Mathematical Certainty, Computer-Assisted Proofs, and the Mind: A Short Argument Against Materialism

In the philosophy of mathematics, there is a debate over whether computer-assisted proofs are true mathematical proofs. Those who argue that they are not hold that computer-assisted proofs are partially empirical and rely on the outcome of a physical experiment in the form of the execution of a computer program on physical computer hardware. As such, a computer-assisted proof cannot have the kind of epistemic certainty that mathematical proofs are traditionally thought to enjoy. Instead, the epistemic certainty of such a proof is reduced to the certainty had by the results of the natural sciences (e.g., physics and chemistry). This is because a computer is a physical system and as such we can only have as much confidence in its results as we can have in the theoretically predicted outcomes of physical experiments obtaining in practice and in the reliability of human-engineered machines, and this confidence obviously falls short of the kind of certainty that we typically associate with the results of mathematics.