Kevin Kelly

Belief revision theory aims to describe how one should change one's beliefs when they are contradicted by newly input information. The guiding principle of belief revision theory is to change one's prior beliefs as little as possible in order to maintain consistency with the new information. Learning theory focuses, instead, on learning power: the ability to arrive at true beliefs

Ockham's razor impels scientists to seek ever greater unity in nature. That seems to saddle science with a metaphysical presupposition of simplicity that might be false. The objection is apt if scientiflc method is understood as a system of inductive logic or proof, for then the unity of science must, somehow, function as an unjustifled premise in scientiflc arguments. But

. We argue that uncomputability and classical scepticism are both reflections ofinductive underdetermination, so that Church's thesis and Hume's problem ought to receiveequal emphasis in a balanced approach to the philosophy of induction. As an illustrationof such an approach, we investigate how uncomputable the predictions of a hypothesis canbe if the hypothesis is to be reliably investigated by a computable scientific method.1. RELATIONS OF IDEAS AND MATTERS OF FACTFollowing an...

ABSTRACT. Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent's ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the ...

Both in learning and in natural science, one faces the problem of selecting among a range of theories, all of which are compatible with the available evidence. The traditional response to this problem has been to select the simplest such theory on the basis of “Ockham’s Razor”. But how can a fixed bias toward simplicity help us find possibly complex truths? I survey the current, textbook answers to this question and find them all to be wishful, circular, or irrelevant. Then I present a new approach based on minimizing the number,of reversals of opinion prior to convergence to the truth. According to this alternative approach, Ockham’s razor is a good idea when it seems to be (e.g., in selecting among parametrized models) and is not a good idea when it feels dubious (e.g., in the inference of arbitrary computable functions). Hence, the proposed vindication of Ockham’s razor can be used to separate vindicated applications of Ockham’s razor from spurious ones. 0.1 Introduction In scien...

Many distinct theories are compatible with current experience. Scientific realists recom- mend that we choose the simplest. Anti-realists object that such appeals to “Ockham’s razor” cannot be truth-conducive, since they lead us astray in complex worlds. I ar- gue, on behalf of the realist, that always preferring the simplest theory compatible with experience is necessary for ecient,convergence to the truth in the long run, even though it may point in the wrong direction in the short run. Eciency,is a matter of minimizing errors or retractions prior to convergence to the truth. 0.1 Realism and Ockham’s Razor There are infinitely many, incompatible theories consistent with any finite amount of

This paper presents a new explanation of how prefer- ring the simplest theory compatible with experience assists one in finding the true answer to a scientific question when the answers are theories or models. Inquiry is portrayed as an unending game be- tween science and nature in which the scientist aims to converge to the true theory on the basis of accumulating information. Simplicity is a topological invariant reflecting sequences of theory choices that nature can force an arbitrary, convergent scientist to produce. It is demonstrated that among the methods that converge to the truth in an empirical problem, the ones that do so with a minimum number of reversals of opinion prior to convergence are exactly the ones that pre- fer simple theories. The approach explains not only simplicity tastes in model selection, but aspects of theory testing and the unwillingness of natural science to break symmetries without a reason.

Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to