Proof-theoretic harmony: towards an intensional account

Synthese 198 (Suppl 5):1145-1176 (2016)
  Copy   BIBTEX

Abstract

In this paper we argue that an account of proof-theoretic harmony based on reductions and expansions delivers an inferentialist picture of meaning which should be regarded as intensional, as opposed to other approaches to harmony that will be dubbed extensional. We show how the intensional account applies to any connective whose rules obey the inversion principle first proposed by Prawitz and Schroeder-Heister. In particular, by improving previous formulations of expansions, we solve a problem with quantum-disjunction first posed by Dummett. As recently observed by Schroeder-Heister, however, the specification of an inversion principle cannot yield an exhaustive account of harmony. The reason is that there are more collections of elimination rules than just the one obtained by inversion which we are willing to acknowledge as being in harmony with a given collection of introduction rules. Several authors more or less implicitly suggest that what is common to all alternative harmonious collection of rules is their being interderivable with each other. On the basis of considerations about identity of proofs and formula isomorphism, we show that this is too weak a condition for a given collection of elimination rules to be in harmony with a collection of introduction rules, at least if the intensional picture of meaning we advocate is not to collapse on an extensional one.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,569

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
Stable Harmony.Nils Kurbis - 2008 - In Peliš Michal (ed.), Logica Yearbook 2007.
Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
Against Harmony.Ian Rumfitt - forthcoming - In Bob Hale, Crispin Wright & Alexander Miller (eds.), The Blackwell Companion to the Philosophy of Language. Blackwell.
On the Equivalence Conjecture for Proof-Theoretic Harmony.Florian Steinberger - 2013 - Notre Dame Journal of Formal Logic 54 (1):79-86.

Analytics

Added to PP
2016-09-23

Downloads
42 (#276,043)

6 months
2 (#278,199)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Luca Tranchini
Universität Tübingen

References found in this work

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.

View all 26 references / Add more references