Geodesic
Universality of Logic
Bulletin of the Section of Logic, Tome 46 (2017) no. 1-2.

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This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity (truth in all models). All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic. The categorical approach to logic is presented as associated with the last understanding of universality. The author concludes that two senses of universality should be sharply discriminated and defends the first-order thesis.
Keywords: universality, logica docents, logica utens, first-order logic, consequence operation, model, syntax, semantics, expressive power 
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     author = {Wole\'nski, Jan},
     title = {Universality of {Logic}},
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Woleński, Jan. Universality of Logic. Bulletin of the Section of Logic, Tome 46 (2017) no. 1-2. http://geodesic.mathdoc.fr/item/BSL_2017_46_1-2_a9/