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Logics and languages

Transcendental phenomenology and possible worlds semantics

It is very interesting question whether time if a priori in mankind's thinking or whether it is a category which results from experience. Each human being has a memory so that he is able to distinguish between the past and the present, but not every language has a word expressing the common idea of time. In hunting and gathering populations such as Bushmen and Yumbri no one can state his own age. In chronobiology, the most important zeitgebers are the sun and the moon. Certain peasant peoples, such as the Santals and Mundas in India, even today use the same word to express sun, Sun-God, daylight, day, day-time, and hour. The first generalized idea of "time" seems to have arisen in the civilization of Old Mesopotamia. While the general meaning was still unknown to Sumerian, Accadian priest-astronomers presumably created the conception by generalization of the (Sumerian) foreign word itu(d) "mouth" and its mingling with the Accadian ittu(m) "sign (as an eclipse, monstrous birth, etc.), term, moment". We find the same root in the Etruscan itus "ides" from which it came as a loan-word into Latin (idus "ides"). Newton's term duratio can be found in earliest Iranian as yav- "yoke" and Vedic Indian as yugam "yoke" (i.e., a "bound" time). Some remarks are made concerning mankind's earliest chronobiological thinking where menstruation serves as a model. West African Kwa languages (predominantly Ewe), Old Indian, and early-classical chinese are evaluated. A brief survey is given of prehistoric peoples' migrations in terms of languages. The presentation concludes with an attempt to define time as an abstraction of abstractions, a fussy set (of ideas and definitions) in terms of post-classical set theory.

Time and language.

One of the most influential achievements of Kazimierz Ajdukiewicz, a prominent representative of the Warsaw-Lemberg School, is an idea of syntactic description by means of logical types, underlying the theory of grammar later called categorial grammar. Many essential components of this idea can be found in earlier logico-linguistic speculations of Frege (functor-argument analysis, compositional semantics), Husserl (categories as substitution classes), Russell (types in syntax and ontology), and others; Ajdukiewicz (1935) acknowledged his new indebtedness to Stanislaw Lesniewski, whose work in deep foundations of mathematics contributed so much to the theory of typed languages. We may also presume that Ajdukiewicz’s attempt to elaborate a universal method of syntactic description was not quite independent of the goals and results of logical syntax, a theory promoted and highly advanced by Rudolf Carnap. In the fifties, both Carnap and Ajdukiewicz influenced Bar-Hiller’s investigations in the formal theory of categorial grammars and their applications to natural language (cf. Bar-Hillel (1953), Bar-Hillel et al. (1960)). In general, as clearly demonstrated by Hiz (1967) the principles of categorial grammar have much in common with the doctrine of logicism, a philosophical orientation guiding the major enterprises of the Warsaw-Lemberg School and the Vienna Circle

Principles of Categorial Grammar in the Light of Current Formalisms

The aim of the paper is to outline an idea of solving the problem of the vagueness of concepts. The starting point is a definition of the concept of vague knowledge. One of the primary goals is a formal justification of the classical viewpoint on the controversy about the truth and object reference of expressions including vague terms. It is proved that grasping the vagueness in the language aspect is possible through the extension of classical logic to the logic of sentences which may contain vague terms. The theoretical framework of the conception refers to the theory of Pawlak’s rough sets and is connected with Zadeh’s fuzzy set theory as well as bag (or multiset) theory. In the considerations formal logic means and the concept system of set theory have been used. The paper can be regarded as an outline of the logical theory of vague concepts.

Logics and languages

Citations

Transcendental phenomenology and possible worlds semantics

Time and language.

Principles of Categorial Grammar in the Light of Current Formalisms

Knowledge vagueness and logic

Sign meaning, cognitive content, and pragmatics

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