This chapter discusses the relation between Kant’s views on the foundations of syllogistic inference in ‘The False Subtlety of the Four Syllogistic Figures’, the views of eighteenth-century German authors who wrote on syllogism, and the conception of metaphysics that Kant developed in 1762-1764. Kant’s positions are, on the whole, rather original, even though they are not as independent from the intellectual context as Kant’s later, Critical philosophy. Despite Kant’s polemical tone, his views on syllogism are not (...) primarily motivated by polemical purposes. They are strongly influenced by his views on the method of metaphysics. (shrink)

Kant’s early work The False Subtlety of the Four Syllogistic Figures is typically considered a narrow, technical work still embedded in the tradition of Wolffian logic. I argue instead that it needs to be considered in light of Kant’s developing theory of cognition and his corresponding criticism of the Wolffian single faculty theory. Whereas the mature Kant criticizes the rationalists for misrepresenting the nature of sensibility, the urgent task facing him at this stage seems to have been (...) a proper determination of the nature of the understanding. On the Wolffian framework, the latter is defined in a merely nominal manner, in terms of a generic cognitive task: the distinct representation of the possible. On Kant’s view, however, distinctness entails a capacity to relate representations, which only happens in the act of judgment. Thus, the stated aim of the False Subtlety notwithstanding, the work attempts to reorganize the logical operations around the capacity to judge. In turn, by defining the higher faculty of cognition in terms of an act of relating representations, Kant wants to show that this faculty cannot stem from a power of representation that we share with non-rational animals and must instead rest on a different fundamental power, which at the time he alternatively calls “inner sense” or “consciousness”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:New Light from Arabic Sources on Galen and the Fourth Figure of the Syllogism NICHOLAS RESCHER The Problem of the Origin of the Fourth Figure FLYING IN THE FACE of the long-standing tradition--going back in Europe to Renaissance times--which credits Galen of Pergamon with the origination of the fourth syllogistic figure, recent authorities have almost to a man evinced doubt about Galen's claim to this innovation. Heinrieh Scholz (...) speaks of "the Galenian syllogistic figure which has been attributed to him, probably wrongly." i j. W. Stakelum concludes his careful discussion of the matter with the categorical assertion that "Galen did not teach the fourth figure." ~ I. M. Bochenski--following Lukasiewicz (see below)--says that the fourth figure "was only ascribed to Galen by a misunderstanding." : William Kneale (also following Lukasiewicz) writes that "it is easy to see how misunderstanding.., by some Arabian philosopher... could have given rise to the tradition that Galen added a fourth figure to Aristotle's syllogistic theory." 4 The currently received account of the matter is that of Jan Lukasiewicz who, in his book on Aristotle's Syllogistic (1951; 2d ed., 1957), presents the known reports about Galen and the fourth figure as follows (I list them in the order in which they came to light) : 1) Several passages in Averroes' (d. 1198) Middle Commentary on Prior Analytics credit Galen with introducing a fourth figure (ad Anal. Pr. I, 5; I, 8; I, 23). These passages, known in Europe through a Renaissance Latin translation of a Hebrew version, provided the basis upon which Zabarella in his work, De Quarta Syllogismorum Figura (in his Opera [Leiden: 1587], pp. 41-53), popularized the "Galenian figure" in European logic. 2) In 1844 Minoides Mynas published in the Preface to his edition of Galen's EisagSg~ dialektik~ an anonymous Greek fragment (late, perhaps 6th century) which states that certain "later scholars" transformed the indirect moods of the first figure added by Theophrastus and Eudeffms into a new fourth figure, citing Galen as the originator of this doctrine.~ 1Abriss der Geschichte der Logik (Miinster: 1931), trans, into English by K. F. Leidecker, ConciseHistory of Logic (NewYork: 1961);p. 38ofthe Englishversion. "Why 'Galenian' Figure?" The New Scholasticism, XVI (1942),289-296. s Formale Logik (Miinchen-Freiburg:1956; 2nd. ed., 1962), trans, into English by Ivo Thomas, A History of Formal Logic (Notre Dame: 1961);p. 142of the Englishversion. Williamand Martha Kneale, The Developmentof Logic (Oxford: 1962),p. 184. Alsoprinted in Karl Kalbfieisch, ~ber Galen s Einleitung in die Logik, 2~. Supplementband der Jahrbi~cherfi~r klassische Philologie (Leipzig:1897), p. 707. This datum casts some 28 HISTORY OF PHILOSOPHY 3) A Greek fragment was found around 1858 by Karl Prantl in a logical work of the Byzantine scholar Ioannes Italus (llth century) which says that Galen taught the existence of a fourth figure, adding sarcastically that he (Galen) thought thus to appear cleverer than the older logical commentators (presumably Theophrastus and Eudemus are intended), but fell far short.6 4) In 1899 Maximilian Wallies published7 an anonymous Greek scholium (of perhaps the 6th or the 7th century) on Ammonins' commentary on Prior Analytics which states that Galen "says in his Apodictic that there are four figures, because he looks at the compound syllogisms consisting of four terms (i.e., with three premisses )" rather than the simple (three-term, two-premiss) syllogisms of Aristotle. (The scholiast goes on to explain at some length how such compound syllogisms can be sorted into four groups.) It is readily seen that, given these data, two possibilities stand before us: a) Galen did actually invent the traditional fourth figure. Reports (1)-(3) are correct, and the anonymous scholiast of (4) was put on the wrong track by the fact that Galen also said that compound syllogisms of four terms can be classed into four groups. b) Galen did not invent the traditional fourth figure. Only after his time when once the indirect moods of the first figure had--somehow--become systematized into a separate "figure," was this credited to Galen by a mistake along the lines described by the anonymous scholiast. Thus (4) alone is right, and (1)-(3) are mistaken. Which of... (shrink)

