Semantiniai svarstymai apie modalinę logiką
Saul A. Kripke. Semantical Considerations on Modal Logic (translation)

Summary/Abstract: The article by Saul Kripkė (1940–2022), the Lithuanian translation of which is presented to the readers, is one of the foundational studies of modal logic. For the first time, the modern semantics of quantifier modal logic is developed in detail in it, the semantic relations of the logical sequence of different systems of this logic are formally identified, the relations adequate to these relations are presented, i.e. i.e. comprehensive and consistent, axiomatic systems. Perhaps, Kripke's key idea is that modalities should and should be interpreted not as quantifiers whose domain is non-modal models, but as quantifiers whose domain depends on the modal aspects in the models themselves - the possible worlds and the accessibility relationship between them. This idea allowed him to demonstrate several important points. First, by assigning a (possibly different) set of individuals to each possible world and introducing actualist quantifiers sensitive to these sets, the semantics developed by Kripke allowed him to formally establish the conditions under which the Barcan formula and/or its conversion are (not) identically true. Secondly, this idea made it possible to show that modalities are not metalinguistic, but metaphysical in nature, which in turn made it possible to formulate and justify the foundational arguments for a whole set of theses in the philosophy of language and metaphysics, for example, the arguments expressed in Kripke's lectures Names and Necessity, for the fact that, that names are rigid designators, for semantic externalism, essentialism, etc.

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