Logic and Skepticism

Abstract

The problem of justification of logical truths is presented in a dialogue between a skeptic and a dogmatist discussing the classical Carroll's “What the tortoise said to Achilles”. The skeptic claims that justification is either circular or it leads to regressus ad infinitum. The notion of a rule of inference is analyzed and typical mistakes and ambiguities identified (following the rule, accepting the rule, justifying the rule). Justification for the rule of inference cannot figure as a premise in this same rule on the same level as original premises. The skeptic places his usual strict demands on justification. For deduction to be justified it has to be proven that it is justified. But he does not notice that justification is not necessarily derivation - being justified that p does not mean that p logically follows from the basis of justification. Also, in his argumentation the skeptic himself is bound to use logical rules which are unjustified according to his own standards.