Ma`rifat Falsafi

One of the important principles used in proving some of the basic propositions in new logic as well as many propositions in mathematics is ‘mathematical induction’. The question is whether this principle is an axiomatic one. Apparently, common sense does not prove it as axiomatic. Thus, the clarity of the demonstration for propositions based on the above principle is doubtful, and the justification of such demonstrations is contingent upon acknowledging the accuracy of the principle of mathematical induction. The authors think that the above principle is provable by relying on primary notions and principles governing the set of natural numbers; and thus by proving it, the probable concern about the doubt on logical strength of the principle of mathematical induction and the propositions based on it in new logic is removed.