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)

Chapter 1 presents BS, a basic syllogistic system based on Aristotle's logic, in natural deduction form. Chapters 2 and 3 treat the metatheory of BS: consitency, soundness, independence, and completeness. Chapter 4 and 5 deal with syllogistic and, in turn, propositional and predicate logic, chapter 6 is on existential import, chapter 7 on subject and predicate and chapter 8 on classes. Chapter 9 adds negative variables to BS, and proves its soundness and completeness.

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)

The present book is the English version of a monograph 'Die aristotelische Syllogistik', which first appeared ten years ago in the series of Abhand 1 lungen edited by the Academy of Sciences in Gottingen. In the preface to the English edition, I would first like to express my indebtedness to Mr. J. Barnes, now fellow of Oriel College, Oxford. He not only translated what must have been a difficult text with exemplary precision and ingenuity, but followed critically every argument and (...) check ed every reference. While translating it, he has improved the book. Of those changes which I have made on Mr. Barnes' suggestion I note only the more important ones on pages 4, 12, 24sq, 32, 39, 6lsq, and 158. Since the second edition of the German text appeared in 1963 some further reviews have been published, or come to my notice, which I have 2 been able to make use of in improving the text of this new edition. I must mention here especially the detailed critical discussions of my results and arguments published by Professor W. Wieland in the Philosophische Rundschau 14 (1966), 1-27 and by Professor E. Scheibe in Gnomon 39 (1967), 454-64. Both scholars, while agreeing with the main drift and method of my interpretation, criticise some of my results and disagree with some of my arguments. It would not be possible to discuss these technical matters here with the necessary thoroughness. (shrink)

"Alexander's commentary on Book 1 concerns the definition of Aristotelian syllogistic argument; its resistance to the rival Stoic theory of inference; and the character of inductive inference and of rhetorical argument. Alexander distinguishes inseparable accidents, such as the whiteness of snow, from defining differentiae, such as its being frozen, and considers how these differences fit into the schemes of categories. He speaks of dialectic as a stochastic discipline in which success is to be judged not by victory but by (...) skill in argument. Alexander also investigates the subject of ambiguity, which had been richly developed since Aristotle by the rival Stoic school."--BOOK JACKET. (shrink)

Aristotle (b. 322 BC) was the first philosopher in the history of thought to examine all modes and types of belief acquisition such as knowledge, supposition, error and indirectly imagination. In his _Prior Analytics_, which he wrote primarily to clarify his theory of demonstration, Aristotle examined in detail the syllogism, which he saw as the most important form of reasoning, and his analysis was subject to interpretation by different traditions of thought for centuries. Aristotle’s _Prior Analytics_ was translated (...) into Arabic in the classical period and later interpreted by many Islamic logicians. This article aims to show how Aristotle’s definition of the syllogism in the _Prior Analytics_ was taken up and interpreted in the Peripatetic Islamic logical tradition. These interpretations of the definition of the syllogism will provide us with an idea about the unique features of the commentaries on the _Prior Analytics_ in the Islamic world. Here, introductory information about the translation of the _Prior Analytics_ into Arabic and its commentators in Arabic will be given, Aristotle’s definition of the syllogism and its versions in Peripatetic Islamic logicians will be indicated, and the interpretation of the basic terms in the definition by Peripatetic Islamic logicians will be revealed. (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)

In the present paper, I want to contribute to a correct understanding of Aristotle's action theory by explaining just how two of the key concepts which it involves are connected and by showing that, contrary to what a number of commentators have said, there are causal concepts. The concepts in question are those of deliberation and the so-called "practical syllogism.".