The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status over the (...) other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)

In Prior Analytics A7 Aristotle points out that all valid syllogistic moods of the second and third figures as well as the two particular moods of the first figure can be reduced to the two universal first-figure moods Barbara and Celarent. As far as the third figure is concerned, it is argued that Aristotle does not want to say, as the transmitted text suggests, that only those two valid moods of this figure whose premisses are both universal statements (...) are directly reducible to Barbara and Celarent, but rather that it is those four valid moods of this figure whose respective minor premisses are universal statements of which this is true. It is shown that in order to carry this sense the transmitted text has to be corrected by inserting just one word, which seems to have dropped out. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain (...) how the syllogistic is a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a (...) syllogism is a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)

In the present article, the author deals with the role of the middle term in the four figures of conjunctive syllogism. In this regard, he refers to the views of logicians such as Ibn Sina, Fakhr al-Din Razi, Muhaqqiq Tusi, Urmawi, Athir al-Din Abhari as well as Mulla Sadra. The author is of the view that many difficulties in syllogisms arise out of linguistic deficiencies.By resorting to Mulla Sadra's view, the author concludes that we are not compelled to (...) divide the syllogism to its traditional four forms, for on the basis of the Sadrian view, the only condition for the productivity of all forms of syllogism is the repetition of the middle term. Therefore, with regard to the mechanical deduction of the conclusion of premises, it seems unneccessary for us to distinguish the figures of a syllogism from each other. (shrink)

In 1951 Lukasiewicz [[sic]] linked Aristotle's Prior Analytics with modern formal logic. This book attempts to analyze Aristotle's syllogistic theory in the light of Lukasiewcz's work and the whole tradition of classic interpretations of Aristotle's logic. The first of the book's five chapters shows that for Aristotle the syllogism is basically a relationship of terms couched in conditional form; a relationship of variables rather than concrete terms; and a relationship that sees S linked with P not by the copula (...) but by less metaphysical expressions. The classical S is P form is not Aristotelian at all but a much later renovation. The second chapter maintains that Aristotle distinguishes "relative necessity" from "absolute necessity." Aristotle himself ignores his own distinction at times and thus creates logical difficulties for himself. The oft-fought sea battle is fought again in this chapter. Chapter three deals with the controversial notions of "perfect" and "imperfect" syllogisms. The author asserts that by "perfect syllogism" Aristotle means self-evident syllogisms that serve as axioms for deducing other proofs. Chapters four and five deal with the figures of the syllogism and the syllogism as a deductive system respectively. Patzig concludes that Aristotle's syllogistic theory is purely formal in its structure and can only be properly understood if it is not tied to a metaphysics and converted into a philosophical logic. He denies that it is a universal logic, but rather sees it as a specialized theory of relations.--J. J. R. (shrink)

