberative argument and public address can be said to have been called into question, whether one was an antiwar activist who hated LBJ's war in Vietnam or a pro-establishment stalwart trying to make sense of the rhetoric of protest and demonstration. Years later, scholars would characterize war itself as rhetorical. What counted as rhetorical practice was up for grabs.At about the same time, our understanding of rhetorical theory was being expanded. Here we can identify two main strands of thought. For ease of reference I will call one the symbolic interactionist rationale and the other the epistemological rationale. The symbolic interactionist rationale can be boiled down to a syllogism: All persuasive actions are rhetorical. All symbol/language-use is persuasive. Therefore: All symbol/language-use is rhetorical. Perhaps the two most significant pronouncements of this approach--for my generation of rhetoric scholars, at any rate--are by Richard Weaver and Kenneth Burke. Weaver claims that "language is sermonic" in the sense that whenever we offer a description or label a phenomenon, we are "preaching" a particular way of making sense of it (1970, 201-25). Burke, of course, has two famous (or infamous) statements in Rhetoric of Motives: first, that rhetoric is "the use of language as a symbolic means of inducing cooperation in beings that by nature respond to symbols" (1950, 43); and second, that "something of the rhetorical motive comes to lurk in every 'meaning,' however purely 'scientific' its pretensions. Wherever there is persuasion, there is rhetoric. And wherever there is 'meaning,' there is 'persuasion'" (1950, 172). Obviously, such pronouncements serve as encouragement to [End Page 261] those who would define rhetoric broadly, and arguably fueled the popularization of rhetorical studies within the ranks of NCA.The epistemological rationale is fueled... (shrink)

In the eighth chapter of De Sophisticis Elenchis, Aristotle introduces a mode of sophistical refutation that constitutes an addition to the taxonomy of the earlier chapters of the treatise. The new mode is pseudo-scientific refutation, or “the [syllogism or refutation] which though real, [merely] appears appropriate to the subject matter”. Against the grain of its most commonly accepted reading, I argue that Aristotle is not concerned in SE 8 to establish that both the apparent refutations of SE 4–7 (...) and pseudo-scientific refutations issue in false conclusions. His concern rather is to provide a causal analysis of both classes of apparent refutation alike which will explain why both kinds of apparent refutation are sophistical – and whose solutions are therefore the task of no special science but of a dialectical σλλογιστιϰή τέχνη. I conclude my analysis with the observation that Aristotle exploits the results of SE 8 to fend off inSE 9, 10, and 11 respectively a triad of threats to the very existence of a τέχνη of the resolution of sophistical refutation. The three threats are: the impossibility of omniscience; the relativity of semantic beliefs; and the incapacity of a questioner ignorant of a science to expose the ignorance of a pretender to scientific expertise. (shrink)

The so-called “Trinitarian paralogisms” are apparently legitimate instances of syllogistic inference-schemes with premises and conclusions containing expressions of the language of the Trinity doctrine, which fail to be truth- or acceptability-preserving. The logical problem of the Trinity splits into two levels of analysis. First, the technical aspects of Trinitarian paralogisms are analysed in terms of logical innovations in theories of “suppositio” and “distributio”. Second, the philosophical aspect of Trinitarian paralogisms translates into the question of formality as general applicability of logic. (...) The sixteenth century tradition can be reconstructed as a reaction to the fourteenth century nominalist logical analysis. As opposed to post-medieval scholasticism developing the medieval approach, humanism and reformation criticise scholastic logic in terms of diff erent specifi c anthropological theories. (shrink)

The paper reviews some conceptions of logical form in the light of Andrea Iacona’s book Logical Form. I distinguish the following: logical form as schematization of natural language, provided by, for example, Aristotle’s syllogistic; the relevance to logical form of formal languages like those used by Frege and Russell to express and prove mathematical theorems; Russell’s mid-period conception of logical form as the structural cement binding propositions; the conceptions of logical form discussed by Iacona; and logical form regarded as an (...) empirical hypothesis about the psychology of language processing, as in the Discourse Representation Theory tradition. Whereas neither schematization, nor the use of special languages for mathematics, raise general methodological or empirical difficulties, other conceptions of logical form raise at least apparent problems. (shrink)

