On the equivalence conjecture for proof-theoretic harmony. (English) Zbl 1301.03014

The author discusses and analyzes the logical relations between three prominent accounts of harmony: harmony-as-conservative extension (see [N. Belnap, Analysis 22, 130–134 (1962); M. Dummett, The logical basis of metaphysics. Cambridge, MA: Harvard University Press (1991)]), harmony-as-levelling procedure (see [D. Prawitz, Theoria 43, 2–40 (1977; Zbl 0361.02008); Dummett, loc. cit.]), and harmony-as-deductive equilibrium (see [N. Tennant, Anti-realism and logic. Oxford: Oxford University Press (1987); The taming of the true. Oxford: Clarendon Press (1997; Zbl 0929.03001)], and concludes that there is no core notion of harmony toward which all three accounts of harmony converge.


03A05 Philosophical and critical aspects of logic and foundations
03F03 Proof theory in general (including proof-theoretic semantics)
Full Text: DOI Euclid


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