TY - JOUR
AU - Paseau, Alexander
PY - 2011/02/15
TI - Proving Induction
JF - The Australasian Journal of Logic; Vol 10 (2011): Australasian Journal of LogicDO - 10.26686/ajl.v10i0.1821
KW -
N2 - The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in ZFC, states that a predictive function M exists with the following property: whatever world we live in, M ncorrectly predicts the world’s present state given its previous states at all times apart from a well-ordered subset. On the usual model of time a well-ordered subset is small relative to the set of all times. M’s existence therefore seems to provide a solution to the hard problem. My paper argues for two conclusions. First, the theorem does not solve the hard problem of induction. More positively though, it solves a version of the problem in which the structure of time is given modulo our choice of set theory.
UR - https://ojs.victoria.ac.nz/ajl/article/view/1821