In two experiments we tested the hypothesis that the mechanisms that produce belief bias generalise across reasoning tasks. In formal reasoning (i.e., syllogisms) judgements of validity are influenced by actual validity, believability of the conclusions, and an interaction between the two. Although apparently analogous effects of belief and argument strength have been observed in informal reasoning, the design of those studies does not permit an analysis of the interaction effect. In the present studies we redesigned two informal reasoning tasks: the (...) Argument Evaluation Task (AET) and a Law of Large Numbers (LLN) task in order to test the similarity of the phenomena concerned. Our findings provide little support for the idea that belief bias on formal and informal reasoning is a unitary phenomenon. First, there was no correlation across individuals in the extent of belief bias shown on the three tasks. Second, evidence for belief by strength interaction was observed only on AET and under conditions not required for the comparable finding on syllogistic reasoning. Finally, we found that while conclusion believability strongly influenced assessments of arguments strength, it had a relatively weak influence on the verbal justifications offered on the two informal reasoning tasks. (shrink)

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is the result of comparing it with an inappropriate logical standard. In this article, we contrast the probabilistic approach with other approaches to explaining rationality, and then (...) show how it has been applied to three main areas of logical reasoning: conditional inference, Wason's selection task and syllogistic reasoning. (shrink)

In 2004, I explained the absurdity of Moore-paradoxical belief via the syllogism (Williams 2004): (1) All circumstances that justify me in believing that p are circumstances that tend to make me believe that p. (2) All circumstances that tend to make me believe that p are circumstances that justify me in believing that I believe that p. (3) All circumstances that justify me in believing that p are circumstances that justify me in believing that I believe that p. I (...) then took (3) to mean (EP) Whatever justifies me in believing that p justifies me in believing that I believe that p.1 Now suppose that I am justified in believing anything of the omissive Mooreparadoxical form: (Om) p and I do not believe that p. Then I am justified in believing the first conjunct. So by (EP) I am justified in believing that I believe that p. But since I am also justified in believing the second conjunct, I am justified in believing that I do not believe that p. I claimed that this is impossible, because anything that justifies me in believing that something is the case renders me unjustified in believing that it is not the case. This syllogism is plausible from an externalist view of justification, according to which circumstances such as seeming to see rain under normal perceptual conditions, justify me in believing that it is raining. In support of (1), if my apparent perceptions of rain are reliably connected with rain, so as to justify me in thinking that it is raining, they also tend to make me believe that it is raining. In support of (2), my apparent perceptions of rain are also reliably connected with my coming to believe that it is raining. However, Anthony Brueckner (2006) argues that (1) and (EP) are both false once justification is thought of evidentially. Against (EP), he claims that my evidence that p is not evidence that I believe that p unless I possess the evidence, in the sense that I believe it and were I to believe that p on its basis. (shrink)

La critique cartésienne de la logique est souvent reconduite à celle du syllogisme et d’une dialectique dont l’Organon aristotélicien fournit l’exposé canonique. On veut montrer ici, en resituant le propos cartésien dans son cheminement initial , que cette critique vise aussi, sinon en premier lieu, une conception alternative d’inspiration lulliste qui tend à s’imposer dans la Schulmetaphysik allemande contemporaine, et par le biais de laquelle celle-ci, déjà, prétend pouvoir se constituer en système encyclopédique du savoir. Le point culminant de cette (...) critique ne se trouve nullement dans le rappel de l’humaine finitude, et la dénonciation d’une vaine prétention à l’omniscience, car l’universalité de la méthode cartésienne lui permet tout aussi bien de viser la connaissance de toutes choses, même les plus « cachées » et les plus « éloignées ». Il se trouve en revanche dans une théorie des « natures simples » , qu’on peut juger lacunaire et inachevée au vu de l’incapacité apparente de Descartes à en établir la nomenclature exacte. Mais le statut propre de la logique cartésienne est indissociablement lié à celui de ces « natures simples » et au refus motivé d’en établir une liste exhaustive.Descartes’ criticism of logic is often reduced to criticism of syllogism and to the dialectic which can be perfectly represented and illustrated in Aristotle’s Organon. Going back to the very roots of Descartes’ thought , this article tries to demonstrate that above all else, his criticism also includes an alternative representation of logic widely diffused in contemporary German Schulmetaphysik which asserts itself as an encyclopaedic knowledge system. The climax of this criticism does not consist in the idea of human finitude nor in the pretension of universal knowledge. In fact universality of Descartes’ method can be applied to everything, even the « deepest » and « most distant » ones. This climax lies in the theory of « simple natures » which can be judged as incomplete as regards Descartes’ apparent inability to establish an exact list and description. Nevertheless, the exact status of Descartes’ logic is precisely linked to the status of these simples natures and to Descartes’ conscious refusal to establish a list. (shrink)

