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SEMANTIC POLLUTION AND SYNTACTIC PURITY

Published online by Cambridge University Press:  07 August 2015

STEPHEN READ
STEPHEN READ*
Affiliation:
UNIVERSITY OF ST ANDREWS
*
*UNIVERSITY OF ST ANDREWS ARCHÉ RESEARCH CENTRE 17-19 COLLEGE ST. ST ANDREWS KY16 9AA SCOTLAND, U.K. E-mail: [email protected]
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Abstract

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion of semantics into syntax. The charge is shown to be mistaken. It is argued on inferentialist grounds that labelled deductive systems are as syntactically pure as any formal system in which the rules define the meanings of the logical constants.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 649 - 661
Copyright
Copyright © Association for Symbolic Logic 2015 

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References

BIBLIOGRAPHY

Avron, A. (1996). The method of hypersequents in the proof theory of propositional non-classical logic. In Hodges, W., Hyland, M., Steinhorn, C., and Strauss, J., editors. Logic: From Foundations to Applications. Oxford: Oxford University Press, pp. 1–32.Google Scholar
Basin, D., Matthews, S., & Viganò, L. (1997). Labelled propositional modal logics: Theory and practice. Journal of Logic and Computation, 7, 685–717.Google Scholar
Beth, E. W. (1969). Semantic entailment and formal derivability. In Hintikka, J., editor. The Philosophy of Mathematics. Oxford: Oxford University Press, pp. 9–41. Originally published in Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afdeling Letterkunde, N.R. 19 no. 13 (Amsterdam 1955), pp. 309–342.Google Scholar
Brandom, R. (2000). Articulating Reasons. Cambridge, MA: Harvard University Press.Google Scholar
Curry, H. (1950). A Theory of Formal Deducibility. Notre Dame, Indiana: University of Notre Dame Press.Google Scholar
Dummett, M. (1973). Frege: Philosophy of Language. London: Duckworth.Google Scholar
Dummett, M. (1991). Logical Basis of Metaphysics. London: Duckworth.Google Scholar
Dutilh Novaes, C. (2011). The different ways in which logic is (said to be) formal. History and Philosophy of Logic, 32, 303–332.CrossRefGoogle Scholar
Dutilh Novaes, C. (2012). Formal Languages in Logic. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Fitch, F. (1952). Symbolic Logic: An Introduction. New York: The Ronald Press Co.Google Scholar
Fraenkel, A., Bar-Hillel, Y., & Levy, A. (1973). Foundations of Set Theory (second revised edition). Amsterdam: North-Holland Publishing Co.Google Scholar
Gentzen, G. (1969). Investigations concerning logical deduction. In Szabo (1969), editor. pp. 68–131.Google Scholar
Gerhardt, C., editor (1859). Leibnizens Mathematische Schriften. Halle: H. W. Schmidt.Google Scholar
Goré, R. (1999). Tableau methods for modal and temporal logics. In D’Agostino, M., Gabbay, D. M., Hähnle, R., and Posegga, J., editors. Handbook of Tableau Methods. Dordrecht: Kluwer, pp. 297–396.Google Scholar
Humberstone, L. (2011). The Connectives. Cambridge, MA: MIT Bradford.CrossRefGoogle Scholar
Knuuttila, S. (1982). Topics in late medieval intensional logic. Acta Philosophica Fennica, 35, 26–41.Google Scholar
Krämer, S. (2003). Writing, notational iconicity, calculus: On writing as a cultural technique. Modern Languages Notes (German Issue), 118, 518–537.Google Scholar
Kripke, S. A. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 83–94.Google Scholar
Leibniz, G. (1985). Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil. Open Court, La Salle, Ill. Edited, with an introduction, by Austin Farrer; tr. E. M. Huggard.Google Scholar
Negri, S. (2005). Proof analysis in modal logic. Journal of Philosophical Logic, 34, 507–544.Google Scholar
Negri, S. (2007). Proof analysis in non-classical logics. In Dimitracopoulos, C., Newelski, L., Normann, D., and Steel, J., editors. Logic Colloquium ’05: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Athens, Greece, July 28–August 3, 2005. Cambridge: Cambridge University Press, pp. 107–128.Google Scholar
Nolt, J. (2014). Free logic. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Summer 2014 edition), http://plato.stanford.edu/archives/sum2014/entries/logic-free/.Google Scholar
Paoli, F. (1991). Bolzano e le dimostrazioni matematiche. Rivista di Filosofia, 78, 221–242.Google Scholar
Poggiolesi, F. (2011). Gentzen Calculi for Modal Propositional Logic. Studia Logica Library, Trends in Logic. Dordrecht: Springer.CrossRefGoogle Scholar
Poggiolesi, F., & Restall, G. (2012). Interpreting and applying proof theories for modal logic. In Restall, G. and Russell, G., editors. New Waves in Philosophical Logic. Basingstoke, Houndmills: Palgrave Macmillan, pp. 39–62.CrossRefGoogle Scholar
Prawitz, D. (1965). Natural Deduction. Stockholm: Almqvist & Wiksell.Google Scholar
Prawitz, D. (1979). Proofs and the meaning and completeness of the logical constants. In Hintikka, J., Niiniluoto, I., and Saarinen, E., editors. Essays on Mathematical and Philosophical Logic. Dordrecht: Reidel, pp. 25–40.Google Scholar
Read, S. (2000). Harmony and autonomy in classical logic. Journal of Philosophical Logic, 29, 123–154.Google Scholar
Read, S. (2005). The unity of the fact. Philosophy, 80, 317–342.Google Scholar
Read, S. (2008). Harmony and modality. In Dégremont, C., Kieff, L., and Rückert, H., editors. Dialogues, Logics and Other Strange Things: Essays in Honour of Shahid Rahman. London: College Publications, pp. 285–303.Google Scholar
Read, S. (2014). General-elimination harmony and higher-level rules. In Wansing, H., editor. Dag Prawitz on Proofs and Meaning, Studia Logica Library, Trends in Logic. Cham: Springer, pp. 293–312.Google Scholar
Rumfitt, I. (2008). Knowledge by deduction. Grazer Philosophische Studien, 77, 61–84.Google Scholar
Schroeder-Heister, P., & Olkhovikov, G. (2014). On flattening elimination rules. Review of Symbolic Logic, 7, 60–72.Google Scholar
Simpson, A. (1994). The Proof Theory and Semantics of Intuitionistic Modal Logic. PhD Thesis, University of Edinburgh.Google Scholar
Smullyan, R. (1968). First-Order Logic. Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 43. Berlin, Heidelberg, New York: Springer.Google Scholar
Szabo, M., editor (1969). The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland.Google Scholar
Tennant, N. (1997). The Taming of the True. Oxford: Oxford University Press.Google Scholar
Viganò, L. (2000). Labelled Non-Classical Logics. Dordrecht: Kluwer.Google Scholar