Validity, Paradox, and the Ideal of Deductive Logic
Thomas Hofweber · 2007
Abstract There are three basic ingredients that together give rise to the semantic paradoxes, and correspondingly there are three basic strategies for a straightforward solution to them. The first ingredient is a logic, like classical logic. This we can simply take as a set of inference rules associated with certain logically special expressions. The second is a truth predicate, or something like it, and some rules or schemas that are associated with it, say introduction and elimination rules, or the Tarski schema. The third ingredient is some other expressive resources that allow one to formulate one of the trouble inducing sentences, like the liar sentence, or the Curry conditional. Once we have these three we can derive contradictions and anything whatsoever using only the rules we have, with the help of the problematic sentences.