La relación entre máxima lógica y principio sintético de la razón pura ocupa un lugar fundamental en la "Dialéctica trascendental". Esto se nota en la formulación de los problemas que la Dialéctica se propone abordar, pues hace una referencia explícita al pasaje de la máxima al principio mencionado ; sin embargo, Kant no explica cómo se haría tal pasaje. Aquí se propone una explicación de dicho pasaje a través de un estudio pormenorizado de la premisa mayor del silogismo cosmológico, donde (...) éste ocupa un lugar fundamental. se sostendrá que tal pasaje sólo es comprensible suponiendo una máxima lógica restringida que permita deducir legítimamente, para el caso de la lógica general, lo incondicionado dado a partir de lo condicionado dado. El principio trascendente será una pretendida extensión de esta máxima a las cosas en sí. The relationship between the logical maxim and the synthetic principle of pure reason plays an important role in the "Transcendental Dialectic". This is apparent by noting that the formulation of the problems treated in the Dialectic has an explicit reference to the transition from the maxim to the principle . Nevertheless, Kant doesn't explain how this transition is made. I intend to explain this transition through a detailed study of the major premise of the cosmological syllogism, where it has an important role. I claim that this passage is understandable only by assuming a restricted logical maxim that allows inferring legitimately the unconditioned given from the conditioned given. The transcendental principle will be an extension of this maxim to things in self. (shrink)

Jean-Luc Marion’s phenomenology has received much attention recently, both critical and constructive, but much less work has been done looking at the relationship between Marion’s work on Descartes and his phenomenological project. The present article begins by making a point of clarifying Marion’s understanding of the meaning of Descartes’s cogito, and contrasting it with the standard understanding as found in Leibniz, Kant, and Heidegger. Following the discussion of these various interpretations of the cogito, we examine some of the similarities between (...) Marion’s particular interpretation of Descartes’s cogito as a performative exercise and Marion’s particular phenomenological analyses of givenness and the saturated phenomenon. Notably, in Marion’s view both the cogito and givenness overcome incorrect conceptions of objectness and being, both of them exceed the limits of syllogistic logical formulations, and both are irreducible to their apparent constituting parts. (shrink)

The incompleteness and artificiality of the ?traditional logic? of the textbooks is reflected in the way that syllogisms are commonly enumerated. The number said to be valid varies, but all the numbers given are of a kind that logicians should find irritating. Even the apparent harmony of what is almost invariably said to be the total number of syllogisms, 256, turns out to be illusory. In the following, it is shown that the concept of a distribution-value, which is related (...) to the traditional theory of distribution, and the familiar concept of quantity together suffice to produce a far better way of enumerating syllogisms and a more complete understanding of the systematic features of syllogistic logic. (shrink)

Psychoanalytic accounts offer a mix of reasons and causes to explain action. Adolf Grünbaum argues that these fail to be proper explanations because they are neither justified by inductively established laws, nor fit the standard form of rational explanation, the belief-plus-desire-yields-action structure of the practical syllogism. Grünbaum accepts rational explanation as cogent and transparently causal because, he asserts, reasons are causes. Yet he omits to show how they can be, especially in the face of the apparent fact that (...) reasons, being defined in terms of their propositional content, cannot be causes. Clarifying the position of psychoanalytic explanation does involve seeing it and rational explanation as similarly causal. This requires a realist analysis showing how reasons may be understood, not as defined in terms of their propositional contents or objects, but as states of persons caused by entering into relations with situations, and how reasoning is a causal process. Freud's philosophical intuitions on this were correct. His much criticized metapsychology offers a causal account of motives defined by source, not object, and sketches an account of the way these cause action in interaction with external situations. 2012 APA, all rights reserved). (shrink)

