Aristotelian Syllogism Research Articles

Deductive Reasoning Based on the Valid Aristotelian Syllogism AEE-2

This paper firstly formalizes Aristotelian syllogisms based on the tripartite structure of categorical propositions, and then uses the truth definitions of categorical propositions to prove the validity of the Aristotelian syllogism AEE-2. Then, the remaining 23 valid syllogisms are derived from the syllogism AEE-2 with the help of relevant facts, inner and outer negation definitions of quantifiers, and deductive rules. In other words, this paper reveals the reducible relationship between/among these 24 syllogisms and establishes a succinct formal reason system for Aristotelian syllogistic. The deductive reasoning not only ensures consistency in its results, but also provides a concise mathematical paradigm for other types of syllogisms.

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”.

A NECESSIDADE DA JUSTIFICAÇÃO POR DEDUÇÃO NA CONSTRUÇÃO DA RATIO DECIDENDI DE CASOS FÁCEIS A PARTIR DA TEORIA DE NEIL MACCORMICK: UMA ANÁLISE DO RESP 1.745.333/RS

O objetivo deste artigo é analisar o Recurso Especial n. 1.745.333/RS a partir da argumentação justificada exclusivamente pela dedução. Neil MacCormick propõe uma teoria integradora para argumentar por justificação as decisões jurídicas, nesse sentido, ele apresenta um método para casos fáceis e difíceis. A partir do método defendido por ele para justificar casos fáceis é que o presente artigo se fundamenta. Desse modo, para construir este artigo é utilizado o método hipotético-dedutivo, por meio de análise bibliográfica e documental, assim, possui abordagem qualitativa, do tipo básica e exploratória. Inicialmente, são expostos os pressupostos teóricos dessa abordagem, como o silogismo aristotélico. Depois, apresenta-se a justificação por dedução proposta por Neil MacCormick, para então analisar o referido acórdão. Ao final são apresentados os pressupostos e limites dessa teoria. A partir dessa análise, foi possível chegar à conclusão de que a justificação por dedução é possível, mas única e exclusivamente nos casos fáceis, o que confirma a teoria de MacCormick.

Knowledge Reasoning about the Aristotelian Syllogism IAI-4

Knowledge Reasoning about the Aristotelian Syllogism IAI-4

Logic and Metaphysics in Vilnius during 16th–18th Centuries: The Most Important Sources of Vilnius Libraries

The aim of the article is to present the results of research conducted as part of the project Polonica Philosophica Orientalia: namely, to give an overview of the most important logical and metaphysical treatises (both manuscripts and printed editions) written in Vilnius between the sixteenth and eighteenth centuries that are currently accessible in some of the Vilnius libraries. Although the research focused primarily on the Vilnius University Library and its resources, some interesting results were also obtained while researching the Wróblewski Library of the Lithuanian Academy of Sciences. Most sources containing information about the state and the nature of metaphysical and logical investigations conducted in Vilnius during the period discussed are the manuscripts of lecture courses delivered for the students of Vilnius University and other schools. The analysis of those manuscripts has revealed a strong and long-lasting influence of scholastic Aristotelianism in both logic and metaphysics. Namely, up to the mid-eighteenth century, the main questions discussed in logic were Aristotelian syllogism, the square of opposition and the medieval topics of semantical antinomies, modalities and supposition theory, while investigations into metaphysical issues were limited to commentaries on Aristotle’s theoretical treatises without seriously questioning their main theses. In the second part of the eighteenth century, a moderate shift towards subjectivism and psychologism was observed in both of these disciplines. This was influenced by modern epistemologists (George Berkeley, John Locke and others). Logicians and metaphysicians of Vilnius University developed an interest in the topics of human understanding and cognition. However, this shift did not take a radical form – while the majority of eighteenth-century authors sought a combination of scholastic and modern ideas, a critical and even hostile stance towards modern philosophy and science is still noticeable in many of the analysed sources. An overview of the research supported by statistical data is followed by some preliminary remarks on how and where investigation of this topic might be continued in the future.

Yaʿqūb al-Qirqisānī on Human Intellect, Legal Inference, and the Meaning of the Aristotelian Syllogism

Abstract In the fourth treatise of his legal-theological work Kitāb al-Anwār wa-al-Marāqib, Yaʿqūb al-Qirqisānī analyzes a criticism of the Aristotelian syllogism and its epistemological foundations. Qirqisānī defends Aristotelian logic by quoting a passage from an unknown commentary on Aristotle in which the Aristotelian theory of syllogism is explicated. This paper focuses on the historical, theological, and philosophical meanings of the criticism of the syllogism in Qirqisānī’s discussion and analyzes his interpretation of the syllogism as a source of knowledge that should be applied in the realm of legal reasoning and in the interpretation of biblical law.

