Theory Of Syllogism Research Articles

“SUBJECT GENERALITY” AND DISTRIBUTION IN MEDIEVAL ARABIC SYLLOGISTIC

AbstractA relatively well-known medieval Latin innovation is the doctrine of distributive supposition. This notion came to be used in syllogistic theory in the late medieval and early modern periods, as Latin logicians sought to establish general rules for syllogistic productivity across the various figures. It is much less well-known that some logicians in the medieval Arabic tradition also attempted to establish general rules for the syllogism, appealing to what they called “subject generality.” In the present article, I introduce this use of “subject generality” in some influential Arabic works on logic from the thirteenth century to the sixteenth, specifically Al-ǧumal by Afḍal al-Dīn al-Ḫūnaǧī (d. 1248) and Tahḏīb al-manṭiq by Saʿd al-Dīn al-Taftāzānī (d. 1390) and some of their commentators. I also compare this concept of “subject generality” to the Latin concept of “distribution.”

Aristotle’s Logic of Biological Diversity

Abstract Aristotle’s biology is based on his method of division of animal kinds by multiple differentiae. This results in complex clusters of non-subordinate terms, between which Aristotle seeks to establish universal correlations. The form of these, however, does not correspond to that prescribed by his theory of syllogism. Mereological relations between terms are not linear and quantification is far more complex than the distinction between universal and particular propositions. Thus the axiomatisation of Aristotle’s biology requires a tool designed for analysing such complex universal correlations into valid syllogistic premises. Prosleptic-like premises turn out to be the solution outlined by Aristotle. They make it possible to handle both the logic of consequence which translates from and into mereological relations between term clusters, and the complex quantification required by division based on multiple differentiæ, through the instantiation of a variable ideally consisting of indivisible groups of animals.

LUKASIEWICZ’S APPROACH TO SYLLOGISTIC: A CRITICAL ANALYSIS STUDY

There is no theory which has received a big interest historically as Aristotelian syllogistic, despite the criticisms to which the theory was exposed by philosophers and logicians like Francis Bacon and Jean Stuart mill in their philosophical and logical works, they considered it as an epistemological obstacle to the development of scientific knowledge, and there is a need to get over it to new method and process, but It is still an interesting subject of study and updated by many logicians to nowadays. The most prominent attempts: the Intentional approach opposite to the comprehensive one, then the approach of the logician and philosopher Ian Łukasiewicz, who tried to read the syllogistic theory with the use of accurate and rigorous analysis tool in classical logic, which is the calculi of propositions where he considered the real form of Aristotelian syllogism moods is conditional (If ... so), i.e., as computable logical laws not inferential rules (If ... then). In order to reach this purpose Łukasiewicz present his hypotheses, some of them are verified for the others he have had to make several interpretations to make his theory consistent. These interpretations took him away from the spirit of the theory and from the essence of what did Aristotle. This made his approach the subject of numerous and harsh criticisms. This is what we will try to show it through a critical analysis to some hypotheses which he presented in his book “Aristotle’s Syllogistic from the standpoint of Modern Formal Logic”.