Despite renewed interest in T.H. Green’s social and political theory, little attention has as yet been given to his metaphysics and epistemology — even more neglected, though, are his views on logical matters. It is unclear why this is. I suspect that the obscurity of his discussion has much to do with it. Green routinely refers to writers in whom there is little interest today; and a good deal of effort is required to penetrate his technical vocabulary. Still, I believe (...) we miss something important when we ignore his specifically logical writings. Green has much to say about classical syllogism and its influence on his contemporaries. And, while the discussion is always grounded in his own idealist theory of knowledge, Green’s analysis often reveals surprising aspects of the problem being considered. In what follows, then, I shall consider one such analysis: his account of the logical/epistemological doctrine of Sir William Hamilton and H.L. Mansel — individuals whose writings, in Green’s eyes, made apparent all that was wrong with the “formal logic” of the day. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Aristotle’s Rhetoric: Philosophical EssaysCarol PosterAristotle’s Rhetoric: Philosophical Essays, edited by David J. Furley and Alexander Nehamas; xv & 322 pp. Princeton: Princeton University Press, 1994, $45.00.Scholars will find Aristotle’s Rhetoric, Philosophical Essays fascinating both for what is present and what is absent. As Alexander Nehamas states (pp. xi–xiv), this volume attempts to rectify the neglect by philosophers of Aristotle’s Rhetoric in particular and rhetoric in general. While the (...) volume’s introduction and eleven essays are erudite, readable, and well-argued within their own logical and philosophical disciplinary traditions, the absence of reference both to contemporary rhetorical scholarship and ancient rhetorical traditions is somewhat disappointing.M. F. Burnyeat’s essay typifies both the strengths and weaknesses of the collection. Burnyeat presents a reception history of the Aristotelean enthymeme [End Page 361] in the logical tradition, and argues convincingly for reading the enthymeme as a relaxed rather than truncated syllogism. Missing, however, is a sense of how the enthymeme changed in response to large scale movements in ancient rhetorical theory and reference to contemporary rhetorical scholarship on the enthymeme, which covers much territory Burnyeat treats as unexplored.Several contributors compare the Rhetoric with Aristotle’s other works. Jacques Brunschwig claims that the Rhetoric and the Topics contextualize rhetoric differently and address different audiences. Glenn Most argues quite persuasively that Aristotle constructs a hierarchy of argumentative precision, with logic using the most precise, ethics and politics somewhat less precise, and rhetoric the least precise arguments. He shows that Aristotle’s treatment of endoxa (opinions) in the Rhetoric, Nichomachean Ethics, and Politics reflects this hierarchy. John Cooper points out that rhetoric looks to ethics/politics for its subject matter, but his argument applies only to one of the three genres of oratory and overlooks the heuristic potential of the topoi. Both Most and Cooper, though providing solid philosophical analyses of endoxa, do not discuss the rhetorical use of endoxa as gnômai, and thus useful premises for enthymemes. Stephen Halliwell also reconciles the Rhetoric with Aristotle’s ethical works by showing how the advantageous tends to, rather than opposes, the good.Alexander Nehamas builds a coherent theory of the emotions as amenable to reason by investigating fear and pity in the Rhetoric and Poetics. André Laks, drawing on the work of Paul Ricoeur, discusses two traditions of metaphor, ornamental and transformative, in the Poetics and Rhetoric. Jean-Louis Labarrière contributes a solid and highly original comparison of painting and oratory in Plato and Aristotle.Jürgen Sprute sees rhetoric not only as a solution to a Platonic impasse, but as a necessary and effective tool for Aristotelian political philosophy. Mary McCabe argues that Aristotle refutes both Phaedrus and Gorgias by showing that rhetoric is a technê and consequently a legitimate political tool. Eckart Schütrumpf presents the compelling and original suggestion that Aristotle’s Rhetoric should be read as extending the framework of the late Platonic Laws rather than as refuting earlier Platonic dialogues.Many of these essays share two serious flaws. The first is an unstated tendency to read the Aristotelian corpus as unproblematically systematic and polished, and all apparent contradictions as susceptible to reconciliation. More explicit attention to interpretative assumptions, as is commonplace in Platonic scholarship but rare in Aristotelian, might be desirable. The second flaw is disciplinary insularity. As Nehamas points out (pp. xi-xiv), rhetoric and philosophy were not clearly demarcated in antiquity. To respond to Aristotle’s Rhetoric adequately, scholars need to transcend contemporary disciplinary divisions, and attempt to synthesize rhetorical, logical, philosophical, and literary scholarship, something this volume, despite its many strengths, fails to do.Carol PosterUniversity of Northern IowaCopyright © 1995 The Johns Hopkins University Press... (shrink)

