Computers as a Source of A Posteriori Knowledge in Mathematics

TY - JOUR

T1 - Computers as a Source of A Posteriori Knowledge in Mathematics

AU - Johansen, Mikkel Willum

AU - Misfeldt, Morten

PY - 2016/4/2

Y1 - 2016/4/2

N2 - Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has recently been challenged by Mark McEvoy, who claims that computer calculations can constitute a priori mathematical proofs, even in cases where the calculations made by the computer are too numerous to be surveyed by human agents. In this article we point out the deficits of the traditional literature that has called for McEvoy’s correction. We also explain why McEvoy’s defence of mathematical apriorism fails and we discuss how the debate over the epistemological status of computer-assisted mathematics contains several unfortunate conceptual reductions.

AB - Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has recently been challenged by Mark McEvoy, who claims that computer calculations can constitute a priori mathematical proofs, even in cases where the calculations made by the computer are too numerous to be surveyed by human agents. In this article we point out the deficits of the traditional literature that has called for McEvoy’s correction. We also explain why McEvoy’s defence of mathematical apriorism fails and we discuss how the debate over the epistemological status of computer-assisted mathematics contains several unfortunate conceptual reductions.

U2 - 10.1080/02698595.2016.1265862

DO - 10.1080/02698595.2016.1265862

M3 - Journal article

SN - 0269-8595

VL - 30

SP - 111

EP - 127

JO - International Studies in the Philosophy of Science

JF - International Studies in the Philosophy of Science

IS - 2

ER -