Die Aristotelische Logik—Erklärt von Ihren Antiken Interpreten by Beatrix Freibert

Reviewed by: Die Aristotelische Logik—Erklärt von Ihren Antiken Interpretenby Beatrix Freibert Paolo Fait Beatrix Freibert. Die Aristotelische Logik—Erklärt von Ihren Antiken Interpreten. Studien zu Literatur und Erkenntnis 10. Heidelberg: Winter, 2017. Pp. 393. Cloth, €48.00. Aristotle's Organonreceived sedulous attention throughout late antiquity. This is reflected in the surviving corpus of commentaries written, in different exegetical and didactic styles, by peripatetic and Platonic authors. Does this collection constitute a single tradition? Beatrix Freibert is confident that the answer to this difficult question is yes, and sets out to explain the differences and vindicate the connectedness of what she takes to be a unified intellectual construction. She insists that, despite the many peculiarities, all commentators participate in a progressive effort to discern the purpose ( skopos) of the Organon, and, with its purpose, understand its unity and achieve some fundamental exegetical uniformity (13–18). In her exposition, Freibert follows the traditional order and provides extensive discussions of the following topics: language as the expressive medium of arguments ( Categories), truth bearers ( De Interpretatione), the syllogism ( Prior Analytics), the different kinds of syllogisms ( Posterior Analyticsand Topics), and demonstration and its principles (especially the principle of non-contradiction). The chapter on language, cetnered on commentaries on the Categories, is the only section where Freibert examines the diachronic development of the commentaries and adopts a traditionally historical approach. She offers this aperçuas an example, as if the results could be straightforwardly extended, or easily adapted, to the following chapters. What she does [End Page 554]in the rest of the book, however, is rather different. She expounds interpretative views taken from different commentaries and pieces them together in a systematic reconstruction of supposedly universal value, which pays little attention to the historical and chronological connections between the materials presented. In other words, she cherry-picks the salient points and changes her primary texts in the course of the exposition. So, for example, chapter 4, devoted to the syllogism, begins by quoting Ammonius's claim that logikēincludes, beyond what we would call 'logic,' also the disciplines of rhetoric and poetics (101). Freibert presents this account as the standard description of logikēamong the commentators. Far from that (see for instance the beginning of Alexander of Aphrodisias's commentary on the Prior Analytics), the broad meaning of the adjective logikē, here deployed to qualify the discipline of all sorts of logoi, seems to serve a precise purpose. It appears to be part of the answer to the difficult question whether (in virtue of their alleged logico-linguistic and/or instrumental nature) Aristotle's Rhetoricand Poeticsshould be grouped with the logical works, thus becoming an integral part of the Organon. But which answer to this question did Ammonius advocate? Freibert appears to commit herself to the view that Ammonius's generous understanding of logic implies that he would include more texts in the Organonthan we do. I doubt that this is the case, but, whatever the right answer, the problem of whether to extend the Organonwas mooted by several commentators and resolved in different ways. Freibert should have provided an overview of the different positions. The chapter proceeds to discuss Aristotle's definition of the syllogism, and focuses on the claim, taken from Ammonius's commentary on Porphyry's Isagoge, that the syllogism is a sunthetos logos, a 'composite discourse.' Freibert suggests that this claim is tantamount to Łukasiewicz's contention that an Aristotelian syllogism is a conditional. She does not stop to defend this controversial claim, but connects the two Ammonian views to the results of her chapter on language. Then come new topics and authors: Philoponus's idea that syllogism is a sort of motion ( kinēsis) from what is assumed to what is concluded, followed in turn by an exposition of Themistius's paraphrase of Posterior AnalyticsII 2–3, centered on the distinction between knowing that something is the case and knowing the meaning of a term. And so on, always adding new materials. At the end of the chapter, the reader sees a pattern, but cannot help suspecting that the result of this piecemeal approach is more Freibert's...

The essential and the derivative moods of Aristotelian syllogism

It is generally accepted that it is a mistake that Aristotle ignore the moods of the fourth figure in his syllogism. In this paper, I shall argue the Aristotelian syllogism consisting of the essent...

The openness of attitudes and action in ambivalence

Ambivalence of desire and action in light of it are ordinary human engagements and yet received conceptions of desire and action deny that such action is possible. This paper contains an analysis of the possibility of fertile ambivalent compromises conjointly with a reconstruction of (Davidsonian) basic rationality and of action-desire relations. It is argued that the Aristotelian practical syllogism ought not to be conceived as paralysing the ambivalent agent. The practical syllogism makes compromise behaviour possible, including compromise action in the strong sense of acting to satisfy both of one's contrary desires at once. One's action can to a certain extent fulfil both desires by not exactly satisfying either. In showing this, attitudes including desires are analysed in terms of a soft identity, according to which they are both defined by concrete interlinkages with other attitudes and actual and possible behaviour, and transcend any such connections. In particular, not only do desires have a range, but rather the relation of desire and fulfilment is such that to want something allows a wider range as to what counts as fulfilment.