In 1934 a most singular event occurred. Two papers were published on a topic that had (apparently) never before been written about, the authors had never been in contact with one another, and they had (apparently) no common intellectual background that would otherwise account for their mutual interest in this topic.1 These two papers formed the basis for a movement in logic which is by now the most common way of teaching elementary logic by far, and indeed is perhaps all (...) that is known in any detail about logic by a number of philosophers (especially in North America). This manner of proceeding in logic is called ‘natural deduction’. And in its own way the instigation of this style of logical proof is as important to the history of logic as the discovery of resolution by Robinson in 1965, or the discovery of the logistical method by Frege in 1879, or even the discovery of the syllogistic by Aristotle in the fourth century BC. (shrink)

BEFORE Frege’s Begriffsschrift, propositional logic was submerged in the often murky theory of the "hypothetical syllogism." With the exception of the Stoa, a handful of astute mediaeval logicians, Leibniz, and Bolzano, one might well obtain the impression from studying the history of logic that Frege created his theory ex nihilo—which is substantially true, since Frege was apparently little influenced by previous work. One might also obtain the impression, especially by reading Frege himself, that very little was being done on (...) propositional logic in the 19th century. This claim would be false. As one might expect from a philosopher who is sometimes grouped with Frege and De Morgan as one of the greatest nineteenth century logicians, Charles S. Peirce dealt extensively with propositional logic, or as he would have called it, with the theory of the hypothetical syllogism. (shrink)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of (...) metalogical sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (shrink)

The taxonomy and analysis of fallacies in Aristotle's Sophistical Refutations pre-date the formal logic of his Prior Analytics A4-6. Of the 64 fully described examples of ?sophistical refutations? which are fallacious because they are only apparently valid, 49 have the wrong number of premisses or the wrong form of premiss or conclusion for analysis by the Prior Analytics theory of the categorical syllogism. The rest Aristotle either frames so that they do not look like categorical syllogisms or analyses in (...) a quite different way than by categorical syllogistic. (shrink)

Is the history of philosophy primarily a contribution to PHILOSOPHY or primarily a contribution to HISTORY? This paper is primarily contribution to history (specifically the history of New Zealand) but although the history of philosophy has been big in New Zealand, most NZ philosophers with a historical bent are primarily interested in the history of philosophy as a contribution to philosophy. My essay focuses on two questions: 1) How did New Zealand philosophy get to be so good? And why, given (...) that is so good (a point I am at pains to establish), has it apparently had so slight a cultural impact within New Zealand itself? Did we get the wrong Anderson – the uninspiring William, who was Professor at Auckland, rather than his talented younger brother John, who had such a huge cultural influence as Professor of Philosophy at Sydney? Perhaps but that can only be part of the story since we managed to attract even bigger stars, (notably Karl Popper) as well as breeding bigger talents of our own (Prior, Baier, Bennett, Mulgan, Hursthouse, Waldron and many more). Do we export our best talent? Sometimes – but the stars that stay and the stars who arrive don’t seem to have much impact in New Zealand itself however brightly they shine in the international philosophical firmament. Is it too esoteric? Perhaps, but esoteric philosophy can still have a cultural impact, witness, Moore, Popper and the younger Anderson. Is it, like many of New Zealand’s cultural products (from romance novels to movies), primarily intended for an international audience? That’s a large part of the answer but only a part. Another part of the answer is that philosophy HAS had a cultural impact but that impact is not readily apparent. For NZ philosophers have been less keen to push their ideological barrows and more keen to produce critical thinkers, and critical thinkers don’t all think alike. The logician George Hughes was apparently a life-changing teacher not because he had a nostrum but because he taught people to think. As one of his students said ‘the only ism you believe in is the syllogism’. On the whole the history of New Zealand Philosphy is a ‘From Log Cabin to White House’ tale, ‘From colonial obscurity through struggle and adversity to philosophical excellence’. But there are shadows in the picture. Some departments have nearly come to grief through bureaucratic and political misadventures, and it is hard to resist the suspicion that there is often an element of hostility to philosophers on the part of both university bureaucrats and fellow-academics. I speculate as to why this is the case (we are too argumentative and don’t confine our argumentative tendencies to the cloister) but conclude with some upbeat reflections. on the future of New Zealand Philosophy. (shrink)

