CONTEXT DEPENDENCE OF MATHEMATICAL SENTENCES AND THE CHOICE BETWEEN SEMANTICS
Ilya Andreevich Gushchin
Ural Institute of Humanities, 51, Lenin av., Ekaterinburg, 620000, Russia
Keywords: proof, semantics, pragmatics, meaning, visibility, knowledge, epistemic contextualism
Abstract
The article considers the application of the “semantics with an agent” and “semantics without an agent” proposed by O.A. Kozyreva to mathematical sentences. If it is possible to prove that mathematical sentences are context-dependent, these sentences will need semantic interpretation along with other context-dependent sentences. The author presents an interpretation of mathematical sentences as context-dependent by appealing to the epistemic contextualism and the epistemology of computer proof. Based on this interpretation, he argues that the understanding of semantics as “semantics with an agent” is compatible with the thesis of context dependence of mathematical sentences, while the understanding of semantics as “semantics without an agent” will require additional formalization of pragmatic factors to achieve compatibility with such sentences.
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