Troubadour, Griot and Evangelist: The Compelling Narrative Rhetoric of ‘Erujeje’

AbstractThe power of narratives as didactic tools, the repository of history, cultural knowledge and cultural identity is well known. Walter Fisher depicts stories as the sum of rhetorical expressions and applications of the pre-existing values of a community. Narratives and its corollaries—narrator, receptor (audience)—form a tightly woven knit. To be effective, the receptor must be complicit in the narrator’s jeu (game) which is to persuade the receptor of the fidelity and plausibility of the story. Numerous agents exploit the digital age as a new medium which has appropriated them a special niche in the arena of communication. In evangelism, Michael Fasina, also known as Erujeje, is at the heart of such a movement. This article is a treatment of Fisherian narrative and Aristotelian syllogism in an attempt to suggest that Erujeje, the Nigerian dramatist extraordinaire, combines those elements coupled with topoi familiar to his audience in order to proselytize.1

Necesidad práctica y akrasía

En este artículo examino la noción aristotélica de necesidad práctica en la Ética Nicomaquea. Este tema ha recibido poca atención a pesar de su importancia cara a la comprensión del silogismo práctico aristotélico. Concentro mi análisis en el controvertido ejemplo de razonamiento acrático en EN VII, 3, 1147a 26-30, en el cual Aristóteles parece mostrar las propiedades del razonamiento práctico conectadas con la acción. No obstante, tal como espero mostrar, el acercamiento aristotélico a este problema es insuficiente para apoyar una interpretación fuerte de la necesidad práctica.

Universal vs. particular reasoning: a study with neuroimaging techniques

The article investigates some general properties of universal vs. particular propositions occuring in syllogistic arguments, in order to explore the kind of interaction played by these two forms of reasoning inside cognition. The theoretical framework of our analysis is represented by recent developments of linear logic, focusing on the distinction between positive vs. negative status of logical operators (connectives and quantifiers). In the first part of the article, this distinction is introduced and applied to the analysis of the categorical propositions occurring in Aristotelian syllogism, the deductive paradigm particularly considered in psychological studies about human reasoning. In the second part of the article, an experimental research is presented in which the positive vs. negative alternation is studied in the transition from a universal (vs. a particular) categorical proposition to its contradictory, a particular (vs. a universal) categorical proposition; the experimental research is based on a reasoning task which shows that significant differences are exhibited by the two types of transitions.

Michael Wolff über Beweise für vollkommene Syllogismen bei Aristoteles

This paper is a reply to Michael Wolff’s refusal of my critique of his „Vollkommene Syllogismen und reine Vernunftschlusse bei Aristoteles und Kant“, as far as Aristotle concerned. Wolff claims (1) that a perfect Aristotelian syllogism is not characterized by its evidence and (2) that, therefore, it is in need of a proof. Against Wolff’s first claim I point out that to talk of „making the necessity apparent/evident“ in Aristotle’s definition of the perfect syllogism at An. Pr. I 1, 24b22f. speaks in favour of the view that a perfect syllogism is a syllogism in which the validity of the inference is evident. I further argue that in order to make the validity evident, Aristotle uses the wording of a term „to be contained in another as in a whole“ atAn.Pr. I 4, 25b32–35with the effect that there is a logically valid passage from the predicate term of theminor to the subject term of themajor premise. As toWolff’s second claim I argue, first, that nowhere in the An. Pr. does Aristotle give a proof for a perfect syllogism, and, second, that Wolff’s attempts to make his claim plausible rely either on a misreading of the Aristotelian texts or else are question-begging. In particular, I argue that the dictum de omni/de nullo, respectively, are not meant to function as proofrules but rather as translation-rules: they have a role in licensing the switch from the ‚terminological‘ formulations Aristotle mostly uses for his syllogisms (e.g.‚ A belongs to every B’) to the ‚being contained as in a whole‘-wording.

Media Educational Situations and Two Primary School Teachers' Practical Reasoning

This article is about two teachers, Sini and Visa, and how they reason about their actions in the context of media education in a Finnish primary school. Their reasoning was studied through stimulated recall interviews and elicitation of the practical arguments originating from an Aristotelian practical syllogism. This was followed by a data-based content analysis. During the 2007–2008 school year, the two teachers planned together but conducted in parallel classes three school projects with the themes of movies, newspapers, and learning with information and communications technologies. Four examples of practical arguments are presented. Sini's practical arguments included several empirical premises and focused on actions in media educational situations where the way students learned was focal. Data-based content analysis shows that Sini's reasoning in these situations was associated with student volition and self-regulated learning, as well as students’ level of development. Visa's practical arguments in...