At Prior Analytics II 22.68a16–21, Aristotle argues that if A is predicated of all B and C and nothing else, and B is predicated of all C, then A and B convert. In justifying his argument, however, he appears to claim that B is not predicated of all A. This claim has long been a cause of puzzlement to commentators. A widespread view is that the kind of conversion discussed in the passage at issue should be explained in both extensional (...) and intensional terms. After providing some textual evidence that Aristotle only apparently claims that B is not predicated of all A, I give a purely extensional account of Aristotle’s argument. This account is plausible, conservative and simpler than any of the intensional accounts that have been proposed so far. (shrink)

There is the famous anecdote about Freud: upon being reminded by a disciple that to smoke cigars is clearly a phallic activity, Freud, cigar in hand, is said to have responded, “Sometimes a good cigar is just a good cigar.” The anecdote demonstrates, it seems to me, a problematic central to psychoanalysis: the discipline which insists on transference and, perhaps even more significantly, on displacement as fundamental principles, ultimately must insist in turn on seeing everything as being “really” something else. (...) Such an ideology of metamorphosis is so much taken for granted that unlike the rest of the world, which generally has difficulty in being convinced that a pipe, for example, is not necessarily a pipe at all, psychoanalysis needs at times to remind itself, in a type of return to an adaequatio, that it is possible for a cigar really to be a cigar. Psychoanalysis, in other words, has not only an economy which is hydraulic , but has as well an economy of seepage: each apparent object, whether in dream, literature, or psychic narrative, splashes over onto at least one “something else.” Not only is there always a remainder, but the remainder generally proliferates, multiplies, from more than one quotient, such that the original “thing” in question becomes merely the agent for production. Its status as thing-in-the-world is easily lost.Such seepage has, of course, appeared almost everywhere. Psychoanalysis has infiltrated such diverse areas as literature , linguistics, philosophy, anthropology, history, feminism, psychology, archeology, neurology, to name some. And it is in the notion of “some,” perhaps, that lies the crux of the problem. For there is in psychoanalysis an overt conviction that it exists as the ultimate totality, of which everything else is a part. Not content to see itself as one in a number of enterprises, the psychoanalytic project has at its foundation a vision of itself as the meaning which will always lie in wait; the truth which lies covered by “the rest.” Jacques Derrida has, of course, pointed to this tendency. Psychoanalysis, he noted, wishes a peculiar logic for itself, one in which “the species would include the genus.”1 Moreover, says Derrida in the same essay, once psychoanalysis has discovered itself, what it then again proceeds to discover around it is always itself.2 What happens, then, is that psychoanalysis becomes a ubiquitous subject, assimilating every object into itself. But it is also a Subject which sees itself as omnipresent, omniscient, and without a center—precisely the terms in which God has been described. It is not then by chance that the unconscious is likened to a divinity: always present but revealing itself only obliquely and at privileged moments, the unconscious takes the place of the Judeo-Christian God. It is within every being, but inaccessible unless it “chooses” to manifest itself. And in a peculiar reversal of the notion of the partitive, psychoanalysis would have the unconscious reveal itself in fleeting moments and fragments, thereby suggesting its fullness and totality; and it would have “other” intellectual enterprises be only apparent totalities which are revealed through psychoanalysis alone to be “really” incomplete because they exist without recognizing the unconscious and its mother, psychoanalysis itself. 1. Jacques Derrida, “Graphesis,” “The Purveyor of Truth,” trans. Willis Dominggo et al., Yale French Studies 52 : 32.2. See the syllogism with which Derrida opens his “Purveyor of Truth,” p. 31. Part of what I am calling the “syllogism” appears at the beginning of Stephen Melville’s article in the present issue. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Skeptical Selves: Empiricism and Modernity in the French NovelDaniel GordonSkeptical Selves: Empiricism and Modernity in the French Novel, by Elena Russo; 225 pp. Stanford: Stanford University Press, 1996, $35.00.Skeptical Selves explains how linguistic relativism has shaped French literature from the Enlightenment to the present. Elena Russo provides three cases: Prévost’s Histoire d’une Grecque moderne (1740), Constant’s Adolphe (1816), and des Forêts’s Le Bavard (1946). Her fascinating scholarly goal (...) is to portray the inexorable decline of the novel in a climate of ever growing doubt about the truthfulness of narration. Her remarkably ambitious philosophical goal is to save the novel by refuting skepticism!More precisely, Russo’s target is not every form of doubt but rather a specific current of French skeptical consciousness. In recent years, the representatives of this current have been Derrida and Blanchot. Its main feature is a denial of the correspondence notion of the language-truth relationship combined—paradoxically—with an intense nostalgia for a perfectly mimetic language that has allegedly been lost. The seemingly most radical critics of the sign, Russo claims, never overcome the perverse yearning for the very mimesis whose possibility they deny (p. 3).Russo is getting at an interesting distinction here, the distinction between epistemological modesty, which she upholds, and French skepticism, which she deplores. Epistemological modesty means the redefinition of truth according to some criterion other than perfect representation of the external world. French skepticism for her means the insistence on an absolute standard of mimetic reliability and a simultaneous denial that this standard can ever be reached. “Much of the language of negativity we have grown accustomed to in contemporary criticism rests upon the following syllogism: to know is to know directly and without mediation; this is not possible; therefore, the world is unknowable. Any conceptualization is ipso facto viewed as suspect, hence the flight towards nonverbal forms of expression, such as music and silence” (p. 13).After suggesting in her first chapter that French skepticism is a specific style of thought, not a final answer to our epistemological queries, Russo goes on to illustrate the impact of this skepticism on the novel. Prévost’s text, she observes, is one of the first novels built around the distorted point of view of a fallible [End Page 179] narrator. The narrator is the French ambassador to Constantinople who falls in love with a woman, Théophé, recently freed from a seraglio. Both his love and his comprehension are frustrated by the woman’s apparent simplicity and virtue. “Signs acquire a meaning opposite to their manifest one,” Russo notes. “It is precisely the discourse that should have made Théophé look credible that makes her appear suspicious. She is cunning and deceptive because she appears ‘naive’ and ‘innocent’; she is opaque because of her ‘simplicity’ and ‘openness’” (p. 42). The whole point of the novel is to show that we are imprisoned in subjectivity and there is no way out. For a time the narrator attempts to resolve his doubts regarding Théophé’s words by concentrating instead on her body. But here as well he can discover only ambiguity: nothing reveals clearly whether she is conquerable and whether she already has another lover.The novel ends with the unexplained death of Théophé, and Russo comments: “we are given the impression that, rather than ending his text, Prévost is ridding himself of an intractable problem” (p. 66). Artfully, the rest of the book helps us see that the tendency to thematize philosophical problems that have no solutions is intensified in the nineteenth and twentieth centuries—to the point where not merely the ending of novels but novels themselves disappear. (Of course, Russo means not that people no longer write novels but that the genre has succeeded in diminishing its own stature by so frequently decrying the limits of language.)The chapter on Constant did not strike me as the strongest part of the book. The problem is due perhaps to the fact that Constant was a truly great thinker, a brilliant political theorist and philosopher of religion as well as a romantic novelist. One chapter does not... (shrink)

