Deductive foundation and analytic propositions

Abstract

1. The deductive foundation or the deductive proof is usually identified with the deductive inference. The deductive inference is defined as an inference whose conclusion follows logically from its premisses. The deductive proof defined in such a way is an indirect foundation of the truth of some proposi? tions (conclusions) by appealing to the truth of other propositions (premisses). The sequence of inferences which we can perform is always finite; hence there are always in our inferences ? if we avoid the fallacy of vicious circle ? some propositions which are not founded indirectly. It is obvious therefore that ? when using such a concept of a deductive proof ? we cannot say that some propositions are proved (or provable) deductively but only that they are proved (or provable) deductively by virtue of certain other propositions. The deductive science is defined as a science in which only deductive in? ference is performed. It is also almost commonly assumed that each deductive science is an axiomatic system. It follows from our previous remarks that we cannot say that a proposition of a given deductive science is proved (or pro? vable) deductively. We can only say that it is proved (or provable) deductively by virtue of the axioms. But the axioms cannot be founded deductively. Such a conception of the deductive proof as an indirect foundation is com? monly accepted in the methodology of sciences. As I know it has not been criticized till now.