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 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. (shrink)

The subject matter of this work covers the issues or problems listed below: * The problem of the ontological status of language signs and a more general philosophical problem connected with it: * What is language as a system of signs, which – on the one hand – serves to: 1) represent our knowledge about the reality which is being recognized, and, on the other one to: 2) a. explore and better cognize or discover it, b. describe it in an (...) adequate manner, and c. enable users to make interpersonal communication? All the pragmatic functions of language require carrying out its logical-philosophical analysis, and this means both regarding its syntax and semantics. Such an analysis is not possible without determining the following: How are signs perceived and what is their ontological nature in the so-called functional approach towards logical semiotics of natural language, founded on two ways of their usage: either as signs which we use in concrete situational or situational-language contexts or as isolated signs detached from such contexts? In the first case, they are language tokens (concretes), existing material objects perceived through the senses, with a fixed temporal-spatial location, in the other one – they are non-concretes and as such (as the majority of researchers in the field of philosophy and linguistics accept) – abstract objects, language types. The type-token distinction (differentiation between abstract and concrete) has already acquired a certain status in contemporary philosophy and is of considerable importance to metaphysics and epistemology in particular. Indeed, it is most often illustrated with reference to language signs (words, expressions) as the distinction type/token of a sign, introduced into semiotics by Ch. S. Peirce. In the semiotic analysis, and also in the linguistic one, there are used both types and tokens of signs, however, often without paying due attention to when it is said about types and when about tokens. This is related to the problems which are still considered by the philosophy of language: What is the type? What is the token (specimen)? What are the mutual relations between the type and the token? Disputes concerning providing answers to these questions are related to existential issues dealing with the ontological status of these language signs and two currents within the ontology of language, remaining under the influence of two fundamental concepts formed in the debate: nominalism and realism. The author presents in brief different stances on the above-mentioned issues or problems, as well as argues that from the logical point of view: 1) working out any theoretical conception of language must take into account its bi-aspectual characteristics: as a language of expression-tokens and as a language of expression-types; 2) advocating either of the standpoints: (a) types exist independent of their tokens, or (b) it is not so, can be omitted in syntactic considerations on language; 3) mutual relations between sign-tokens differ from the mutual relations between sign-types, yet; 4) determination of the mutual relation between sign-types and sign-tokens depends on accepting either of the standpoints: (a) or (b); 5) semantic or semantic-pragmatic concepts of language, such as meaning, denotation, interpretation should be defined exclusively for types of tokens, but their definitions require certain reference to the functions which sign-tokens perform in the language (words, expressions), or to relations between them; 6) The concept of an act of language communication differs from general language communication: the first one is defined by means of sign-tokens, whereas the other one – with the use of sign-types. (shrink)

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)