An Overview of Logic in Avicenna

Avicenna, who defines logic as a method of reaching non-actual information based on actual information, or a method that protects people from mistakes while thinking, basically aims to reach information in the art of logic. In this respect, logic is a tool that leads to knowledge. Although Ibn Sînâ included the logic in all his works, he dealt with logic in more detail in his works called Kitâb Al-Shifâ and Remark and Admonitions. Besides, in Kitâb Al-Shifâ, written by Ibn Sînâ in accordance with the Peripatetic tradition, all the logic topics that Aristotle examined were the subject of research in the order put forward by Aristotle after Isagoci, while the Ishârât did not include categories and five arts were also included. very little has been mentioned. Avicenna's corpus of logic is more voluminous than Aristotle's texts. In this, besides Avicenna's making the subjects of logic a subject of wider examination, it was effective that he also made the comments after Aristotle the subject of examination. After him, the approach in Ishârât was more effective than the approach in Kitâb Al-Shifâ in terms of the handling of logic issues in the Islamic world. Concentrating on thought rather than the relationship between language and thought, Ibn Sînâ determines the subject of logic as second intelligibles based on the first intelligibles in terms of reaching the unknowns from the known. The unknown is basically reached through the mind. However, intuition (hads) is one of the ways to reach knowledge. Avicenna bases his understanding of logic on the following three basic principles: the distinction between language and thought, the distinction between matter (content) and form, and the distinction between essence and existence. The distinction between existence and essence is one of the most fundamental distinctions in the mind's perception of essences and the separation of logic into tasawwur and tasdîq. Although the concepts of tasawwur and tasdîq are taken as far as Aristotle and the Stoics, Avicenna interpreted these two concepts as the basic concepts that make up the logical system. The part of the logic up to the propositions, which we can describe as conceptual logic, constitutes imagination, and after propositions, affirmation. Introduction to Logic (Îsâgûcî/Al-Madhal) is a preparation for Categories, and Categories is an introduction to Peri Hermeneias. While the Prior Analytics is the book in which the theory of syllogism is revealed, the five arts consisting of Burhân (demonstration), Jadal (topics), Safsata (fallacies), Khatâba (rhetoric) and Shi’r (poetry) constitute the content of logic and are the application area of syllogism. Conceptual (imaginative) knowledge is an act of visualizing the existence by abstracting it and does not contain judgment. However, since the judgment is made with at least two concepts, there is no judgment without the concept. “What is it” and “which/which one” are the basic questions in reaching the concept obtained with the definition indicating the nature of something. In the proposition, which is the basis of confirmation and divided into simple and compound, the basic questions are "is there" and "why" questions. The one that leads to tasdîq, which means making a positive or negative judgment by establishing a connection between the two concepts, is hujjah/ihtijâj, that is, proof, reasoning, and the most basic reasoning method is syllogism. In classical logic, the main purpose is to reach syllogism, and in syllogism, the aim is to reach the demonstration that allows precise knowledge. According to Avicenna, who successfully adapted the concept of matter-form to logic, it is possible to talk about the form and substance of the proposition, which is the simplest form of tasdîq, as well as the substance and form, that is, the content and form, of the competent form of qiyâs. While the form of the proposition is shaped according to its quantity, quality and modality, its content is classified based on truth and falsity. Qiyâs is also divided into two according to its form and content. According to its form, syllogism is basically called iqtirânî and exceptional qiyâs, while according to its matter, it consists of propositional classes and five arts based on it in terms of truth value.

Pre-Critical Kant on Traditional Logic: What is the Mistake in Syllogistic Theory?

Immanuel Kant held nearly two decades before (1762) the beginning of his ‘Critical period’ (1781) that the traditional tripartite/quadripartite division of the figures in categorical syllogistic remained a ‘mistaken subtlety’ (falsche Spitzfindigkeit), given (i) that the Aristotelian perfect moods were the only ‘pure’ patterns of reasoning that exemplify the term order – called the first figure – prescribed by the general rule of ratiocination per se, and (ii) that every imperfect mood in the same theory could be ‘reduced’ to one of those four. There really are sheer logical problems, already noted in the literature, in Kant’s reading of the standard reductive scheme for categorical syllogistic as a set of instructions for restoring the first figure within the premises of a given imperfect mood. However, the real issue is the way Kant benefits from these points to justify his ‘mistaken subtlety thesis’ (MST), which translates in turn into the issue of the correct interpretation of the thesis itself. This paper aims to show that, contrary to appearance, MST might fail to make any definite sense; to that end, it first presents and evaluates Kant’s own special conception of judgment and reasoning that centers around the notion of syllogistic mediation, on which basis Kant states MST; then it shows that a tenable reading of MST answering to the Kantian conception and to common facts about inference and deduction cannot be made. The paper concludes by proposing to connect this negative result to Kant’s wavering between descriptive and prescriptive perspectives on purely logical matters.

Theory of Syllogisms with Categorical, Conditional and Disjunctive Connectives Developed by Arabian Logicians

Abstract In this paper, we are trying to summarize the peak of achievement of the Arabian logicians of the fifteenth century by making a classification and sketching in familiar terms the conditional and subjunctive syllogisms in Muḥammad Ibn Yusūf al-SSinūsī’s (1426-1490) work, i.e. in his explanation of Kitāb al-Muḫtaşar fī al-Manṭiq of al-Imām Muḥammad Ibn ʿArafa (1316- 1401).

