Research On The Problem Of Justification Of Deduction

The inductive problem proposed by Hume is an extremely important problem in the history of philosophy.Under the influence of the inductive problem,logicians have gradually begun to question the deductive reasoning that had been firmly believed in the past,and questioned the rationality of deductive reasoning.Similar to the antinomies of the inductive problem,Susan Huck put forward the antinomies of the deductive problem,that is,for the justification of deduction,we cannot justify it inductively,because it is too weak.And we also cannot justify deduction deductively,because such a justification would be circular.Despite many efforts,the deductive problem has not yet achieved its justification.This paper starts with Carroll’s puzzle,and then discusses the justification of deduction.The core of the justification of deduction is to prove the validity of the inference rules.And,the process of the proof of soundness justifies the inference rule MP.The proof of soundness uses complete inductive reasoning,which is different from deductive reasoning.It is an inductive reasoning with a necessary connection between premise and conclusion.Using complete inductive reasoning to justify deduction would not be circular.And this way can provide an effective justification.Finally,to prove the validity of the rules,it is necessary to clarify the corresponding formal system of the inference rules.To discuss the validity of inference rules,we should focus on the interpretation of conjunctions.And the conjunction’s best explanation is the truth table.According to experience,explaining the conjunctions with the truth table can exhaust all possibilities of the propositions’ truth value.On the other hand,there is no counterexample that can overturn the usage of the connection words.