Induction and Inherent Similarity

T. Mark Ellison

Abstract Our perceptions are often logically compatible with abstractions we would never imagine entertaining. The problem of induction is to account for this disparity: how does evidence confirm one generalisation to the exclusion of others with which it is also logically compatible? In particular, how do we justify the claim that the future will be like the past?
This paper introduces the problem of induction, and then proposes a solution based on similarity measures and topographic mapping. The premisses of this solution are the following. (i) Naturally occurring data and representations are embedded in spaces with non-trivial similarity structures. (ii) Natural cognitive mappings between spaces of representation are topographic mappings. The uniformity presumption can be justified by these two premisses.