Impossible antecedents entered the scene of medieval logic around the 1120s and soon started to dominate this scene, becoming one of the most debated issues from the second half of the twelfth century onwards. This article focuses on theories of counterpossibles from this period and aims to offer an overview of the different responses offered by twelfth-century logicians on whether everything, something, or nothing follows from an impossible statement. Rather than trying to historically reconstruct the positions of the different authors (...) – an operation that may be premature given the insufficient notions we still have of the authorship and dating of sources – I aim to provide a provisional map of the main arguments that were advanced in favour of or against the ex impossibili quodlibet principle. The article also aims to show that the strategies developed by twelfth-century logical schools in their approach to counterpossibles survive in logical discussions of the same topic during the thirteenth and the early fourteenth century, especially in the syncategoremata and sophistaria traditions. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 201 - 221 This paper summarizes medieval definitions and divisions of consequences and explains the import of the medieval development of the theory of consequence for logic today. It then introduces the various contributions to this special issue of _Vivarium_ on consequences in medieval logic.

This is a dialogue between Lisa and Max on Dag Prawitz's work concerning the concept of deductive validity. Lisa first explains Prawitz's criticisms of the presently prevailing non‐epistemic analyses of validity. Then Lisa describes three different ways in which Prawitz attempted to develop an epistemic concept of validity. Max asks questions for clarification, raises some objections and compares Prawitz's three approaches with other lines of thought. Two inference rules are specially discussed: disjunction introduction and ex contradictione quodlibet. Max and Lisa (...) view Prawitz's contribution as part of a variegated, ongoing research pursuing an explication of the concept of validity, which began with the Socratic and Platonic distinction between merely persuasive arguments and good arguments and with Aristotle's definition of syllogism. Throughout the history of philosophy, logicians have aimed at clarifying a pre‐theoretic idea of good deduction and have proposed, criticized, refined, adjusted precise theoretical concepts of validity. Prawitz has criticized current views about validity, has advanced new proposals and revised them. His work is an important chapter of the long pursuit of the concept of validity. (shrink)

According to Tarski's model-theoretic analysis of logical consequence, the sentence X is a logical consequence of a set of sentences Γ if and only if any model for Γ is also a model for X. Etchemendy, however, does not accept the analysis and critiques it. According to Etchemendy, Tarski’s analysis 1- involves a conceptual mistake: confusing the symptoms of logical consequence with their cause; 2- cannot properly explain the necessity of logical consequence; 3- faces the problem of overgeneration; and 4- (...) faces the problem of undergeneration. In the present article, by evaluating these critiques and examining the effectiveness of some of the answers presented in defense of Tarski's analysis, we try to show that among these critiques, only the problem of undergeneration is not acceptable. According to our common sense understanding, if an argument is valid, it is truth-preserving, and by assuming the truth of the premises, the conclusion will be true as well. But it does not mean that we can reduce the logical consequence relation to truth preservation. This flaw leads Tarski’s analysis to be an unacceptable analysis of logical consequence. (shrink)