Воображаемая логика – 2 Н.А. Васильева как силлогистическая теория.

Воображаемая (неаристотелева) логика Н.А. Васильева, одного из основоположников современной неклассической логики, является его самой известной логической системой. Дедуктивная система, преложенная им, представляет собой силлогистику особого типа, в языке которой вместе с формами утвердительных и отрицательных суждений содержатся формы противоречивых (индифферентных) суждений. Последние представляют собой суждения нового качества и содержат связку <<есть и не есть одновременно>>. Статья посвящена изложению результатов исследования одного из вариантов Воображаемой логики Николая Александровича Васильева. Этот вариант Воображаемой логики отличается не только от традиционной силлогистики, но и от основной версии. Здесь с каждым термином категорического суждения связывается не множество индивидов, а совокупность признаков, а силлогистические константы рассматриваются как обозначающие интенсиональные отношения между понятиями. Исследование предполагало рассмотрение этого варианта Воображаемой логики как силлогистической теории и производилось на базе системы, построенной для данной логики В.И. Маркиным и Д.В. Зайцевым. В статье кратко изложена система Воображаемой логики – 2, доказаны: законы тождества, законы противоположностей, законы подчинения, законы обращения и законы исключённого четвёртого, принимаемые в этой логике. Далее последовательно рассмотрены все четыре фигуры силлогизмов. В каждой фигуре рассмотрены все возможные комбинации посылок (36 комбинаций, для каждой фигуры) со всеми возможными заключениями (шесть возможный заключений, для каждой комбинации посылок). Произведено доказательство правильных силлогизмов каждой фигуры, а также приведены примеры возможных контрмоделей для опровержения всех неправильных модусов. Результатом работы является выделение законов данной силлогистической теории, а также намечено дальнейшее направление исследования, ставится вопрос о возможности формулирования общих правил силлогизма данного варианта Воображаемой логики.

아리스토텔레스의 삼단논법과 보에티우스의 삼단논법

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.

Protasis and Apophansis in Aristotle’s Logic

Normal 0 21 false false false TR X-NONE AR-SA /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Normal Tablo"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Calibri","sans-serif"; mso-bidi-font-family:"Times New Roman";} This essay examines how Aristotle creates propositions. It evaluates his use of quality and quantity in his theory of syllogism. In De Interpretatione, Aristotle used the term, ‘apophansis’, but he preferred ‘protasis’ in Analytica Priora. While Aristotle classified these as affirmative and negative due to their qualities, he embraced a different point of view about classifications based on quantity. Differences in apophansis are evaluated on the basis of their singular and universal structures, and their predications are also taken into consideration. As he studied protasis, however, he re-arranged the classifications of apophansis and re-shaped them according to their predicative properties. The structural difference between De Interpretatione and Analytica Priora are revealed through a careful examination of Aristotle’s use of these two concepts.

" ﻧﻈﺮﻳﺔ اﻟﻘﻴﺎس ﺑﻴﻦ أﺛﻴﺮ اﻟﺪﻳﻦ اﻷﺑﻬﺮي ّ وﻧﺼﻴﺮ اﻟﺪﻳﻦ اﻟﻄﻮﺳﻲ ّ" "ﻣﻘﺎرﻧﺔ دراﺳﺔ ﺗﺤﻠﻴﻠﻴﺔ " “Theory of Syllogism between Atheer Al-Din Alabhary, and Nasir Al-Din-Al-Tusi “ “A comparative analytic study “

" ﻧﻈﺮﻳﺔ اﻟﻘﻴﺎس ﺑﻴﻦ أﺛﻴﺮ اﻟﺪﻳﻦ اﻷﺑﻬﺮي ّ وﻧﺼﻴﺮ اﻟﺪﻳﻦ اﻟﻄﻮﺳﻲ ّ" "ﻣﻘﺎرﻧﺔ دراﺳﺔ ﺗﺤﻠﻴﻠﻴﺔ " “Theory of Syllogism between Atheer Al-Din Alabhary, and Nasir Al-Din-Al-Tusi “ “A comparative analytic study “

