In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of contradictions in a mathematical system. ‘Contradiction. Why just this (...) spectre? This is really very suspicious.’ ( Philosophical Remarks III–56) In the last decades, several authors (e.g. Arrington, Hintikka, Van Heijenoort, Wright, Wrigley) have been digging into Wittgenstein’s rather non-standard standpoint on what concerns the interpretation and import of contradiction in logic and mathematics, and many other authors (e.g. da Costa, Goldstein, Granger, Marconi) have been investigating the possibility of taking Wittgenstein seriously as one of the early forerunners of paraconsistency. While many advances have been made on the first front, the second set of investigations has led almost exclusively to negative results: no, no operational proposal about the construction of a logic in which (some) contradictions are made inoffensive can be read from Wittgenstein’s philosophical work; in fact, it appears that the most one can find there is the exhortation for mathematicians to alter their attitude with respect to contradictions and to consistency proofs. The play is done, and one looks for a resume of the opera. This paper fills that blank, as a thorough investigation of the possible relations between Wittgenstein and paraconsistency. DOI:10.5007/1808-1711.2010v14n1p135. (shrink)

This paper opens by reviewing Aristotle’s conception of the natural slave and then familiar treatments of the internal conflict between the ruling and subject parts of the soul in Aristotle and Plato; I highlight especially the figurative uses of slavery and servitude when discussing such problems pertaining to incontinence and vice—viz., being a ‘slave’ to the passions. Turning to Campanella, features of the City of the Sun pertaining to slavery are examined: in sketching his ideal city, Campanella both rejects Aristotle’s (...) natural slave and is critical of the European institutions of slavery. The fact that slavery has no place in the City of the Sun takes on added significance when complemented with Campanella’s remarks on dominion and servitude in his Quaestiones de politiciis: I show that Campanella’s conception of slavery is intimately bound to sin, and consider whether his employment of the trope of slavery within the context of vice diverges from familiar usage. (shrink)

Infinity and negation are in various relations and interdependencies one to another. The analysis of negation and infinity aims to better understanding them. Semantical, syntactical, and pragmatic issues will be considered.