Musings on Newcomb’s problem

June 28, 2010

Newcomb’s paradox posits a game with a transparent box containing $1 and an opaque box containing either $0 or $1,000. A Player is offered the choice between only the opaque box or both boxes. Before the Player makes this choice, a Predictor has attempted to predict the Player’s choice. The Predictor puts $1,000 into the opaque box, if the prediction is that only this box will be chosen. Otherwise, the Predictor puts $0.

The Predictor neither has a time machine nor some gift for backward causation. It is assumed, however, that the Predictor is rather reliable, though not necessarily infallible. Should the Player choose the opaque box only or both boxes? Read the rest of this entry »

Shogenji’s new measure of Bayesian justification

April 6, 2010

Proponents of Bayesian epistemology have invented several different quantitative measures of how available evidence bears on different hypotheses. These measures are referred to as measures of evidential support, coherence, confirmation, or justification, depending a bit on the precise significance ascribed to them. Presently, Bayesians disagree over which of these measure is the most useful, but a new paper by Shogenji provides very appealing alternative measure and, with some luck, may even settle this debate.

At first sight, it might appear that the posterior probability P(h|e) of a hypothesis h conditional on observed evidence e is the perfect measure for a Bayesian. However, a hypothesis sometimes has a high posterior probability simply by virtue of a high prior probability, without necessarily being support/confirmed/justified by virtue of the observed evidence. Read the rest of this entry »

Is information, or constraints on inference, all there is?

July 26, 2009

“What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds.” — Ariel Caticha (eprint: 0710.1068)

“Perhaps physics is nothing but inference after all.” — Ariel Caticha (eprint: 0808.1260)

“Physics is the ability to win a bet.” — Attributed to J. R. Buck by C. A. Fuchs (eprint: quant-ph/0105039, p. 125)

Some theories present us with intruiging conceptual puzzles. This is the case with probability theory and statistics. Originally the notion of ‘probability’ was introduced in the study of games of chance, where players who are uncertain about outcomes in a game need to decide on a strategy. Read the rest of this entry »

Science, metaphysical underdetermination, and religion

July 16, 2009

Sean Carroll at Cosmic Variance has added his view on the compatibility of science and religion. In the past few days, many bloggers (PZ Myers at Pharyngula, Chris Mooney at The Intersection, Jerry Coyne at Whyevolutionistrue, John Wilkins at Evolving Thoughts, …) have expressed views about the extent to which science and religion are compatible. See Coyne’s Accommodationism: onward and downward for a brief review of the issue with links to other blog posts.

Carroll makes a very clear argument for his view. Read the rest of this entry »

Thermodynamics and statistical mechanics of self-gravitating systems

July 13, 2009

It is not uncommon among scientists to consider philosophy of science to be an uninteresting distraction from more important matters. When it comes to the foundations of thermodynamics and statistical mechanics, however, some philosophers have made genuinely useful contributions, doing an excellent job of summarizing the current situation and bringing clarity to the strengths and weaknesses of different foundations. Jos Uffink’s article on what, strictly speaking, is asserted by the second law of thermodynamics comes to mind—it has been well received by both philosophers and physicists. To specialists in the field, there may not be much new, but philosophers have at the very least managed to provide clear presentations of successes and problems to a potential wider audience of philosophers, physicists, and lay-men.

I’d like to highlight two preprints by Callender and Wallace, respectively, on the subject of thermodynamics of self-gravitating systems. Read the rest of this entry »