LA NAQLA, ÉTUDE DU CONCEPT DE TRANSFERT DANS L’ŒUVRE D’AL-FĀRĀBĪ

AbstractThis article aims at presenting for the first time a central concept in al-Fārābī’s work that constitutes a keystone in understanding his thought, be it in its logical or political aspects. This concept is that of naqla, which, in terms of transmission and translation, its generic transcription can be rendered as ‘transfer’. The naqla is a notion that pertains to rupture in linguistic, logical or temporal continuities, and hints at confusing contiguities in the use of words, in demonstrations and in historical processes. This notion of naqla is at the centre of the preoccupations of al-Fārābī in his various domains of thinking. First of all, in terms of his linguistic reflection that consists of thinking about the transfer (naqla) of a given word in between its notions of first and second imposition. Then, in logic, the integration of the modes of reasoning of the theologians in Aristotelian syllogism, which passes by way of a mechanism of logical transference in the case of induction and the shift in paradigm. Finally, the Fārābian conception of intellectual history, as a transmission of knowledge, cannot be grasped in its fullest scope except through an understanding, not only of the common notion of naqla, but rather in terms of its particular Fārābian sense; namely as a concept that entirely renews the question of transmission and translation.

The logical systematist: George Bentham and hisOutline of a new system of logic

George Bentham was not only a great natural historian, he was, initially, a philosopher and logician of enormous promise. His first published work, the oft-forgotten Outline of a new system of logic (1827) has been heralded by some as the opening salvo in the overthrow of the Aristotelian syllogism's grip on logical inference. The move was a defiant political gesture. The young Bentham composed Outline in close concert with his famous uncle, the great utilitarian Jeremy Bentham, expanding and evolving Jeremy's attempts at a new logical system. Bentham meant Outline to be a contribution to the development of the whole utilitarian project. Yet, after 1827, Bentham was never again to write explicitly on logic and philosophy. His heart seemed to lie in natural history, his first love. However, Bentham never really abandoned the utilitarian picture of logic and philosophy. Recent discoveries in the Bentham papers reveal the strong connection between the Benthamite attack on received philosophical categories and George's role in the development of modern institutional natural history. Bentham the logician can be discovered in Bentham the reformist naturalist. This paper examines Bentham's role in the development of the “new” logic and attempts to explore the notions of a reformed naturalism in his later works. This offers an explanation for Bentham's cautious response to the second great revolution of the nineteenth century: the Darwinian revolution.

The happiest thought of Einstein's life

Finally, let us have a closer look at the place of the equivalence principle in the logical scheme of Einstein's general relativity theory. First, Einstein new well, from Minkowski's geometric formulation of his own special relativity, that accelerated motions should be represented as curved lines in a flat space-time. Second, the Galileo principle asserts that all bodies are accelerated in the same way in a given gravitational field, and consequently their motions are represented in the flat space-time by curved lines, all exactly in the same way. Third, since all lines representing free motions are curved exactly in the same way in the flat space-time, one can say that the lines remain straight (as far as possible) but the space-time itself becomes curved. Fourth, and last, since acceleration is (locally) equivalent to a gravitational field (here we have the equivalence principle), one is entitled to assert that it is the gravitational field (and not acceleration) that is represented as the curvature of space-time. This looks almost like an Aristotelian syllogism. However, to put all the pieces of evidence into the logical chain took Einstein a few years of hard thinking. The result has been incorporated into the field equations which quantitatively show how the curvature of space-time and gravity are linked together.

Inquiries into Classical Chinese Logic

SINCE THE PERIOD of the May Fourth Movement in 1919, it has been an unsettled question in contemporary Chinese philosophy whether Chinese thought possesses a in the Aristotelian sense, and, if not, whether it has its own distinctive logic. Indeed, many have suggested that the ancient Chinese School of Names had little to do with strict logic, and, consequently, pay no attention to the principles of arguments and methods of reasoning used by that school. On the other hand, there are a few who claim that Chinese philosophy has its own unique concern, but they use the word logic or logical in such a broad sense that analytical understanding of Chinese thought is impossible. Both of these extreme views commit the twofold crime of vagueness and generality. For whether Chinese thought in the classical period contained contributions in in the Aristotelian or Western sense or in a unique Chinese way depends upon how we define contributions. In this regard, we understand that there is no non-equivocal understanding even of Aristotelian logic. It has been frequently pointed out that the form of the Aristotelian syllogism in many modem texts is not the same as that found in Aristotle's Prior Analytics.1 In fact, much of what we find in Aristotle's De Interpretatione and Categories does not belong to the theory of inference, but belongs, rather, to theories of categories and predications which are important, nevertheless, in the development of Aristotelian logic. It is true that Chinese thought does not present an over-all explicit formulation of all laws of reasoning, nor does it evolve into a system of useful symbolism for the purpose of abstract thinking.2 It is true, further, that until