Meaning is Use: the Case of Propositional Identity

Authors

DOI:

https://doi.org/10.18778/0138-0680.2024.05

Keywords:

intuitionistic logic, non-Fregean logics, proof-theoretic semantics

Abstract

We study natural deduction systems for a fragment of intuitionistic logic with propositional identity from the point of view of proof-theoretic semantics. We argue that the identity connective is a natural operator to be treated under the elimination rules as basic approach.

References

S. L. Bloom, R. Suszko, Investigations into the Sentential Calculus with Identity, Notre Dame Journal of Formal Logic, vol. 13(3) (1972), pp. 289–308, DOI: https://doi.org/10.1305/ndjfl/1093890617.
Google Scholar DOI: https://doi.org/10.1305/ndjfl/1093890617

S. Chlebowski, M. Gawek, A. Tomczyk, Natural Deduction Systems for Intuitionistic Logic with Identity, Studia Logica, vol. 110(6) (2022), pp. 1381–1415, DOI: https://doi.org/10.1007/s11225-022-09995-0.
Google Scholar DOI: https://doi.org/10.1007/s11225-022-09995-0

S. Chlebowski, D. Leszczyńska-Jasion, An investigation into intuitionistic logic with identity, Bulletin of the Section of Logic, vol. 48(4) (2019), pp. 259–283, DOI: https://doi.org/10.18778/0138-0680.48.4.02.
Google Scholar DOI: https://doi.org/10.18778/0138-0680.48.4.02

M. Dummett, The logical basis of metaphysics, Harvard University Press, Cambridge, Mass. (1991).
Google Scholar

N. Francez, On the notion of canonical derivations from open assumptions and its role in proof-theoretic semantics, Review of Symbolic Logic, vol. 8 (2015), pp. 296–305, DOI: https://doi.org/10.1017/S1755020315000027.
Google Scholar DOI: https://doi.org/10.1017/S1755020315000027

N. Francez, Proof-theoretic Semantics, vol. 57 of Studies in Logic, College Publications, Rickmansworth (2015).
Google Scholar

N. Francez, Views of proof-theoretic semantics: Reified proof-theoretic meanings, Journal of Logic and Computation, vol. 26 (2016), pp. 479–494, DOI: https://doi.org/10.1093/logcom/exu035.
Google Scholar DOI: https://doi.org/10.1093/logcom/exu035

G. Gentzen, Investigations into logical deductions, American Philosophical Quarterly, vol. 1(4) (1964), pp. 288–306, URL: http://www.jstor.org/stable/20009142.
Google Scholar

A. Klev, The harmony of identity, Journal of Philosophical Logic, vol. 48(5) (2019), pp. 867–884, DOI: https://doi.org/10.1007/s10992-018-09499-0.
Google Scholar DOI: https://doi.org/10.1007/s10992-018-09499-0

P. Milne, Inversion principles and introduction rules, [in:] H. Wansing (ed.), Dag Prawitz on Proofs and Meaning, Springer, Cham (2013), pp. 189–224, DOI: https://doi.org/10.1007/978-3-319-11041-7_8.
Google Scholar DOI: https://doi.org/10.1007/978-3-319-11041-7_8

S. Negri, J. von Plato, Proof Analysis. A Contribution to Hilbert’s Last Problem, Cambridge University Press, Cambridge (2011), DOI: https://doi.org/10.1017/CBO9781139003513.
Google Scholar DOI: https://doi.org/10.1017/CBO9781139003513

D. Prawitz, On the idea of a general proof theory, Synthese, (1974), pp. 63–77, DOI: https://doi.org/10.1007/BF00660889.
Google Scholar DOI: https://doi.org/10.1007/BF00660889

S. Read, Identity and harmony, Analysis, vol. 64(2) (2004), pp. 113–119, DOI: https://doi.org/10.1093/analys/64.2.113.
Google Scholar DOI: https://doi.org/10.1093/analys/64.2.113

P. Schroeder-Heister, Validity Concepts in Proof-theoretic Semantics, Synthese, vol. 148 (2006), pp. 525–571, DOI: https://doi.org/10.1007/s11229-004-6296-1.
Google Scholar DOI: https://doi.org/10.1007/s11229-004-6296-1

P. Schroeder-Heister, Proof Theoretical Validity Based on Elimination Rules, [in:] E. H. Haeusler, W. de Campos Sanz, B. Lopez (eds.), Why is this a Proof? Festschrift for Luiz Carlos Pereira, College Publications, Rickmansworth (2015), pp. 159–176.
Google Scholar

P. Schroeder-Heister, Proof-Theoretic Semantics, [in:] E. N. Zalta, U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy, fall 2023 ed., Metaphysics Research Lab, Stanford University (2023), URL: https://plato.stanford.edu/archives/spr2018/entries/proof-theoretic-semantics/.
Google Scholar

Downloads

Published

2024-05-20

How to Cite

Kupś, L., & Chlebowski, S. (2024). Meaning is Use: the Case of Propositional Identity. Bulletin of the Section of Logic, 24 pp. https://doi.org/10.18778/0138-0680.2024.05

Issue

Section

Research Article

Most read articles by the same author(s)