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2017 | 46 | 1/2 |
Tytuł artykułu

Universality of Logic

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
46
Numer
1/2
Opis fizyczny
Daty
wydano
2017-06-30
Twórcy
  • University of Information, Technology and Management Rzeszów, Poland
Bibliografia
  • [1] J. Barwise, Model-Theoretic Logics: Background and Aims, [in:] J. Barwise, S. Feferman, (eds.), Model-Theoretic Logics, Springer, Berlin (1985), pp. 3–23.
  • [2] J.-Y. Béziau, A. Costa-Leite (eds.), Perspective on Universal Logic, Polimetrica, Monza (2007).
  • [3] C. C. Chang, H. J. Keisler, Model Theory North-Holland, Amsterdam (1977).
  • [4] J. P. Cleave, A Study of Logics, Clarendon Press, Oxford (1991).
  • [5] J. Czelakowski, Protoalgebraic Logic, Kluwer, Dordrecht (2001).
  • [6] R. Diaconescu, Institution-Independent Model Theory, Birkhäuser, Basel (2008).
  • [7] J. M. Font, Abstract Algebraic Logic An Introductory Textbook, College Publications, London (2016).
  • [8] D. Gabbay, (ed.), What is a Logical System?, Clarendon Press, Oxford (1994).
  • [9] R. Goldblatt, Topoi. The Categorical Analysis of Logic, North-Holland, Amsterdam (1979).
  • [10] P. Halmos, S. Givant, Logic as Algebra, Mathematical Association of America, New York (1998).
  • [11] A. Heyting, D. Monk, A. Tarski, Cylindric Algebras, Part I, North-Holland, Amsterdam (1971).
  • [12] J. Lambek, P. J. Scott, Introduction to Higher Order Categorical Logic, Cambridge University Press, Cambridge (1986).
  • [13] M. Makkai, G. E. Reyes, First Order Categorical Logic, Springer, Berlin (1977).
  • [14] A. Rayo, G. Uzgquiano (ed.), Absolute Generality, Clarendon Press, Oxford (2006).
  • [15] H. Rasiowa, R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa (1970).
  • [16] A. Tarski, Logic, Semantics, Metamathematics, Clarendon Press, Oxford (1956).
  • [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] 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] J. Woleński, Normativity of Logic, [in:] J. Stelmach, B. Brożek, L. Kwiatek (eds.), The Normative Mind, Copernicus Center, Kraków (2016), pp. 169–195.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_46_1_2_03
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