Abstract
Exploring the proofs and refutations of an abstract statement, conjecture with the aim to give a formal syntactic treatment of its proving–refuting process, we introduce the notion of extrapolation of a possibly unprovable statement having the form if A, then B, and propose a procedure that should result in the new statement if A′, then B′, which is similar to the starting one, but provable. We think that this procedure, based on the extrapolation method, can be considered a basic methodological tool applicable to prove–refute–improve any conjecture. This new notion, extrapolation, presents a dual counterpart of the well-known interpolation introduced in traditional logic sixty-five years ago.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference15 articles.
1. PROOFS AND REFUTATIONS (I)
2. Conjectures and Refutations: The Growth of Scientific Knowledge;Popper,1962
3. The Reach of Abduction;Gabbay,2005
4. Model, proving and refuting;Boričić,2018
5. Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory