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Paradox of Analyticity and Related Issues
Abstract
This paper formulates the paradox of analyticity similar to the Liar Antinomy. The proposed analysis shows that T-equivalences play a crucial role in generating both logical puzzles. The main lesson derived from the paradox of analyticity suggests that the concept of analytic sentences should be defined in a metalanguage, at least if it is understood in the semantic manner.
This chapter outlines an intuitive approach to STT, very closely related to Tarski’s original approach. The essential role of the Liar antinomy and its solution by introducing the language/metalanguage distinction is stressed as well as the role of interpreted languages is pointed out. Finally, heuristics of forming the semantic truth definition via the concept of satisfaction is reported.
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
The division of human cognitive faculties into those based on reason and those based on experience belongs to the standard epistemological vocabulary. The controversy between empiricism and rationalism, which is one of the most important in epistemology, is organized around these categories. Both parties occur in their genetic and methodological versions. Within the former version, we have nativism (genetic rationalism) and genetic empiricism, but apriorism (methodological rationalism) and aposteriorism (methodological rationalism) are connected with the latter.1 This chapter deals mainly with apriorism and aposteriorism, although their connections with the genetic issue will be also noted. The distinctions pointed out in the title are usually regarded as helpful in explaining how apriorism and empiricism are related. In particular, since both views appear in radical or moderate versions, it is important to see where the borderline between them should be drawn.
Pojęcie prawdy w językach nauk dedukcyjnych, Towarzystwo Naukowe, Warszawskie, Warszawa 1933; Eng. translation, The Concept of Truth in Formalized Languages in A. Tarski, Logic, Semantics, Metamathematics. Papers from
- A Tarski