Logic and Sense

Abstract

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl's ideas of pure grammar, Leśniewski-Ajukiewicz's theory syntactic/semantic categories and in accordance with Frege's ontological canons, Bocheński's famous motto-syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic (extensional and intensional) categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism 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, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science.

What Is the Sense in Logic and Philosophy of Language

“…A characteristic feature of categorial syntax is that each composed wfe of the set S has a functor-argument structure, so that it is possible to distinguish in it the main part (the so-called main functor ) and the other parts (called arguments of this functor), yet each constituent of the wfe has a determined syntactic category. Categorial intensional and extensional semantics is connected with meaning and denotation of wfes of S and with their membership in appropriate semantic categories: intensional and extensional, respectively (see [25,61,63,64,65,66]). Each constituent of the composed wfe has a determined semantic (intensional and extensional) category, can have a meaning (intension) assigned to it, and thus also a category of knowledge (the category of constituents of knowledge) and also denotation (extension), and thus -an ontological category (the category of ontological objects).…”

“…The postulate of categorial compatibility defining an aspect of the logical sense of wfes of L has the following form [65,66,67]:…”

“…4). The idea of unification of the type of the logical term of the natural language, its intension and extension, is also one of the features of the type-theoretic object theory of E. Zalta [70,71].…”

“…The above-mentioned adequacy requires, first of all, syntactic and semantic characterisation of language expressions as generalised by a grammar [57,66]. Languages structured by grammar and logic are important tools of thinking, cognition of reality and knowledge acquisition, which stand for the foundations of our sense of existence [43].…”

A Logical Conceptualization of Knowledge on the Notion of Language Communication

“…The notion of meaning is defined by means of the relation ∼ = of having the same manner of Using wfe-types and the notion of interpretation -by means of the relation ∼ = i . of having the same manner of Interpreting (understanding) wfe-types (see Wybraniec-Skardowska, 2007a, b;2015, 2016. The definitions of these relations are as follows: DEFINITION 7 (having the same manner of Using types): e ∼ = e ′ iff ∀u ∈ User [(u Use e ⇔ u Use e ′ ) ∧ ∧ ∀o ∈ Ont (∃e ∈ e (use(u, e) = o) ⇔ ∃e ′ ∈ e ′ (use(u, e ′ ) = o))].…”