Close attention to Kant’s comments on animal minds has resulted in radically different readings of key passages in Kant. A major disputed text for understanding Kant on animals is his criticism of G. F. Meier’s view in the 1762 ‘False Subtlety of the Four Syllogistic Figures’. In this article, I argue that Kant’s criticism of Meier should be read as an intervention into an ongoing debate between Meier and H. S. Reimarus on animal minds. Specifically, while broadly (...) aligning himself with Reimarus, Kant distinguishes himself from both Meier and Reimarus on the role of judgement in human consciousness. (shrink)

The article examines the relevance of Aristotle’s analysis that concerns the syllogistic figures. On the assumption that Aristotle’s analytics was inspired by the method of geometric analysis, we show how Aristotle used the three terms, when he formulated the three syllogistic figures. So far it has not been appropriately recognized that the three terms — the major, the middle and the minor one — were viewed by Aristotle syntactically and predicatively in the form of diagrams. Many (...) scholars have misunderstood Aristotle in that in the second and third figure the middle term is outside and that in the second figure the major term is next to the middle one, whereas in the third figure it is further from it. By means of diagrams, we have elucidated how this perfectly accords with Aristotle's planar and graphic arrangement. In the light of these diagrams, one can appropriately capture the definition of syllogism as a predicative set of terms. Irrespective of the tricky question concerning the abbreviations that Aristotle himself used with reference to these types of predication, the reconstructed figures allow us better to comprehend the reductions of syllogism to the first figure. We assume that the figures of syllogism are analogous to the figures of categorical predication, i.e., they are specific syntactic and semantic models. Aristotle demanded certain logical and methodological competence within analytics, which reflects his great commitment and contribution to the field. (shrink)

: I give two interpretations of the supreme rules of all syllogisms provided by Kant in his pre-critical essay “The False Subtlety of the Four Syllogistic Figures”. One interpretation understands literally, i.e., grammatically, the expressions ‘positive syllogism’ and ‘negative syllogism’; the other interprets them non-literally, i.e., it interprets them logically.

This book is a printed dissertation directed by Norbert Hinske and defended at Trier in 1996. It deals with the relationship between formal and transcendental logic from the standpoint of the history of Kant’s development, of Kant’s sources, and, more generally, of the history of concepts. In 1932, Klaus Reich summarized the status quaestionis thus, “Observing the destiny of Kant’s sketch on pure general or formal logic, which lies at the foundation of both the edifice and the realization of the (...) Critique of Pure Reason, one cannot help to marvel at the discrepancy of the opinions of the interpreters and of Kant himself”. Vázquez Lobeiras mentions three main Kant interpretations in the twentieth century: one based on the theory of knowledge, the second based on metaphysics, and the third based on the history of logic. She declares to follow the logical-historical interpretation. The first chapter is dedicated to a detailed reconstruction of the status quaestionis, beginning with Kant’s contemporaries, going through the famous controversy between Norman Kemp-Smith and Herbert Paton, the former maintaining the primacy of transcendental against formal logic, the latter the opposite, and ending with Gerold Prauss and Giorgio Tonelli. The second chapter explores the fate of the distinction between transcendental and formal logic in the history of Kant’s development. Vázquez Lobeiras concentrates her attention on a famous section of the Critique of Pure Reason, the “Introduction: Idea of a Transcendental Logic”. Her intention is to interpret it by relating it with pertinent passages from Kant’s Lectures on Logic, Lectures on Metaphysics, the program on the False Subtlety of the Four Syllogistic Figures, and the dissertation, De mundi sensibilis atque intelligibilis forma et principiis. “Form” is the concept she focuses on, on the basis of an impressive list of parallels she has found that connect the distinction between formal and transcendental logic with the distinction between usus logicus and usus realis of the dissertatio. She points to a telling argument Kant makes in Reflection 1599, that namely the subject of formal logic is “the usage of the understanding in general,” while that of metaphysics are “the objects of pure reason.” But what would these “objects of pure reason” be? Vázquez Lobeiras refers them to the rationis purae objecta of the dissertatio, which are free from sensible determinations while remaining subject to the laws on the intellectual world. In this reflection she sees the stage that immediately precedes the “Introduction: Idea of a Transcendental Logic” of the Critique of Pure Reason. The third chapter concludes by investigating the progressive establishment of new boundaries set by Kant to metaphysics. (shrink)

