From Foundations to Science: Justifying and Unwinding Proofs
Zbornik radova, Tome 2 (1977) no. 10, p. 63
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
The first part of this paper recapitulates the general scheme of using techniques
developed for discredited foundational aims; specifically, proof theoretic techniques developed
for carrying out HiIbert's programme. Since this programme relies on formalization, that is,
mechanization, an obvious use is in the mechanical 'handling' of proofs. - The second part of the
paper considers three different kinds of 'handling:' finding, checking and unwinding (transforming)
proofs. The principal, generally neglected conclusion is that mechanical unwinding presents the
most promising application of proof theoretic techniques; particularly where the passage from
the informal proof considered to a formalization of its relevant features is not particularly problematic.
Examples of such cases are proposed.
@article{ZR_1977_2_10_a4,
author = {Georg Kreisel},
title = {From {Foundations} to {Science:} {Justifying} and {Unwinding} {Proofs}},
journal = {Zbornik radova},
pages = {63 },
publisher = {mathdoc},
volume = {2},
number = {10},
year = {1977},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZR_1977_2_10_a4/}
}
Georg Kreisel. From Foundations to Science: Justifying and Unwinding Proofs. Zbornik radova, Tome 2 (1977) no. 10, p. 63 . http://geodesic.mathdoc.fr/item/ZR_1977_2_10_a4/