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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 prooftheoretically 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 firstorder logic, and the usual formalizations of Aristotle's sentenceforms. I explain how the syllogistic is (...) 

This paper (1) criticizes Patzig's explanation of Aristotle's reason for calling his first figure syllogisms perfect syllogisms, i.e. the transitivity relation: it can only be used for Barbara, not for the other three moods. The paper offers (2) an alternative interpretation: It is only in the case of the (perfect) first figure moods that we can move from the subject term of the minor premiss, taken to be a predicate of an individual, to the predicate term of the major premiss. (...) 

There is very little information about the proving by Aristotle’s ecthesis method both in Aristotle’s and his commentators’ articles. Researches on ecthesis which were made by recent commentators are only on expository term. In our study, comments have been evaluated, points that are subject to contradiction have been determined, and opinions about ecthesis have been cited by giving proofs obtained by the ecthesis method. 



We elaborate on the approach to syllogistic reasoning based on “case identification” (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition ( ecthesis ), and that there are traces of this method in the strategies described by a number of psychologists, from St rring (1908) to the present day. We hypothesised that by rendering individual cases explicit (...) 

“Natural syllogisms” are arguments formally identifiable with categorical syllogisms that have an implicit universal affirmative premise retrieved from semantic memory rather than explicitly stated. Previous studies with adult participants have shown that the rate of success is remarkably high. Because their resolution requires only the use of a simple strategy and an operational use of the concept of inclusion, it was hypothesized that these syllogisms would be within the grasp of nonadult participants, provided they have acquired the notion of deductive (...) 

Natural syllogisms are expressed in terms of classes and properties of the real world. They exploit a categorisation present in semantic memory that provides a class inclusion structure. they are enthymematic and typically occur within a dialogue. Their form is identical to a formal syllogism once the minor premise is made explicit. It is claimed that reasoners routinely execute natural_syllogisms in an effortless manner based on ecthesis, which is primed by the class inclusion structure kept in long term memory. 

"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.. 

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 (...) 



The dissertation is an investigation into the structure of Aristotle's modal propositions through careful attention to the text of the Prior Analytics. I take account not only of recent attempts to formalize Aristotle's modal syllogistic but also of the discussion that Aristotle himself provides about modal statements. I provide evidence that his modal propositions are to be construed in a de re manner and then go on to investigate the problems raised by a de re analysis, particularly those problems concerned (...) 

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A17. This reconstruction will be much closer to Aristotle's original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by BenYami [2014. ‘The quantified argument calculus’, The Review of Symbolic Logic, 7, 120–46] called ‘QUARC’. This system is apt for a more adequate reconstruction (...) 

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) 

I argue that, in the Prior Analytics, higher and above the wellknown ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truthvalue consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘nonexistent’, the system is also completed by rejecting any invalid combinations of terms (...) 

In his 1910 book On the principle of contradiction in Aristotle, Jan Łukasiewicz claims that syllogistic is independent of the principle of contradiction . He also argues that Aristotle would have defended such a thesis in the Posterior Analytics. In this paper, we first show that Łukasiewicz's arguments for these two claims have to be rejected. Then, we show that the thesis of the independence of assertoric syllogistic visàvis PC is nevertheless true. For that purpose, we first establish that there (...) 

Three distinctly different interpretations of Aristotle?s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premiseconclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A46)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle?s remarkable degree of metalogical (...) 

Two main claims are defended. The first is that negative categorical statements are not to be accorded existential import insofar as they figure in the square of opposition. Against Kneale and others, it is argued that Aristotle formulates his o statements, for example, precisely to avoid existential commitment. This frees Aristotle's square from a recent charge of inconsistency. The second claim is that the logic proper provides much thinner evidence than has been supposed for what appears to be the received (...) 