Perhaps the strangest controversy in the history of logic is that over the fourth figure of the syllogism. There was never any argument as to what syllogisms are valid, but merely as to how they should be arranged. Aristotle had divided syllogisms into figures according to whether the middle term was subject of one premiss and predicate of the other, or predicate of both premisses, or subject of both. Theophrastus and Eudemus subdivided the first figure into those moods in (...) which the middle term was subject of the major premiss and those moods in which the middle was predicate of the major premiss. The latter moods were termed indirect. Galen said they constituted a separate figure; and so the controversy started. It has continued to the present with many writers objecting to the fourth figure, generally on grounds that it does not represent a genuine process of thought, and even ascribing this objection to Aristotle. The issue has been joined by writers who believe that it does represent a genuine process of thought. (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)

Espino and Santamaria experimentally demonstrate that, if the syllogisms in the first figure are not presented as is the usual practice, that is, separating their two premises into two different lines, but linking the two premises into one line by means of a full stop, individuals tend to draw from such premises conclusions in which the subject and the predicate are not in the customary order, but rotated. In their view, this finding is consistent with the assumptions of the mental (...) models theory. Nevertheless, in this paper, I will show that what this fact really depends on the approach that is adopted, since a framework based on formal logic also has resources to explain it, and hence can lead us to assume theses different from those proposed by Espino and Santamaria. Espino y Santamaría demuestran experimentalmente que, si los silogismos de la primera figura no son planteados como se hace tradicionalmente, esto es, separando sus dos premisas en dos líneas diferentes, sino en una sola línea uniendo las dos premisas mediante un punto seguido, los individuos tienden a deducir a partir de tales premisas conclusiones en las que el sujeto y el predicado no se encuentran en el orden habitual, sino invertidos. Desde su punto de vista, este hallazgo es consistente con los supuestos de la teoría de los modelos mentales. No obstante, en este trabajo, vamos a mostrar que lo que tal hecho significa verdaderamente depende del enfoque que se adopte, ya que un marco basado en la lógica formal también cuenta con los recursos para explicarlo y, por tanto, puede conducirnos a asumir tesis diferentes a las propuestas por Espino y Santamaría. (shrink)

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory (...) or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz, a scholar equally at home in philosophy, classics, mathematics, and logic. Perhaps surprisingly, the then-prominent syllogistic mnemonic played no role in the Łukasiewicz work. His 1950 masterpiece does not even mention the mnemonic or its two earliest champions William and Peter. The syllogistic mnemonic is equally irrelevant to the post-Łukasiewicz paradigm established in the 1970s and 1980s by John Corcoran, Timothy Smiley, Robin Smith, and others. Robin Smith’s comprehensive 1989 treatment of syllogistic does not even quote the mnemonic’s four verses. Smith’s work devotes only 2 of its 262 pages to the mnemonic. The most recent translation of Prior Analytics by Gisela Striker in 2009 continues the post-Łukasiewicz paradigm and accordingly does not quote the mnemonic or even refer to the code—although it does use the terminology. Full mastery of modern understandings of syllogistic does not require and is not facilitated by ability to decode the mnemonic. Nevertheless, an understanding of the history of logic requires detailed mastery of the syllogistic mnemonic, of the logical theories it spawned, and of the conflicting interpretations of it that have been offered over the years by respected logicians such as De Morgan, Jevons, Keynes, and Peirce. More importantly, an understanding of the issues involved in decoding the mnemonic might lead to an enrichment of the current paradigm—an enrichment so profound as to constitute a new paradigm. After presenting useful expository, bibliographic, hermeneutic, historical, and logical background, this paper gives a critical exposition of Smith’s interpretation. (shrink)