Sistema e silogismo em O Capital

Os empreendimentos intelectuais de Hegel e Marx continuam relevantes para um exame do mundo contemporâneo. Ambos os autores analisaram, ainda que a partir de diferentes abordagens, elementos importantes das sociedades capitalistas modernas. Traçar as conexões precisas entre os dois pensadores, no entanto, ainda é um desafio—muito embora atualmente seja claro que essas relações não são de idealismo versus materialismo, mas, que envolvem, precisamente, a superação desse dualismo, conforme mostraram as tradições do Marxismo Ocidental e da Teoria Crítica. Em sua versão anglófona, essas investigações cresceram e se expandiram em diferentes tendências, entre essas, notadamente, a Nova Dialética. Este artigo tem como objetivo analisar a teoria hegeliana do silogismo como chave para a leitura de O Capital de Marx, tal como proposto por Tony Smith. Para isso, o artigo procura reconstruir a interpretação que Smith oferece da teoria hegeliana do silogismo e suas aplicações para a Filosofia do Direito de Hegel, bem como para O Capital de Marx. De acordo com Smith, O Capital, a apresentação das articulações dialéticas das categorias da economia política no modo de produção capitalista como ordem social específica, deriva sua capacidade crítica e sua coerência científica precisamente do recurso à teoria do silogismo hegeliana—que permite a Marx analisar os processos do mundo social como entidades orgânicas constituídas pela articulação de momentos de universalidade, particularidade e individualidade. O resultado é uma investigação que busca aproximar a Lógica de Hegel a O Capital.

Развитие силлогистического учения в эпоху Возрождения

The article is devoted to one of the logical doctrines of the Renaissance – theory of syllogism, reveals the peculiarities of Aristotle syllogism in the framework of the main logical schools of the Renaissance.

Ontology and Logic: The Case of Scholastic and Late-Scholastic Theory of Relations

This paper investigates the reason (or reasons) why, in the tradition of Western philosophy, a logic of relations was developed only in the second half of the nineteenth century. To this end, it moves along two different but interconnected paths: on the one hand, it attempts to reconstruct the main views concerning the ontology of relations during the middle ages; on the other, it focuses on the treatment of so-called oblique terms (termini obliqui) in the logical works of some preeminent authors belonging to the scholastic and late-scholastic tradition. From the ontological point of view, realists and nominalist both denied that polyadic expressions of the language (spoken, written or mental) signify polyadic properties in the world extra. Some authors, such as Peter Auriol, claimed that polyadic expressions signify something merely mental (as contrasted with ‘real’), thus recognizing, even though in a limited ontological domain, the existence of full-fledged relations, that is, of ‘things’ simultaneously ‘inhering’ in a plurality of subjects. These authors too, however, were unable to produce a logic of relations analogous to that developed in the nineteenth century by De Morgan. If we look at the treatment of so-called ‘oblique inferences’ in the scholastic and late-scholastic tradition, we find that the validity of the inferences in which oblique terms (relations) are involved, does not depend on specific properties of relations but on some general principles on which the syllogistic theory is based. This is true even of the logical work of Juan Caramuel y Lobkowitz (1606–1682), a Spanish Catholic scholastic, who wrote extensively on oblique inferences and who is credited with having introduced a kind of ‘proto-logic’ of relations. Thus, whereas medieval thinkers, from the ontological point of view, attributed to relations understood as polyadic properties a very poor role in the ‘fabric of the world’, from the strictly logical point of view, they made no attempt to develop a systematic analysis of the main properties governing inferences composed by relational sentences. In the case of relations, thinkers belonging to the scholastic and late scholastic tradition did not develop something analogous to the theory of consequences: in other words, they did not possess a logic of relations.

Deductively Valid, Inductively Valid, and Retroductively Valid Syllogisms

Charles S. Peirce suggested that a formal distinction between his three types of argumentation, deduction, induction, and retroduction, could be drawn using syllogistic figures. However, he never developed the concept of formal validity for non-deductive arguments beyond that point. His failure to do so may have been due in part to inadequacies in the theory of syllogisms as it was known at the time. Using an expanded syllogistic, with quantifiers between ‘all’ and ‘some’, this paper shows that it is possible to derive distinct groups of deductive, inductive, and retroductive syllogisms.

