Abstract
AbstractThis is a contribution to the idea that some proofs in first-order logic are synthetic. Syntheticity is understood here in its classical geometrical sense. Starting from Jaakko Hintikka’s original idea and Allen Hazen’s insights, this paper develops a method to define the ‘graphical form’ of formulae in monadic and dyadic fraction of first-order logic. Then a synthetic inferential step in Natural Deduction is defined. A proof is defined as synthetic if it includes at least one synthetic inferential step. Finally, it will be shown that the proposed definition is not sensitive to different ways of driving the same conclusion from the same assumptions.
Publisher
Springer Science and Business Media LLC
Subject
General Social Sciences,Philosophy
Reference20 articles.
1. Berto, F., & Jago, M. (2019). Impossible worlds. Oxford University Press.
2. Boolos, G. (1984). Don’t eliminate cut. Journal of Philosophical Logic, 13, 373–375.
3. Carbone, A. (2010). A new mapping between combinatorial proofs and sequent calculus proofs read out from logical flow graphs. Information and Computation, 208, 500–509.
4. Carnap, Y.B.-H. (1953). Semantic information. The British Journal for the Philosophy of Science, 4(16), 147–157.
5. Dummett, M. (1974). The justification of deduction. Duckworth.