In this paper, we discuss the syllogisms from both fronts : Aristotle and Boethius. We mainly focus on the differences with respect to categorical and hypothetical syllogisms in Aristotle and Boethius. Regarding Aristotle’s works on logic, it is not unusual to claim that Aristotle extensively worked on categorical syllogisms. In Prior Analytics, Aristotle gave proofs for many valid moods. However we cannot find a similar treatment for hypothetical syllogism in his works. Thus, it might be a reason for his students (...) to improve Aristotle’s theory of syllogisms by filling the gaps in hypothetical syllogisms. As Boethius already emphasized in the Book I of De Hypotheticis Syllogismis, the Peripatetic School only initiated the start. The remaining and detailed treatise was due to Boethius himself. The impression we got from Boethius’s and Aristotle’s works on syllogisms is that the categorical syllogism is almost entirely developed by Aristotle himself, whereas the extensive and the detailed study of the hypothetical syllogism was carried out by Boethius, although he was not the first figure in the history who gave concise expositions on hypothetical syllogism. Boethius’s translations of syllogisms in medieval era were the primer resource and textbook for Aristotelian logic during the early Medieval ages. Therefore, the scholars of those times had no other chance but to work from Boethius’s commentaries. So, the evident properties of Aristotelian figures were not then visible. Boethius wrote several textbooks in logic. A detailed investigation might yield significant information on Boethius’s logic compared with the influence of Aristotle on Boethius. (shrink)

In this article I explain three puzzling features of Simplicius’ use of syllogistic reconstructions in his commentary on Aristotle’s Physics: (1) Why does he reconstruct Aristotle’s non-argumentative remarks? (2) Why does he identify the syllogistic figure of an argument but does not explicitly present its reconstruction? (3) Why in certain lemmata does he present several reconstructions of the same argument? Addressing these questions, I argue that these puzzling features are an expression of Simplicius’ assumption that formal reasoning underlies (...) Aristotle’s prose, hence they reflect his attempt to capture as faithfully as possible Aristotle’s actual mode of reasoning. I show further that, as a consequence of this seemingly descriptive use of syllogistic reconstructions, logic serves Simplicius not only as an expository and clarificatory tool of certain interpretations or philosophical views, but also motivates and shapes his exegetical stances and approach. (shrink)

Syllogism is a form of logical argument allowing one to deduce a consistent conclusion based on a pair of premises having a common term. Although Aristotle was the first to conceive and develop this way of reasoning, he left open a lot of conceptual space for further modifications, improvements and systematizations with regards to his original syllogistic theory. From its creation until modern times, syllogism has remained a powerful and compelling device of deduction and argument, used by a variety (...) of figures and assuming a variety of forms throughout history. The Aftermath of Syllogism investigates the key developments in the history of this peculiar pattern of inference, from Avicenna to Hegel. Taking as its focus the longue durée of development between the Middle Ages and the nineteenth century, this book looks at the huge reworking scientific syllogism underwent over the centuries, as some of the finest philosophical minds brought it to an unprecedented height of logical sharpness and sophistication. Bringing together a group of major international experts in the Aristotelian tradition, The Aftermath of Syllogism provides a detailed, up to date and critical evaluation of the history of syllogistic deduction. (shrink)

In an earlier article (see J Gen Philos Sci (2009) 40: 357-372) I have discussed the arguments brought forward by Michael Wolff against the interpretation given in the commentary by Ebert and Nortmann on Aristotle's syllogistic theory (Aristoteles Analytica Priora Buch I, übersetzt und erläutert von Theodor Ebert und Ulrich Nortmann. Berlin 2007) and against the critique of Kant's adaption of the syllogistic logic. I have dealt with Wolff's arguments concerning (Ebert/Nortmann's interpretation of) Aristotle in the paper mentioned (...) and with his attempts to defend his critique in this subsequent article (part 1; see J Gen Philos Sci (2010) 41: 215-231). Part 2 (the paper below) is concerned with Wolffs renewed attempts to defend Kant as a logician. In particular I point out that if, as Wolff claims, the nota notae relation in Kant is restricted to subordinated concepts, then it can hardly serve as a principle for syllogistic logic, as Kant claims. Against Wolff's attempts to defend Kant's claim that o-propositions are simpliciter convertible, I point out two arguments: (1) Even if Kant, following the Vernunftlehre by Meier, has assumed that an o-proposition can be turned into an i-proposition (by adding the negation sign to the predicate), this conversion is useless for the reduction to first figure syllogisms since we are no longer dealing with three syllogistic terms but with four. (2) It is quite unlikely that Kant has a conversion of this type in mind since the texts of his students always talk of the group of either the particular propositions or else of the negative propositions. Given Kant's mistakes concerning the convertibility simpliciter of o-propositions, it is no wonder that he overlooks the special status of the moods Baroco and Bocardo. Wolffs attempts to provide Kant with what he claims are direct proofs for these moods can be shown to rely on a reductio ad impossibile. Kant mistook what are parts of the proofs for the validity of moods in figures two to four as parts of these moods themselves. Wolff—who tries to defend Kant on this point—is forced to an artificial and unconvincing reading of the Kantian texts. (shrink)

