Proof-Theoretic Semantics and Hyperintensionality

Ivo Pezlar

Abstract


In his recent book The Impossible: An Essay on Hyperintensionality (2014) Jago states that proof-theoretic semantics (PTS) does not easily deliver hyperintensional contents. I argue against this claim and show that, on the contrary, hyperintensionality is one of the basic features of PTS approaches.


References


Artemov, Sergei and Nogina, Elena. “Introducing Justification into Epistemic Logic. Journal of Logic and Computation.” 15.6 (2005):1059–1073. doi: 10.1093/logcom/exi053.

Block, Ned. “Conceptual Role Semantics,” in Edward Craig (ed.), Routledge Encyclopedia of Philosophy, pp. 242–256. Routledge, 1998. doi: 10.4324/9780415249126-W037-1.

Brandom, Robert. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge; Massachusetts: Harvard University Press, 1994.

Brandom, Robert. Articulating Reasons. Cambridge; Massachusetts: Harvard University Press, 2000.

Cresswell, Max J. “Hyperintensional Logic.” Studia Logica, 34.1 (1975):25–38. doi:10.1007/BF02314421.

Došen, Kosta. Logical Constants: An Essay in Proof Theory. PhD thesis, University of Oxford, 1980.

Došen, Kosta. “Identity of Proofs Based on Normalization and Generality.” The Bulletin of Symbolic Logic, 9.4 (2003):477–503. doi:10.2307/3133721.

Dummett, Michael. The Logical Basis of Metaphysics. Duckworth, London, 1991.

Duží, Marie, Jespersen, Bjørn and Materna, Pavel. Procedural Semantics for Hyperintensional Logic: Foundations and Applications of Transparent Intensional Logic. Springer Netherlands, 2010. doi: 10.1007/978-90-481-8812-3.

Field, Hartry. “Logic, Meaning, and Conceptual Role.” Journal of Philosophy, 74.July (1977):379–409.

Francez, Nissim. “The Granularity of Meaning in Proof-Theoretic Semantics,” in Nicholas Asher and Sergei Soloviev (eds.), Logical Aspects of Computational Linguistics: 8th International Conference, LACL 2014, Toulouse, France, June 18-20, 2014. Proceedings. pp. 96–106. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. doi: 10.1007/978-3-662-43742-1_8.

Francez, Nissim. “Views of Proof-Theoretic Semantics: Reified Proof-Theoretic Meanings.” Journal of Logic and Computation, 2014. doi:10.1093/logcom/exu035.

Francez, Nissim. Proof-Theoretic Semantics. College Publications, 2015.

Gabbay, Dov M. Labelled Deductive Systems. Number v. 1 in Oxford Logic Guides. Oxford University Press, USA, 1996.

Gentzen, Gerhard. “Untersuchungen über das logische Schließen. I.” Mathematische Zeitschrift, 39.1 (1935):176–210. doi:10.1007/BF01201353.

Gödel, Kurt. Unpublished Essays and Lectures (Kurt Gödel Collected Works: Volume III), chapter Vortrag bei Zilsel/Lecture at Zilsel’s, pp. 86–113. Oxford University Press, 1995.

Gilbert Harman. (Nonsolipsistic) Conceptual Role Semantics. In Ernest LePore (ed.), Notre Dame Journal of Formal Logic, pp. 242–256. Academic Press, 1987.

Horwich, Paul. “Meaning, Use and Truth: On Whether a Use-Theory of Meaning Is Precluded by the Requirement That Whatever Constitutes the Meaning of a Predicate Be Capable of Determining the Set of Things of Which the Predicate Is True and to Which It Ought to Be Applied.” Mind, 104.414 (1995):355–368.

Jago, Mark. The Impossible: An Essay on Hyperintensionality. Oxford University Press, 2014. doi:10.1093/acprof:oso/9780198709008.001.0001.

Luo, Zhaohui. “Formal Semantics in Modern Type Theories: Is It Model-theoretic, Proof-theoretic, or Both?” in Nicholas Asher and Sergei Soloviev (eds.), Logical Aspects of Computational Linguistics: 8th International Conference, LACL 2014, Toulouse, France, June 18-20, 2014. Proceedings. pp. 177–188. Springer Berlin Heidelberg, 2014. doi: 0.1007/978-3-662-43742-1_14.

Martin-Löf, Per. Intuitionistic Type Theory. Studies in proof theory. Bibliopolis, 1984.

Peregrin, Jaroslav. Inferentialism: Why Rules Matter. Palgrave Macmillan, 2014.

Piecha, Thomas and Schroeder-Heister, Peter. Advances in Proof-Theoretic Semantics. Springer International Publishing, 2016. doi:10.1007/978-3-319-22686-6.

Prawitz, Dag. Natural Deduction: A Proof-Theoretical Study. Almqvist & Wiksell, 1965.

Prawitz, Dag. “Ideas and Results in Proof Theory,” in J. Fenstad (ed.), Proceedings of the 2. Scandinavian Logic Symposium. pp. 235–309. North-Holland Publishing Company. 1971.

Prawitz, Dag. “Towards a Foundation of a General Proof Theory,” in P. Suppes et al. (eds.), Logic, Methodology and Philosophy of Science IV. pp. 225–250. North-Holland Publishing Company. 1973.

Prawitz, Dag. “Meaning and Proofs: On the Conflict Between Classical and Intuitionistic Logic.” Theoria, 43.1 (1977):2–40.

Prawitz, Dag. “Meaning Approached via Proofs.” Synthese, 148.3 (2006):507–524. doi:10.1007/s11229-004-6295-2.

Prawitz, Dag. “The Epistemic Significance of Valid Inference.” Synthese, 187.3 (2012):887–898.

Jiří Raclavský. “Constructional vs. Denotational Conception of Aboutness.” Organon F, 21.2 (2014): 219–236. doi: 10.12775/LLP.2013.035.

Read, Stephen. “Proof-Theoretic Validity,” in Colin R. Caret and Ole T. Hjortland (eds.), Foundations of Logical Consequence. 2015.

Restall, Greg. “Thomas Piecha and Peter Schroeder-Heister (eds.), Advances in Proof-Theoretic Semantics” [review]. Notre Dame Philosophical Reviews: An Electronic Journal, 2016.05.15, 2016.

Schroeder-Heister, Peter. “Uniform Proof-Theoretic Semantics for Logical Constants.” Journal of Symbolic Logic, 56.1142 (1991).

Schroeder-Heister, Peter. “Validity Concepts in Proof-Theoretic Semantics.” Synthese, 148.3 (2006):525–571. doi:10.1007/s11229-004-6296-1.

Sellars, Wilfrid. Inference and Meaning. Mind, 62.247 (1953):313–338.

Straßburger, Lutz. Proof Nets and the Identity of Proofs. Technical report, Institut National de Recherche en Informatique et en Automatique. 2006.

Sundholm, Göran. “Proofs as Acts Versus Proofs as Objects: Some Questions for Dag Prawitz.” Theoria, 64.2-3 (2000):187–216.

Tennant, Neil. Natural Logic. Edinburgh: Edinburgh University Press, 1978.

Usberti, Gabriele. “Towards a Semantics Based on the Notion of Justification.” Synthese, 148.3 (2006):675–699. doi:10.1007/s11229-004-6272-9.

Więckowski, Bartosz. “Constructive Belief Reports.” Synthese, 192.3 (2015):603–633. doi:10.1007/s11229-014-0540-0.

Więckowski, Bartosz. “Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity.” Journal of Logic, Language and Information 25.2 (2016).

Ludwig Wittgenstein. Philosophical Investigations. Macmillan, 1953.


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