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# Problems of Scientific Method and Philosophy in Terms of Logical Syntax

DOI link for Problems of Scientific Method and Philosophy in Terms of Logical Syntax

Problems of Scientific Method and Philosophy in Terms of Logical Syntax book

# Problems of Scientific Method and Philosophy in Terms of Logical Syntax

DOI link for Problems of Scientific Method and Philosophy in Terms of Logical Syntax

Problems of Scientific Method and Philosophy in Terms of Logical Syntax book

## ABSTRACT

An example here would be instructive. Wittgenstein gives the general form of the series of natural numbers by the formula [o, x, x + r], whereas Russell and Whitehead define the natural numbers as the posterity of zero in respect of the relation immediate predecessor. Wittgenstein then states that the series of numbers is ordered by an internal relation which must be shown because it cannot be expressed. It is not difficult to see that the relation is expressed by the Frege-Russell definition of the ancestral relation. And Carnap has explained that internality of certain relations is expressible in terms of logical syntax. The" interlocking" of two numbers one of which immediately precedes the other in the series of natural numbers is expressed by saying that the relation between these numbers is an analytic predicate. And thus the inexpressible essential features of mathematical terms and sentences become expressible by enriching the object-language by unlimited operators, a typal hierarchy, etc., and by formulating a syntax language in which analytic predicates are defined.