А. В. Хлебалин | Библиотека ELiS

Axiomatics for Disquotational Truth Theory and Non-Conservativity Argument

Submitted by Гость (not verified) on Thu, 09/05/2024 - 00:08

The paper considers the possibilities for the axiomatization of disquotational truth theory in perspective of the general S. Shapiro’s non-conservative argument against deflationary concept of truth. It shows that in a generalized formulation, Shapiro’s argument cannot be automatically extended to any axiomatic formulation of the disquotational theory. It also shows that the epistemological justification of the suitable class of substitutions for the T-scheme is the key to constructing an adequate axiomatic disquotational theory.

LOGICAL AND MATHEMATICAL INFERENCE: SYNTAX AND SEMANTICS OF PROOF

Submitted by Гость (not verified) on Thu, 09/05/2024 - 00:08

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The paper treats the relation between mathematical and logical inferences in mathematics and analyses an ontological approach for explaining the indispensability of the semantic content from mathematical proof. It was shown that such an approach entails serious metaphysical commitments, that is why it is concluded that the epistemological approach is preferable in explaining the nature of the difference between the formal and mathematical inferences.

The Gap between the Intensional and Extensional in Mathematics

Submitted by Гость (not verified) on Wed, 09/04/2024 - 23:54

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The paper is devoted to the study of the divergence of the intensionalist and extensionalist traditions in the foundations of mathematics. One of the important manifestations of this discrepancy was the debate on the status of the Axiom of Choice. In particular, we argue that Russell's challenging Axioms of the Choice is connected with his intensionalist philosophy of mathematics and the extensionalist approach of Zermelo.

Conceptions of intensionality of mathematical discourse: The Stages of Self-reference

Submitted by Гость (not verified) on Wed, 09/04/2024 - 23:54

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The article discusses the reasons for the emergence of intensional structures in mathematical discourse with the example of the proof of the Second Gödel Theorem on the incompleteness of arithmetic. It is shown that one of the reasons for intensionality is the conceptual structure, including the transition from strictly mathematical formulations to their interpretation. Three stages of intensionality are analyzed - coding, constructing a predicate of proof, and constructing a self-reference sentence.