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Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist)

100%

Wójcicki R.

Bulletin of the Section of Logic

2017

tom 46

nr 1/2

In this note I am reflecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of mathematics, (2) Freges idea of truth supported by mathematical intuition, and (3) known as Aristotelian correspondence idea of truth concerning any propositions not merely mathematical.

What Is the Sense in Logic and Philosophy of Language

58%

Wybraniec-Skardowska U.

Bulletin of the Section of Logic

2020

tom 49

nr 2

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions.

Ograniczanie wyników

2 Bulletin of the Section of Logic

1 Wybraniec-Skardowska U.

1 Wójcicki R.

1 2020

1 2017

Wyniki wyszukiwania

Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist)

What Is the Sense in Logic and Philosophy of Language