E. J. Lowe, a prominent figure in contemporary metaphysics, sets out and defends his theory of what there is. His four-category ontology is a metaphysical system which recognizes four fundamental categories of beings: substantial and non-substantial particulars and substantial and non-substantial universals. Lowe argues that this system has an explanatory power which is unrivalled by more parsimonious theories and that this counts decisively in its favour. He shows that it provides a powerful explanatory framework for a unified account (...) of causation, dispositions, natural laws, natural necessity and many other related matters, thus constituting a full metaphysical foundation for natural science. (shrink)

We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

This chapter focuses on one of the common fallacies in Western philosophy called four terms (FT). The fallacy of FT violates the very first rule of constructing a valid syllogism: any syllogism must contain three and only three terms. These terms have, since Aristotle, been called the major, the minor, and the middle. The major and minor are also called the “extremes” of a syllogism, since they lie on either extreme of the middle term. In a valid syllogism, the (...) major and minor terms are related in the conclusion, and their relation is absolutely necessary and completely justified by the premises alone. When there are four terms, either the terms are unrelated and no deduction is possible, or there are multiple syllogisms. It is clear also that in every syllogism either both or one of the premises must be like the conclusion. (shrink)

Aristotle’s Prior Analytics is probably the earliest existing systematic philosophical writing on a syllogistic system and theory of logic. In this work, Aristotle introduces the categorical syllogistic, consisting of three figures and fourteen valid moods. This paper proposes that Aristotle distinguishes a general notion of syllogisms from a more technical notion of syllogisms. Syllogisms that belong to the categorical syllogistic fall under Aristotle’s technical notion of syllogisms that must satisfy two conditions: (1) a conclusion follows necessarily (...) from the premises, and (2) the premises derive a conclusion that necessarily follows from them in regard to attributing the major extreme to the minor. (shrink)

The Lily's Tongue offers a nuanced, sustained reading of what Maughan-Brown calls the "Lily Discourses"--four discourses that Kierkegaard wrote about the instruction in the Gospel of Matthew to "consider the lilies." Kierkegaard suggests that the lilies are "authoritative" rather than merely "figural" or "metaphorical." The aim of this book is to explore what exactly Kierkegaard means by asking, How do texts speak with authority? In Maughan-Brown's reading, Kierkegaard argues that the key to a text's authority is in the act (...) of reading itself. No text can have authority unless the reader grants it that authority. That is because, paradoxically, no text can avoid or escape the use of figural language. If the lilies speak authoritatively it is precisely because they are also figural. Texts do not speak directly; their tongue is always the lily's tongue. Drawing on the work of Kant, Hegel, Nietzsche, Benjamin, and Derrida, The Lily's Tongue situates Kierkegaard's reading of Matthew at the intersection of theological, philosophical, political, and literary investigations of figural language. It uniquely contributes to the ongoing discussion of Kierkegaard's theory and practice of "indirect communication" by introducing four pivotal signed discourses into this debate. In so doing, Maughan-Brown reveals a groundbreaking theory of figure--one that ultimately requires a renewed reading of the major pseudonymous works. (shrink)

