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Après avoir présenté les règles de l’antilogique éléatique, je soutiens que Zénon pratiquait celleci et, à partir de l’étude de passages duParménidede Platon, que ses paradoxes sur la divisibilité et le mouvement ne sont pas des réfutations par l’absurde, mais plutôt de simples dérivations d’impossibilités employées pour ridiculiser les adversaires de Parménide. Zénon ne cherchait donc pas à prouver l’inexistence du mouvement, mais simplement à l’inférer des prémisses de ses adversaires. Je montre en outre que ces paradoxes sont conçus, conformément (...) 

By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms. 

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. (...) 

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11page 1936 Tarski consequencedefinition paper is based on a monistic fixeduniverse framework?like Begriffsschrift and Principia Mathematica. Monistic fixeduniverse frameworks, common in preWWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multipleuniverse framework?like the 1931 Gödel incompleteness paper. A pluralistic multipleuniverse framework recognizes multiple (...) 

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of (...) 

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 consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue that ecthesis (...) 



A formal analysis is offered of PseudoScotus's theory of the conversion of (i) propositions containing singular terms (including propositions with a singular term as predicate): and (ii) propositions with a quantified predicate. An attempt is made to steer a middle course between using the Aristotelian logic as a framework for the analysis, and using a Fregean framework. 