Verification Or Proof- An Undecided Issue?

Abstract

Since Leibniz, Hume, and Kant the realm of cognitively significant statements has been divided into two categories that are mutually exclusive and collectively exhaustive: analytic and synthetic propositions. No doubt, the term ‘synthetic’ is rather ambiguous, and for that reason it has been replaced by the more unequivocal expressions ‘empirical’ or ‘contingent’. These terms render it clear that non-analytic knowledge originates in experience. An analytic proposition is a logically necessary expression (Carnap); its negation leads to a self-contradiction or, in formal symbols, to P• ~ P.1 Its truth or validity depends only on definitions, so that it will hold under all conditions, in all possible worlds, so to speak. In other words, analytic propositions should be a priori, in that they do not appeal to experience. The assertions of logic and mathematics are customarily regarded as presenting the sole domain of analytic statements.KeywordsPure MathematicOperational RuleLogical EmpiricismCounterfactual ConditionalCylindrical AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.