Abstract

The paper introduces the idea that L. Borkowski’s theory of ‘proper quantifiers’ is the salient part of the solution to the problem of the limitation of logic. The philosophical motivation of presented reasoning is grounded in L. Wittgenstein’s early philosophy.The first section is concerned with Wittgenstein’s general claim that logic is decidable, and hence it discusses the idea of logic as the calculus. According to Wittgenstein, logical constants in propositional calculus are ‘punctuation-marks’, i.e., they do not refer to any objects but they are symbols that express truth functions.The second section defines the notion of ‘proper quantifier’ that is characterized by ‘quantifier matrix’, i.e., function from the set of the sets of sequences of logical values to the set of logical values. The notion of ‘proper quantifier’ can be applied to the decision problem in the predicate calculus – it provides the zero-one decision procedure for the expressions of the first order monadic predicate calculus.The third section formulates a new definition of logical constants – logical connectives and quantifiers in the monadic predicate calculus – as functions whose ranges consist only of logical values. Since this definition is consistent with Wittgenstein’s idea of logical constants as ‘punctuation-marks’, it might be considered philosophically interesting contribution to the problem of limitation of logic.