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Horizons of Scientific Pluralism: Logics, Ontology, Mathematics
Discussions on the scientific pluralism typically involve the unity of science thesis, which has been first advanced by Neo-Positivists in the 1930-ies and later widely criticized in the late 1970-ies. In the present paper the problem of scientific pluralism is examined in the context of modern logic, where it became particularly pertinent after the emergence of non-Classical logics. Usual arguments in favor of a unique choice of “the” logical system are of an extralogical nature. The conception of Universal Logic as a theory of mutual translatability and combination of alternative logical systems allows for a more constructive approach to the issue. Logical pluralism gives rise not only to the ontological pluralism but also to non-Classical mathematics based on various non-Classical logics. Our analysis of ontological pluralism rises the following question: is our mathematics globally Classical and locally non-Classical (i.e. having non-Classical parts) or rather, the other way round, is globally non-Classical and only locally Classical? We conclude that in the context of post-non-Classical science the logical pluralism justifies one’s freedom to chose logical tools in conformity with one’s aims, norms and values.