Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to non-empty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.

Buridan endorsed the principles that any impossible, and a fortiori any self-contradictory, proposition entails each proposition. These principles are usually referred to as ‘Ex impossibili quodlibet’ (EIQ) and ‘Ex contradictione quodlibet’ (ECQ). Buridan further considered the instance ECCQ according to which any proposition follows from the conjunction of two contradictory propositions. Buridan showed how ECCQ can be proven by means the usual laws of conjunction and disjunction. Furthermore, he discovered that EIQ can be derived from ECCQ by means of the (...) principle that if a conclusion q follows from two premises, one of which is necessary, then q follows from the other premise alone. Buridan thought that this principle would be provable; but his proof turned out to be circular since it presupposed EIQ. Nevertheless, EIQ is validated by the definition of a ‘bona consequentia’. Somewhat more exactly, according to Buridan one may distinguish between inferences which are formally valid, ‘materially’ valid, and valid ‘as of now’. It is shown that formally valid inferences satisfy ECQ while ‘materially’ valid inferences satisfy EIQ. Furthermore, inferences which are valid ‘as of now’ satisfy the principle ‘Ex falso quodlibet’ saying that any false proposition ‘as of now’ entails every proposition. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed...

The nominalist attitude in medieval logic supported a fully extensional conception of the sense of expressions. Many arguments against this approach were raised at that time. I would like to show in this article that there is a extensional conception of notions in current logic, namely in the interpretation of formal theories and the creation models of them and that, and how, traditional arguments against the extensional conception are relevant also for logic today.

Buridan endorses the basic idea that q follows from p iff it is impossible that p is true but q is false. Since he also accepts the law that, if p is impossible, the conjunction (p ∧ q) must be impossible, he comes to regard the principle ‘Ex impossibili quodlibet’ (EIQ) as basically correct. However, his logic is based on a ‘nominalist’ view according to which propositions are tokens of spoken, written or thought language existing in space of time, and (...) the truth of such a proposition presupposes that it exists. This conception prompted Buridan to modify the definition of ‘consequence’, but none of his attempts was fully successful. Yet, a large part of his theory of consequences is based on the usual account of necessary truth-conservation. As regards principle EIQ, Buridan distinguishes two variants of impossibility. Proposition p is possible iff the state of affairs as described by p is possible; this doesn’t guarantee, however, that p is ‘possibly true’. E.g. ‘No proposition is negative’ is considered by Buridan as describing a possible state of affairs, but this proposition is not possibly true, because in order to be true, it would have to exist, and as soon as it comes into existence, it becomes false. Accordingly, EIQ requires that the antecedent p is really impossible and not only impossibly true. (shrink)

The essay casts doubt upon the view that Albert was criticizing or was dependent upon Thomas Manlevelt's logico-philosophical views, and counter argues that it is in fact Manlevelt who knows and cites Albert's views in his recently edited Porphyrian Questions, rather than vice versa. The argument for this conclusion proceeds in two stages. First, it is argued that the brief comment Albert makes about ‘conjunct descent’ in treating the definition of merely confused supposition his Perutilis Logica does not conclusively show (...) that Albert is criticizing the logico-philosophical view of Thomas Manlevelt, as the notion of ‘conjunct descent’ is already present in the work of Heytesbury. Hence, Albert may have been referring to him, since the unique contribution of Thomas Manlevelt to the definition of merely confused personal supposition appears completely unknown to Albert. Second, it is argued that the views in the Porphyrian Questions on the nature of the continuum, quantity, and disposi.. (shrink)