Logical pluralism and non-classical category theory


V.L. Vasyukov


Logical pluralism prove to be much more intruiging phenomenon if we envisage its impact on elementary logical theories. Breaking the tenet of the unique (namely, classical) logical basis for those we find ourself in the realm of non-classical elementary logical theories based on the various non-classical logics. It is expecially important if we take into account that such theories underlie non-classical mathematics according to the apt slogan “there are as many mathematics as logics” — suffish it to recall relevant arithmetic, quantum set theory, fuzzy set theory, paraconsistent mathematics etc. In the paper non-classical axiomatic category theories are approached which are based on some non-classical categorical constructions.






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