Силлогистика Льюиса Кэрролла с отрицательными терминами

Льюисом Кэрроллом была построена оригинальная силлогистическая теория, отличная от традиционной силлогистики. Причем, он строил свою систему изначально как негативную, т.е. содержащую в списке логических символов ее алфавита терминное отрицание. Это позволило Л. Кэрроллу не рассматривать частноотрицательные высказывания $SoP$ как отдельный вид высказываний, так как они, по его пред- ставлению, эквивалентны частноутвердительным высказываниям с отрицательным предикатом $SiP'$. В предлагаемой статье осуществлена реконструкция силлогистики Льюиса Кэрролла, доказана погружаемость построенной системы в исчисление предикатов посредством «кэрролловской» интерпретации категорических высказываний. Доказательство основано на полученном нами ранее результате погружае- мости системы Негативной фундаметнальной силлогистики в систему Обобщенной позитивной силлогистики а также на факте погружаемости последней в исчисление предикатов.

THE FORMAL AND THE FORMALIZED: THE CASES OF SYLLOGISTIC AND SUPPOSITION THEORY

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 (i.e. theories of formalization). 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 (i.e. the second sub-project). 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.

The eco-cognitive model of abduction: Ἀπαγωγή now: Naturalizing the logic of abduction

Abduction (ἀπαγωγή, in ancient Greek, often translated as “leading away” or “reduction”) is a procedure in which something that lacks classical explanatory epistemic virtue can be accepted because it has virtue of another kind: Gabbay and Woods [15] contend (GW-schema) that abduction presents an ignorance-preserving or (ignorance-mitigating) character. From this perspective abductive reasoning is a response to an ignorance-problem; through abduction the basic ignorance – that does not have to be considered a total “ignorance” – is neither solved nor left intact. Abductive reasoning is an ignorance-preserving accommodation of the problem at hand. Is abduction really ignorance-preserving? To better answer this question I will introduce (and take advantage of) an eco-cognitive model (EC-Model) of abduction. It will be illustrated that through abduction, knowledge can be enhanced, even when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or an inductive phase, as Peirce called it. To further deepen the eco-cognitive character of abduction a simple genealogy of logic is provided: Aristotle clearly states that in syllogistic theory local/environmental cognitive factors – external to that peculiar inferential process, for example regarding users/reasoners, are given up. Indeed, to define syllogism Aristotle first of all insists that all syllogisms are valid and contends that the necessity of this kind of reasoning is related to the circumstance that “no further term from outside (ἔξωθɛν) is needed”, in sum syllogism is the fruit of a kind of eco-cognitive immunization. At the same time Aristotle presents a seminal perspective on abduction: the second part of the article considers the famous passage in Chapter B25 of Prior Analytics concerning ἀπαγωγή (“leading away”), also studied by Peirce. I contend that some of the current well-known distinctive characters of abductive cognition are already expressed, which are in tune with the EC-Model. By providing an illustration of the role of the method of analysis and of the middle terms in Plato's dialectic argumentation, considered as related to the diorismic/poristic process in ancient geometry – also, later on, emphasized by Proclus – I maintain that it is just this intellectual heritage which informs Aristotle' Chapter B25 on ἀπαγωγή. Even if, in general, Aristotle seems to sterilize, thanks to the invention of syllogistic theory, every “dialectic” background of reasoning, nevertheless in Chapter B25 he is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away” (ἀπαγωγή). Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. Finally, the paper presents an excursus on Aristotle's enthymemes from signs, disregarded by Peirce, but extremely important to stress the Aristotelian treatment of what I have called selective abduction. A forthcoming companion paper [35] will further deepen the EC-Model of abduction stressing stricter logical aspects: the first result will be that, contrarily to the classical logical view, relevance and plausibility in abductive reasoning have to be relativized and so the epistemologically embarrassing concepts of irrelevance and implausibility exculpated: they are not always offensive to reason.

