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.