This collection of seven papers by six authors centers about the relation of free action to determinism as both a metaphysical as well as a methodological hypothesis. Chisholm is concerned with the problem of whether a human whose behavior is completely controlled by outside forces can still be considered free; Danto studies the old problem of whether it can be said that actions of men are caused in the same way as the activities of other objects. Richard Taylor examines the (...) problem of free will in light of the apparent asymmetry of the prevention and the postvention—the doing of an act not ruled out by antecedent conditions—of events; Ginet develops a notion of "contingent necessitation" and proceeds to show that humans do not have a choice as to whether their actions satisfy certain conditions, these conditions following by contingent necessity from events not themselves in an individual's control. Wilfrid Sellars contributes two papers; the first is a study of the locution of "intending that," desiring and willing, intending, believing, the condition of being disposed to, and the practical syllogism; the second paper continues the tenor of the first—Sellars formalizes the notions of various kinds of "necessary" states of affairs, and uses this to make a distinction between being able to will and being able to do an act. The editor has the last paper which concerns the matter of whether there can be an empirical disproof of determinism.—P. J. M. (shrink)

This book presents the first study of the development of the theory of modal syllogistic in the Middle Ages.

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed (...) to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship between division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: Allxareyand Somexarey, There are at least as manyxasy, and There are morexthany. Herexandyrange over subsets (not elements) of a giveninfiniteset. Moreover,xandymay appear complemented (i.e., as$\bar{x}$and$\bar{y}$), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. (...) There are efficient algorithms for proof search and model construction. (shrink)

This book uncovers and examines the confusion in antiquity between Aristotle's hypothetical syllogistic and Stoic logic, and offers a fresh perspective on the ...

