The Speed-Optimality of Reichenbach's Straight Rule of Induction

In his Theory of Probability, Hans Reichenbach made a bold and original attempt to ‘vindicate’ induction. He proposed a rule, the ‘straight rule’ of induction, which would guarantee inductive success if any rule of induction would. A central problem facing his attempt to vindicate the straight rule is that too many other rules are just as good as the straight rule if our only constraint on what counts as ‘success’ for an inductive rule is that it is ‘asymptotic’, i.e. that it converges in the limit to the true limiting frequency (of some type of outcome O in a sequence of events) whenever such a limiting frequency exists. In this paper I consider the consequences of requiring speed-optimality of asymptotic methods, that is, requiring that inductive methods must get to the truth as quickly as possible. Two main results are proved: (1) the straight rule is speed-optimal; (2) there are (uncountably) many non-speed-optimal asymptotic methods. A further result gives a sufficient but not necessary condition for speed-optimality among asymptotic methods. Some consequences and open questions are then discussed.

Constraint (computer-aided design) · Induction loop · Inductive reasoning · Limit (mathematics) · Limiting · Mathematical analysis · Mathematical economics · Sequence (biology) · Statistics · Bayesian Modeling and Causal Inference · Computer Science · Mathematics · Philosophy and History of Science · Probability and Statistical Research

• Learning Theory and the Philosophy of Science

  Open Access•Kevin T Kelly, Oliver Schulte et al.•Philosophy of Science•1997

  Add to list

• Speed-Optimal Induction and Dynamic Coherence

  Open Access•Michael Nielsen, Michael A Nielsen et al.•The British Journal for the…•2022

  Add to list

• Means-Ends Epistemology

  Oliver Schulte•The British Journal for the…•1999

  Add to list