Universality of Logic

Jan Woleński

Bulletin of the Section of Logic (2017)

  • Volume: 46, Issue: 1/2
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Jan Woleński. "Universality of Logic." Bulletin of the Section of Logic 46.1/2 (2017): null. <http://eudml.org/doc/295590>.

@article{JanWoleński2017,
abstract = {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.},
author = {Jan Woleński},
journal = {Bulletin of the Section of Logic},
keywords = {universality; logica docents; logica utens; first-order logic; consequence operation; model; syntax; semantics; expressive power},
language = {eng},
number = {1/2},
pages = {null},
title = {Universality of Logic},
url = {http://eudml.org/doc/295590},
volume = {46},
year = {2017},
}

TY - JOUR
AU - Jan Woleński
TI - Universality of Logic
JO - Bulletin of the Section of Logic
PY - 2017
VL - 46
IS - 1/2
SP - null
AB - 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.
LA - eng
KW - universality; logica docents; logica utens; first-order logic; consequence operation; model; syntax; semantics; expressive power
UR - http://eudml.org/doc/295590
ER -

References

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  16. [16] A. Tarski, Logic, Semantics, Metamathematics, Clarendon Press, Oxford (1956). 
  17. [17] J. Woleński, First-Order Logic: (Philosophical) Pro and Contra, [in:] V. Hendricks, F. Neuhaus, S. A. Pedersen, U. Scheffler, H. Wansing (eds.), First-Order Logic Revisited, λoγoς, Berlin (2004), pp. 369–399; reprinted [in:] J. Woleński, Essays on Logic and Its Applications in Philosophy, Peter Lang, Frankfurt am Main (2011), pp. 61–80. 
  18. [18] J. Woleński, Constructivism and Metamathematics, [in:] A. Koslow, A. Buchsbaum (eds.), The Road to Universal Logic. Festschrift for 50th Birthday of Jean-Yves Béziau. Vol I, Birkhäuser, Basel (2015), pp. 513–520. 
  19. [19] J. Woleński, Normativity of Logic, [in:] J. Stelmach, B. Brożek, L. Kwiatek (eds.), The Normative Mind, Copernicus Center, Kraków (2016), pp. 169–195. 

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