ALFARABI ON CONDITIONALS

AbstractI examine the theory of conditional propositions (qaḍāyā šarṭiyya muttaṣila) and conditional syllogisms (qiyāsāt šarṭiyya) in the logical works of Alfarabi (d. 950). I contextualize Alfarabi's logical doctrines related to conditional reasoning against the backdrop of the context-theory of logic, which was developed by Aristotle's ancient commentators. I show that Alfarabi thought that conditional propositions have truth-conditions. I provide conjectural truth-conditions for conditional propositions, and conjectural validity-conditions for connective conditional syllogisms. These truth-conditions and validity-conditions are shown to be sensitive to the pragmatic conditions in which conditional propositions and arguments are deployed. I end by suggesting that Alfarabi's logical pragmatism is a consequence of his adoption of the late antique context-theory of logic rather than a result of his developing Aristotle's formal syllogistic theory adumbrated in thePrior Analytics.

El teatro de marionetas en Bajtín: la crítica como sabotaje ante la polifonía

Este ensayo trata de confrontar la teoría polifónica de Bajtín con la teoría silogística del discurso propia de la crítica como sabotaje. Con esa finalidad se elige la obra de Bajtín Problemas de la poética de Dostoievski, tanto en su versión española como en la rusa. Mediante una lectura atenta, propia del sabotaje, se ponen de relieve las contradicciones del discurso de Bajtin en torno a la polifonía, el discurso ajeno, y la independencia de los personajes en relación al autor. Tales contradicciones demuestran que todos esos conceptos empleados por Bajtín en torno a Dostoievski son en realidad recursos técnicos mediante los que el autor crea un determinado mundo. La crítica como sabotaje recupera la figura del autor como figura no compacta y dividida, pero responsable de la creación de un silogismo y un modelo de mundo complejos.This essay aims to confront Bakhtin’s polyphonic theory and syllogistic theory belonging to Criticism as Sabotage. To this end we choose Bakhtin’s Problems of Dostoievski’s Poetics, both in Spanish version and russian one. Through a close Reading, typical of the kind of criticism called Sabotage, we underline the contradictions of Bakhtin’s discourse around polyphony, speech of the other, and the Independence of the characters in relation to the author. Such a contradictions show that all concepts employed by Bakhtin about Dostoievski are actually technical resources through which the Author creates a concrete wordl. Criticism as sabotaje gets back author’ figure, divided in itself, but responsable for the creation of a syllogism and a complex wordl’s model.

FIGURES OF PROSLEPTIC SYLLOGISMS IN PRIOR ANALYTICS 2.7

In chapters 2.5–7 of the Prior Analytics Aristotle is concerned with what he calls circular proof. He gives an account of circular proofs within the framework of his syllogistic theory, and discusses how they come about in the three figures of categorical syllogisms. The results of this discussion are summarized at the end of chapter 2.7, at 59a32–41. The summary contains several statements to the effect that certain circular proofs come about in the third figure. Some of these statements are problematic because the circular proofs in question are actually not in the third figure of categorical syllogisms; in fact, these circular proofs are not categorical syllogisms at all, but what Theophrastus called prosleptic syllogisms. Hence, the statements are incorrect if they are understood to refer to the third figure of Aristotle’s categorical syllogisms. Since it seems natural to understand them in this way, Ross and others conclude that the passage at 59a32–41 is spurious and should be excised, although it is found in all MSS. 1 By contrast, this paper aims to show that the passage is not spurious. Following Pacius, I argue that the problematic statements in it refer not to the third figure of categorical syllogisms, but to the third figure of prosleptic syllogisms. On this interpretation, the statements are correct and can be regarded as genuine. Given that they are genuine, they show that Aristotle was aware of a classification of prosleptic syllogisms into three figures, even though such a classification does not occur elsewhere in his writings. Thus, the passage at 59a32–41 appears to be the earliest evidence we have of figures of prosleptic syllogisms. I begin with an overview of Aristotle’s treatment of circular proofs in Prior Analytics 2.5–7, focussing on his use of prosleptic syllogisms (§1). Readers familiar with the contents of Prior Analytics 2.5–7 may wish to skip this overview. Next we consider the problematic statements in 59a32–41 (§2). I will argue that these statements refer to the third figure of prosleptic syllogisms, and that there is no reason to doubt Aristotle’s authorship of the passage (§3).