Background There have been different ethical approaches to the issues in the history of philosophy. Two American philosophers Beachump and Childress formulated some ethical principles namely 'respect to autonomy', 'justice', 'beneficence' and 'non-maleficence'. These 'Four Principles' were presented by the authors as universal and applicable to any culture and society. Mawlana, a great figure in Sufi tradition, had written many books which not only guide people how to worship God to be close to Him, but also advise people how (...) to lead a good life to enrich their personality, as well as to create a harmonious society and a peaceful world. Methods In this study we examined the major works of Mawlana to find out which of these 'Four Principles of Bioethics' exist in Mawlana's ethical understanding. Results We have found in our study that all these principles exist in Mawlana's writings and philosophy in one form or another. Conclusions We have concluded that, further to Beachump and Childress' claim that these principles are universal and applicable to any culture and society, these principles have always existed in different moral traditions in different ways, of which Mawlana's teaching might be presented as a good example. (shrink)

Four Phenomenological Philosophers is the first book to examine the major texts of the leading figures of phenomenology in one volume. In separate chapters, the book explores the ideas of Edmund Husserl, Martin Heidegger, Jean-Paul Sartre and Maurice Merleau-Ponty with detailed readings of their most important texts. The constantly evolving ideas of Edmund Husserl, the founder of phenomenology, are presented through a review of the three major periods of his work. Martin Heidegger, who made a decisive and controversial (...) break with his teacher, Husserl, set forth his own phenomenological program in Being and Time. Jean-Paul Sartre, who transplanted the tradition from its origins in Germany to the streets of Paris, set forth his existential phenomenology in Being and Nothingness. The Phenomenology of Perception was the best and most representative work of Maurice Merleau-Ponty, a contemporary of Sartre whose career was cut short by his early death. A knowledge of these key thinkers and their major texts is essential to an understanding of many of the major themes of contemporary philosophy, from hermeneutics and existentialism to postmodernism and deconstructivism. This book provides the ideal introduction to this important philosophical tradition. (shrink)

The follow-up research of Aristotle’s syllogism has different approaches. The traditional syllogism follows Aristotle’s conceptual system and hopes to make improvements within Aristotle’s theory. Mathematical logic proposes a new conceptual system to accurately interpret Aristotle’s syllogism. Lei Ma puts forward an extended syllogism whose conceptual system is different from Aristotelian logic and mathematical logic. He thinks that Aristotle’s syllogism and traditional syllogism have tedious figures, moods, and reasoning rules, which are difficult for us to memorize. It is a theoretical (...) conclusion of the human reasoning process but does not conform to the actual human thinking process. Ma’s syllogism is called substitution logic, which mainly concerns the substitution characteristics of a human thinking process, and summarizes the substitution rules in the reasoning process. Substitution logic appropriately describes the actual human reasoning process, thus inspiring us to establish a unified scientific theory of thinking and carry out normative research on the unity of abstract thinking and imaginative thinking. Substitution logic may be applied to the field of artificial intelligence, making artificial intelligence closer to the reality of human thinking. It seems that the research direction of substitution logic will give birth to human-like AI systems and promote the revolutionary transformation of AI research. (shrink)