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied . Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss (...) two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments . In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize. Pode-se dizer que, enquanto disciplina, a lógica é caracterizada por dois subprojetos: teorias formais da validade de argumentos, baseadas em um número reduzido de esquemas e padrões formais, e teorias de como reduzir a multiplicidade de argumentos em contextos informais, não lógicos, ao pequeno número de padrões formais cuja validade é estudada de maneira sistemática no âmbito do primeiro subprojeto. O segundo subprojeto corresponde à noção de formalização de argumentos. Infelizmente, a tendência atual é de considerar como sendo a lógica propriamente dita exclusivamente o que se encaixa no primeiro subprojeto, em detrimento do segundo subprojeto, igualmente importante. Neste artigo, duas teorias históricas sobre a formalização de argumentos são analisadas: a teoria da silogística apresentada por Aristóteles nos "Primeiros Analíticos" e teorias medievais da suposição. Ambas ilustram o caráter duplo da lógica, que envolve dois subprojetos distintos, e contêm reflexões sofisticadas sobre como formalizar argumentos. Em ambos os casos, os métodos formais utilizados se diferenciam dos métodos atuais de tradução de um argumento em linguagem vernacular para um simbolismo especialmente formulado, ou seja, uma linguagem formal. Em conclusão, o artigo pode ser visto como a defesa de uma conceitualização mais abrangente do que significa 'formalizar' um argumento. (shrink)

This is the best study available of Aristotle’s syllogistic. It combines the insights that have been gained into logical form through the development of modern logic with the traditional philological and philosophical understanding of the Aristotelian text. Such a work has been badly needed since Lukasiewicz first offered his revolutionary interpretation of Aristotle’s syllogistic as a formal system meeting the most rigorous demands of modern logic. Lukasiewicz did little to show how his interpretation could be based on the text of (...) Aristotle, and the question remained whether the result was not rather more Lukasiewicz than Aristotle. Dr Patzig has now offered the detailed textual analysis needed to prove the point and, in doing so, has in many cases corrected and improved upon Lukasiewicz. (shrink)

This is the best study available of Aristotle’s syllogistic. It combines the insights that have been gained into logical form through the development of modern logic with the traditional philological and philosophical understanding of the Aristotelian text. Such a work has been badly needed since Lukasiewicz first offered his revolutionary interpretation of Aristotle’s syllogistic as a formal system meeting the most rigorous demands of modern logic. Lukasiewicz did little to show how his interpretation could be based on the text of (...) Aristotle, and the question remained whether the result was not rather more Lukasiewicz than Aristotle. Dr Patzig has now offered the detailed textual analysis needed to prove the point and, in doing so, has in many cases corrected and improved upon Lukasiewicz. (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)

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..

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)

Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...) the paper develops an account of truth for conditionals which allows them to depend on momentary features of the context in which they are uttered. In the second half of the paper, comparisons with other recent theories of the conditional will be considered. Particular attention will be given to the problem of whether the conditional really violates classical inferences such as Hypothetical Syllogism and Contraposition as has often been claimed in recent years. (shrink)

The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of papers (...) which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a (...) formal foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

Oaksford (2001) considers that the findings of Espino, Santamaria, and GarciaMadruga (2000a) could be explained by the Probability Heuristics Model (PHM) proposed by Chater and Oaksford (1999). He specifically voices three objections, the two main ones being based on the fact that PHM is not a theory about syllogism representation. If this is the case, we consider that PHM cannot explain our data, because most of them were registered before the participants evaluated the conclusion. We argue that only (...) a theory at the representational level can property explain these data. (shrink)

The aim of this study was to examine the predictions of three theories of human logical reasoning, (a) mental model theory, (b) formal rules theory (e.g., PSYCOP), and (c) the probability heuristics model, regarding the inferences people make for extended categorical syllogisms. Most research with extended syllogisms has been restricted to the quantifier “All” and to an asymmetrical presentation. This study used three-premise syllogisms with the additional quantifiers that are used for traditional categorical syllogisms as well as additional (...) syllogistic figures. The predictions of the theories were examined using overall accuracy as well as a multinomial tree modelling technique. The results demonstrated that all three theories were able to predict response selections at high levels. However, the modelling analyses showed that the probability heuristics model did the best in both Experiments 1 and 2. (shrink)