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental (...) rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

This paper reviews current psychological theories of syllogistic inference and establishes that despite their various merits they all contain deficiencies as theories of performance. It presents the results of two experiments, one using syllogisms and the other using three-term series problems, designed to elucidate how the arrangement of terms within the premises affects performance. These data are used in the construction of a theory based on the hypothesis that reasoners construct mental models of the premises, formulate informative conclusions about the (...) relations in the model, and search for alternative models that are counterexamples to these conclusions. This theory, which has been implemented in several computer programs, predicts that two principal factors should affect performance: the figure of the premises, and the number of models that they call for. These predictions were confirmed by a third experiment. Dans cet article sont passées en revue les théories psychologiques du traitement des syllogismes. On établit qu'en dépit de leurs mérites variés toutes sont en défaut en tant que théories de la performance. On présente les résultats de deux expériences, une utilisant des syllogismes et l'autre des problémes avec des séries de trois termes conçues pour élucider comment l'arrangement des termes dans les premises affecte la performance. Ces données sont utilisées pour construire une théorie fondée sur l'hypothése que les gens construisent des modèles mentaux des premises, formulent des conclusions explicites sur les relations dans le modèle et cherchent des modèles qui seraient des contre-exemples pour leurs conclusions. Cette théorie, utilisée dans plusieurs programmes d'ordinateur, prédit que deux principaux facteurs affectent la performance: la figure des premises et le nombre de; modèles qu'ils mettent en jeu. Cette prédiction est confirmée dans les trois expériences. (shrink)

This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...) between contradictories and contraries, and the square of opposition. This strategy helps to improve students’ understanding of metalogic, because it allows the students to integrate these new ideas with their previously acquired knowledge of syllogistics. (shrink)

The syllogism has often been criticized. Yet the theory of the syllogism cannot be omitted from logic. Even if it were not for its historical significance, its nature as a chapter of class logic assigns to it a place in any presentation of logic.The usual exposition of the theory of the syllogism, however, whether given by the use of the familiar rules of the syllogism, or by the help of diagrams, appears clumsy and lacks the lucidity (...) of modern chapters of logic. The reason seems to be given in the inefficient notation, taken over from ancient and medieval logic. In the following I should like to present an improved notation, which combines some of the traditional features with modern ones, and which is based on the criticism of the syllogistic theory which I have given elsewhere. It will be seen that in the revised form the theory of the syllogism is apt to meet the standards of modern logic. (shrink)

Comparative syllogism is a type of scientific reasoning widely used, explicitly or implicitly, for inferences from observations to conclusions about effectiveness, but its philosophical significance has not been fully elaborated or appreciated. In its simplest form, the comparative syllogism derives a conclusion about the effectiveness of a factor (e.g. a treatment or an exposure) on a certain property via an experiment design using a test (experimental) group and a comparison (control) group. Our objective is to show that the (...) comparative syllogism can be understood as encoding a simulation view of counterfactuals, in that counterfactual situations are conceptual constructs that can be correctly simulated by homogeneous comparison groups. In this simulation view, the empirical data from the comparison groups play an evidential role in the evaluation of counterfactuals and in obtaining counterfactual knowledge. We further indicate how successful experimental designs can help us to obtain correct simulations, and thus to bring us to scientifically-empirically based counterfactual knowledge. (shrink)

Does cognition sometimes literally extend into the extra-organismic environment (Clark, 2003), or is it always “merely” environmentally embedded (Rupert, 2004)? Underlying this current border dispute is the question about how to individuate cognitive processes on principled grounds. Based on recent evidence about the active role of representation selection and construction in learning how to reason (Stenning, 2002), I raise the question: what makes two distinct, modality-specific pen-and-paper manipulations of external representations – diagrams versus sentences – cognitive processes of the same (...) kind, e.g. episodes of syllogistic reasoning? In response, I defend a “division of labor” hypothesis, according to which external representations are dependent on perceptually grounded neural representations and mechanisms to guide our behavior; these internal mechanisms, however, are dependent on external representations to have their syllogistic content fixed. Only their joint contributions qualify the extended computational process as an episode of syllogistic reasoning in good standing. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 864-886, December 2021.

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as (...) early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics. (shrink)

Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...) that the ontology of CL enables numerically exact assertions and inferences. (shrink)