Gordon Belot
University of Michigan, Ann Arbor
This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that no matter what method is pursued, failure is incomparably more common that success; and difficult choices must be faced in choosing a method of learning, since no approach dominates all others in its range of success. In the simplest case, the comparison of the set of situations in which a method fails and the set of situations in which it succeeds is a matter of cardinality (countable vs. uncountable); in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre).
Keywords Induction  Learning  Extrapolation  Forecasting  No-Free-Lunch Theorems
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Gravity and GRACE.Gordon Belot - forthcoming - Philosophers' Imprint.

Add more citations

Similar books and articles

How Gruesome Are the No-Free-Lunch Theorems for Machine Learning?Davor Lauc - 2018 - Croatian Journal of Philosophy 18 (3):479-485.
Libet and the Case for Free Will Scepticism.Tim Bayne - 2011 - In Richard Swinburne (ed.), Free Will and Modern Science. Oup/British Academy.
Can Truthmaker Theorists Claim Ontological Free Lunches?Peter Schulte - 2014 - European Journal of Philosophy 22 (2):249-268.
Being Low Along a Sequence and Elsewhere.Wolfgang Merkle & Liang Yu - 2019 - Journal of Symbolic Logic 84 (2):497-516.
Free Associative Prediction of Mediated Learning.Stuart Miller - 1971 - Journal of Experimental Psychology 89 (1):187.


Added to PP index

Total views
92 ( #116,591 of 2,448,110 )

Recent downloads (6 months)
32 ( #21,833 of 2,448,110 )

How can I increase my downloads?


My notes