This paper scrutinizes Everett Nelson's conception of consistency by comparing it with the “standard” account of C. I. Lewis. This conflict surprisingly resembles a related controversy between the ancient logicians Chrysippus and Diodorus. Nelson's intuitions behind his peculiar conception of consistency are analysed and certain features of his logical system are critically examined. In particular, his objections against the law of the transitivity of implication and against the laws of conjunction and disjunction have to be discussed. Although Nelson's considerations contain (...) interesting ideas in favour of a relevantist conception of logic, they fail to convincingly support the hardcore connexive thesis that even a selfcontradictory proposition doesn't entail its own negation. (shrink)

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)

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)

The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...) systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (shrink)