An Expressivist Strategy to Understand Logical Forms
DOI:
https://doi.org/10.12775/LLP.2023.005Keywords
logical expressivism, logical form, Begriffsschrift, sequent calculus, display logicAbstract
This paper discusses a generalization of logical expressivism. It is shown that, in the wide sense defined here, the expressivist approach is neutral with respect to different theories of inference and offers a natural framework for understanding logical forms and their function. An expressivist strategy for explaining the development of logical forms is then applied to the analysis of Frege’s Begriffsschrift, Gentzen’s sequent calculus and Belnap’s display logic.
References
Belnap, N. D., 1982, “Display logic”, Journal of Philosophical Logic, 11 (4): 375–417. DOI: http://dx.doi.org/10.1007/BF00284976
Belnap, N. D., 1996, “The display problem”, pages 79–93 in H. Wansing (ed.), Proof Theory of Modal Logic, Dordrecht: Kluwer Academic Publishers. DOI: http://dx.doi.org/10.1007/978-94-017-2798-3_6
Brandom, R., 1994, Making It Explicit: Reasoning, Representing, and Discursive Commitment, Cambridge (MA): Harvard University Press.
Brandom, R., (2008), Between Saying and Doing, Oxford: Oxford University Press. DOI: http://dx.doi.org/10.1093/acprof:oso/9780199542871.001.0001
Frege, G., 1879, Begriffsschrift, eine der arithmetische nachgebildete Formel sprache des Reinen Denkens, Halle: Nebert. English translation, Begriffsschrift, A Formula Language, Modeled Upon That of Arithmetic, for Pure Thought, pages 1–82 in J. van Heijenoort (ed.), 1967, From Frege to Gödel, Cambridge (MA): Harvard University Press.
Frege, G., 1893/1903, Grundgesetze der Arithmetik, Jena: Verlag Hermann Pohle, Band I/II. English translation in P. Ebert, M. Rossberg and C. Wright (eds.), 2013, Basic Laws of Arithmetic: Derived Using Concept-Script, Oxford: Oxford University Press.
Frege, G., 1919, “Die Verneinung”, Beiträge zur Philosophie des deutschen Idealismus, 1(3–4): 143–157. English translation, “Negation”, pages 117–135 in P. Geach and M. Black (eds.), 1960, Translations from the Philosophical Writings of Gottlob Frege, Oxford: Blackwell.
Frege, G., 1979, Posthumous Writings, Oxford: Blackwell.
Gentzen, G., 1934/35, “Untersuchungen über das logische Schliessen”, Mathematische Zeitschrift, 39: 176–210, 405–431. English translation, “Investigation into logical deduction”, pages 68–131 in M. E. Szabo (ed.), 1969, The Collected Papers of Gerhard Gentzen, Amsterdam: North Holland.
Goré, R., 1998a, “Substructural logics on display”, Logic Journal of the IGPL, 6 (3): 451–504. DOI: http://dx.doi.org/10.1093/jigpal/6.3.451
Goré, R., 1998b, “Gaggles, Gentzen and Galois: How to display your favourite substructural logic”, Logic Journal of the IGPL, 6 (5): 669–694. DOI: http://dx.doi.org/10.1093/jigpal/6.5.669
Hertz, P., 1922, “Über Axiomensysteme für beliebige Satzsysteme. I. Teil. Sätze ersten Grades. (Über die Axiomensysteme von der kleinsten Satzzahl und den Begriff des idealen Elementes)”, Mathematische Annalen, 87: 246–269.
English translation, “About axiomatic systems for arbitrary systems of sentences”, pages 11–29 in J. Y. Béziau (ed.), 2012, Universal Logic: An Anthology. From Paul Hertz to Dov Gabbay, Basel: Birkhäuser.
Iacona, A., 2018, Logical Form. Between Logic and Natural Language, Cham: Springer. DOI: http://dx.doi.org/10.1007/978-3-319-74154-3
Kreisel, G., 1971, “A survey of proof theory II”, pages 109–170 in J. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium, Amsterdam: North-Holland. DOI: http://dx.doi.org/10.1016/S0049-237X(08)70845-0
Macbeth, D., 2005, Frege’s Logic, Cambridge (MA): Harvard University Press. DOI: http://dx.doi.org/10.4159/9780674040397
Negri, S., and J. von Plato, 2001, Structural Proof-Theory, Cambridge: Cambridge University Press. DOI: http://dx.doi.org/10.1017/CBO9780511527340
Peregrin, J., 2014, Inferentialism: Why Rules Matter, New York (NY): Palgrave-Macmillan. DOI: http://dx.doi.org/10.1057/9781137452962
Prawitz, D., 1965, Natural Deduction: A Proof-Theoretical Study, Stockholm: Almqvist & Wiksell. Reprinted by Dover Publications, Mineola (NY), 2006.
Prawitz, D., 1971, “Ideas and results in proof theory”, pages 235–307 in J. E. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium (Oslo 1970), Amsterdam: North-Holland. DOI: http://dx.doi.org/10.1016/S0049-237X(08)70849-8
Restall, G., 1998, “Displaying and deciding substructural logics 1: Logics with contraposition”, Journal of Philosophical Logic, 27 (2): 179–216. DOI: http://dx.doi.org/10.1023/A:1017998605966
Ricketts, T., and J. Levine, 1996, “Logic and truth in Frege”, Proceedings of the Aristotelian Society, Supplementary Volumes, 70: 121–175. DOI: http://dx.doi.org/10.1093/aristoteliansupp/70.1.121
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