Islamic law has an advanced legal theory, apart from the four basic decision-making methods, many judgment-gaining theories based on interpretation and reasoning have been derived which have been developed by Islamic jurists in the process. Islamic jurists have used some of their knowledge and techniques to correct the problematic results that arise from both the incorrect use of methods of obtaining judgments and the expansion of the scope of these methods. With these interdisciplinary studies, it was aimed to interpret (...) the criticisms directed against the analogy process and the causes accurately. One of the methods used at the point of revealing whether these criticisms and objections are based on a justified reason and evidence is the debating method. The method of debating, which has become an independent discipline along with fiqh and kalām in the Islamic scientific tradition, began to form during the periods when sects were formed (II century Hijri). The discipline of debate, which has found a practical field in the methodology of Islamic jurisprudence (fiqh), has been particularly effective in interpreting analogy (qiyas), which constitutes an important part of fiqh, and is even assumed to be among the methods of inference (istidlāl). Many Fasād al-waḍʻ (invalidity of an argument of syllogism) is one of the methods of debating has been used in uṣūl al-fiqh. Fasād al-waḍ‘ has been described as the binding of a provision to a cause (ʻillat) that is the opposite of what that cause requires. This is a situation that completely invalidates the cause. In Fasād al-wad‘, the objector proves that the analogy is erroneous by directing objections to the person who brings the evidence. Since Fasād al-wad‘ is a type of objection directed to the basis of the fiction of analogy, it has been accepted by Islamic jurists as one of the strong objections directed to the cause/analogy. However, the issue of which cause this type of objection can be directed against has been discussed among Islamic jurists. Hanafīs accept Fasād al-wad‘ as a sound objection method, but they think that it is not possible to object to the effective causes (al-ʻillat al-muaththirah) with it. Because, according to Hanafīs, the correctness of the effective quality has been revealed by the Qur’ān, the Sunnah and the consensus (ijmā’). Because these proofs do not produce false qualifications. According to Shafeis, all causes and provision can be objected with Fasād al-wad’. In fact, some Shāfi'ī jurists consider this method as a general type of objection, not aunique one to the analogy. Due to these different interpretations that Islāmic law schools attribute to the conditions of analogy and the nature of Fasād al-wad‘, different results may arise in furû issues. In this study, Fasād al-wad‘as a type of objection to the analogy process in Islamic legal procedure has been examined and the nature of Fasād al-wad‘ has been tried to be revealed by determining the comparative furû. Thus, it is aimed to identify and analyse the diversity of legal reasoning methods, which have an important place in the logic of law in Islam and can be gathered under the name of analogy. (shrink)

This article deals with an alternative interpretation of syllogistics, different from the classical one: an intensional one, in which subject and predicate are not associated with a set of individuals but a set of attributes. The authors of the paper draw attention to the fact that this approach was first proposed by Leibniz in works on logical calculus, which for a long time remained in the shadow of his other philosophical works. Currently, the intensional approach is gaining more and more (...) popularity due to the development of non-classical logics, and the article will present several existing intensional formal syllogistic semantics. The paper will also consider another historical approach to syllogistics, associated with the name of the Russian logician Nikolai Vasiliev, who is not only one of the founders of non-classical but also of a different intensional interpretation of such logic. The authors, along with the already known formalizations of Vasiliev’s ideas, present two new systems. One of them is a reconstruction of one type of imaginary logic with statements of three qualities: affirmative and two types of negative statements. The second system is the one that is adequate to semantics, in which instead of the four classical ones, only three types of statements are presented, and their significance is determined through the relation of the classical logical entailment. Both of them are interpreted intensionally. The intensional approach in logic and, in particular, in syllogistics allows us to expand the class of accepted principles. (shrink)

This paper considers how Kierkegaard self-reflexively portrays the tension between the boundary limit of discursive reason and mythic imagination in his classic analysis of Abrahamic faith. Following some reflections on the nature and philosophical implications of that tension, I examine its salient delineation in the Prelude of Fear and Trembling. Through four non-canonical renderings of the biblical Aqedah myth featured in the Prelude, Kierkegaard depicts the limits of ethical reasoning in the drama of Johannes de Silentio’s struggle to figure-forth (...) Abraham’s “movements” in ethically intelligible terms. I conclude that, as dramatized by Kierkegaard, the tension between mythemic figuration and discursively articulated critical reasoning sets in relief one of the formative aporiai of modern Western culture, namely the conflictive interplay of vision and discourse. (shrink)

In this paper, I attempt to discuss the role played by the figure of Apostel Paul inside several texts of four authors: Heidegger, Badiou, Agamben and Žižek. My hypothesis is that Heidegger and the contemporary philosophers do not turn to Apostle Paul guided primarily or exclusively by theological interest or perspectives, yet they pose a great challenge to the religious thought. Heidegger’s return to Saint Paul has a philosophical-phenomenological aim: highlighting the carrying structures of the temporality of factic life. (...) Badiou, Agamben and Žižek are interested in Paul as a political personality, a poet-thinker of an Event, who has to enforce a universal singularity both against the current legal abstractions and against communitarian and particularistic claims. They rely on Paul when confronting the postmodernism and when examining what constitutes the political. Against the postmodern doxa, Badiou, Agamben and Žižek aim at the revitalization of the politics of universal truth. (shrink)