Posts filed under ‘Bayesianism’
I’ve been reading a lot of Hempel lately, in addition to all the articles, essays, studies, and polls on evolution and creationism. Because of this, I have more than the usual blend of 20th century philosophy of science and epistemology brewing in my brain. Anila Asghar and Brian Alters’ study (forthcoming) introduces an interesting situation for probability theory and Bayesianism, on one of its most controversial topics: that of prior probabilities.
In the study, one of the differences between North American Muslim science teachers and their Pakistani counterparts was that of the separation or blend of science and religion in the classroom. Such separation often seems to extend out of the classroom and into personal beliefs. North American Muslim science teachers favor the separation of science and religion, and one interviewee in particular espouses something similar to Stephen Jay Gould’s idea of Non-Overlapping Magesteria. Pakistani science teachers, on the other hand, see no need for such separation. The textbook chapters on evolution begin with Qu’ranic verses, and the provincial standards of education outline the need to teach science within the context of the Qu’ran.
To tie this into contemporary philosophy of science and probability theory, consider the problem of prior probabilities. A brief outline of the problem is this: before we are faced with evidence for or against a theory, we all have our own prior degree of belief in the facticity of the theory undergoing a test. Because these are subjective probabilities, they are difficult to describe. When faced with the results of a test, it’s difficult to see how someone is to alter their subjective probability from the prior probability to the updated, post-test probability. Bayesians have done a lot of footwork around this problem, but not much of it is convincingly conclusive. I’m not convinced of the entire Bayesian program of describing/reconstructing rationality as a series of probability calculations, but those are thoughts for another time.
For now, I’m interested in how the attitudes of the teachers in the study correspond to the idea of prior probabilities. If North American Muslim science teachers really believe in the separation of science and religion, then their prior probability for a given scientific theory should be free of influence from their religious beliefs. But Pakistani science teachers believe in a blend of science and religious explanation, so their priors for a given scientific theory should be influenced by their religious beliefs. If true, this is an important situation that Bayesians need to consider. The same theory is being tested, but there is an explicit religious influence in the prior probabilities of one evaluator and not in another. This is so even though there is great demographic similarity between the evaluators—both are Muslim science teachers of Pakistani descent. The main difference, in many ways, comes down to where they teach. That this should have such an impact on prior probabilities by way of the introduction of a large category of thought in one situation and its absence in another is a large effect for a relatively small difference (or at least a small difference in terms of Bayesian calculations).
I’m not sure how much work Bayesians have done regarding the effects of culture on prior probabilities, but the teachers described by Asghar and Alters make a strong case for its study. It shouldn’t be news that non-scientific beliefs have an different impact on scientific beliefs that depends on cultural context. When reconstructing rationality as a probabilistic process, though, I think this important idea has been largely overlooked. Both Bayesians and their critics should make sure to include this cultural dimension in their probability calculus at risk of obscurity and irrelevance.
By now I’ve finished the second chapter of Evidence and Inquiry, and I think gathered some material for a Foundherentist support of Bayesianism. One of Haack’s prime objections to Lewis’ formulation of foundationalism is that he demands certainty in order for a belief to be justified. Repeatedly, however, Haack declares that beliefs only need to be justified to “some degree”.
“A’s belief that p cannot be justified to any degree, non-relatively, unless, eventually, the chain ends with a belief or beliefs which is or are justified to some degree independently of further beliefs. But it is not required that the basic belief or beliefs eventually reached be completely justified independently of any further beliefs.” (Haack, 43)
This is the primary reason why foundherintism beats out foundationalism as a coherent epistimological system. While I haven’t yet investigated Haack’s other writings for the same Bayesian thread, this doesn’t seem like a bad line of inquiry to pursue. Also, Haack is so precise in her definition of terms (and so critical of others’ lack of precision, as in her somewhat sarcastic critique of Lewis use of terms on 38) that I doubt it’s a coincidence that she phrases her argument with “to some degree”.
If anyone needed evidence that I try to make as many connections as possible between different readings, this blog would be a smoking gun. Todays philosophy mash-up comes from the beginning of the second chapter of Susan Haack’s Evidence and Inquiry: Towards Reconstruction in Epistemology. As usual, I need to read more of the book, and more of Haack’s other writings, before I can fully flesh out my idea. At this point, however, it seems to me that Haack’s foundherentism may be very sympathetic to Bayesian theories of confirmation.
I wrote a paper this past semester on Clark Glymour’s take on Bayesianism, and was generally sympathetic to his criticism. It seems altogether too subjective a system for something which is supposed to establish whether or not evidence confirms an idea (or perhaps, is justified in believing an idea based on evidence). My views on Bayesianism will probably be fleshed out further on this blog at a later time. Like most of the things I post about.
While I don’t like Bayesian ideas, I do think that Foundherentism has something to it… it will be interesting to see if 1) the correlation between Foundherentism to Bayesianism has more to it and 2) if I look more or less favorably on Bayesian ideas following my reading of Haack.