Journal of Philosophical Investigations

Document Type : Research Paper

Authors

1 Postdoc Researcher of Philosophy, University of Isfahan, Isfahan, Iran.

2 Associate Professor of Philosophy Department, University of Isfahan, Isfahan, Iran.

Abstract

According to Tarski's model-theoretic analysis of logical consequence, the sentence X is a logical consequence of a set of sentences Γ if and only if any model for Γ is also a model for X. Etchemendy, however, does not accept the analysis and critiques it. According to Etchemendy, Tarski’s analysis 1- involves a conceptual mistake: confusing the symptoms of logical consequence with their cause; 2- cannot properly explain the necessity of logical consequence; 3- faces the problem of overgeneration; and 4- faces the problem of undergeneration. In the present article, by evaluating these critiques and examining the effectiveness of some of the answers presented in defense of Tarski's analysis, we try to show that among these critiques, only the problem of undergeneration is not acceptable. According to our common sense understanding, if an argument is valid, it is truth-preserving, and by assuming the truth of the premises, the conclusion will be true as well. But it does not mean that we can reduce the logical consequence relation to truth preservation. This flaw leads Tarski’s analysis to be an unacceptable analysis of logical consequence.

Keywords

Main Subjects

  • Bach, N. Craig (1997) “Tarski's 1936 Account of Logical Consequence”, Modern Logic, 7(2): 109-130.
  • Beall, J. C.; Restall, (2006) Logical Pluralism, Oxford: Oxford University Press.
  • Beall, J. C.; Restall, G.; Sagi, Gil (2019) "Logical Consequence", The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), URL= <https:// plato.stanford.edu/archives/spr2019/entries/logical-consequence/>.
  • Chihara, Charles (1998) “Tarski’s Thesis”, in The Philosophy of Mathematics Today, Edit. Matthias Schirn, US: Oxford University Press.
  • Cohnitz, Daniel; Estrada-Gonzales, Luis (2019) An Introduction to Philosophy of Logic, Cambridge: Cambridge University Press.
  • Dutilh Novaes, Catarina (2014) “The Undergeneration of Permutation Invariance as a Criterion for Logicality”, Erkenntnis, 79: 81-97. DOI. 1007/s10670-013-9469-9.
  • Etchemendy, John (1983) “The Doctrine of Logic as Form”, Linguistics and Philosophy, 6(3): 319-334.
  • Etchemendy, John (1988) “Tarski on Truth and Logical Consequence”, The Journal of Symbolic Logic, 53(1): 51-79.
  • Etchemendy, John (1990) The Concept of Logical Consequence, Cambridge, MA: Harvard University Press.
  • Etchemendy, John (2008) "Reflections on Consequence", in New Essays on Tarski and Philosophy, Edit. Douglas Patterson, Oxford: Oxford University Press.
  • Gómez-Torrente, Mario (1996) “Tarski on Logical Consequence”, Notre Dame Journal of Formal Logic, 37(1): 125-151.
  • Hanson, William H. (2008) “Logic, the A Priori, and the Empirical,” An International Journal for Theory, History and Foundations of Science, 18(2): 171–177. https://doi.org/10.1387/theoria.420.
  • McGee, Vann (1992) “Two Problems With Tarski’s Theory of Consequence”, Proceedings of the Aristotelian Society, New Series, 92: 273-292.
  • McKeon, Matthew W. (2010) The Concept of Logical Consequence, an Introduction to Philosophical Logic, New York: Peter Lang.
  • MacFarlane, John (2000) What Does it Mean to Say that Logic is Formal?, PhD dissertation, University of Pittsburgh. http://fitelson.org/confirmation/macfarlane_ch_7.pdf.
  • MacFarlane, John (2017) "Logical Constants", The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), URL= <https://plato. stanford.edu/archives/win2017/entries/logical-constants/>.
  • Martin, Christopher J. (2018) “The Theory of Natural Consequence,” Vivarium, 56: 340–366. DOI: 1163/15685349-12341357.
  • Priest, Graham (1995) “Etchemendy and Logical Consequence”, Canadian Journal of Philosophy, 25(2): 283-292.
  • Ray, Greg (1996) “Logical Consequence: A Defense of Tarski”, Journal of Philosophical Logic, 25: 617-677.
  • Rumfitt, Ian (2010) “Logical Necessity”, in Modality, Metaphysics, Logic, and Epistemology, Edit. Bob Hale and Aviv Hoffman, New York: Oxford University Press.
  • Shapiro, Stewart (2005) “Logical Consequence, Proof Theory and Model Theory”, in The Oxford Handbook of Philosophy of Mathematics and Logic, Edit. Stewart Shapiro, US: Oxford University Press.
  • Sher, Gila, Y. (1996) “Did Tarski Commit “Tarski's Fallacy”?”, The Journal of Symbolic Logic, 61: 653-686.
  • Smith, Robin (1989) Aristotle’s Prior Analytics, translation & comments: Indianapolis/Cambridge: Hackett Publishing Company.
  • Steinberger, Florian (2017) "The Normative Status of Logic", The Stanford Encyclopedia of Philosophy (Edition), Edward N. Zalta (ed.), URL= https://plato.stanford.edu/archives/spr2017/entries/logic-normative/
  • Tarski, Alfred (2002) “On the Concept of Following Logically”, Trans. M. Stroińska and D. Hitchcock, History and Philosophy of Logic, 23(3): 155-196, DOI: 1080/0144534021000036683.
  • Tarski, Alfred (1986) “What are logical notions?,” History and Philosophy of Logic, 7(2): 143-154. (Transcript of a 1966 talk, edit. John Corcoran)
CAPTCHA Image