More objections and thoughts.
The infinite objection
I discovered another objection to the thesis. Infinite regress. The most defendable version of the thesis is
(T4) S believes that p materially implies that S believes that the probability of p is >0.5 given the evidence available to S.
Suppose Sarah believes p. That and (T4) implies that Sarah believes another and different proposition. That together with (T4) implies that that person believes yet another and different proposition ad infinitum. So (T4) along with any actual belief implies that the person believes an infinite number of propositions. Is that really true? I think not.
Moreover. Because each person believes that each of his believed propositions have a probability of >0.5 of being true. This applies also to the probability-of-propositions propositions. So it follows in the above example that Sarah believes that the probability of “The probability of p is >0.5 given the evidence available to Sarah” is >0.5 given the evidence available to Sarah, and so on. That’s some rather weird beliefs to holding an infinite number of.
The lack of evidence and the web of belief
Supposing that I cannot find any knock-down argument against the thesis, that does not imply that it is a good idea to believe the thesis. (Argument from Ignorance.) There are an infinite number of propositions (and hence theses) that no good argument can be found against. Not all if any of these are a good idea to believe. I suppose that one can find a way to fit one’s other beliefs to this thesis such that there is no inconsistency or blatant incoherence. One could hold some weird beliefs about how abduction (i.e. inference to best explanation) works and some account about what beliefs are and how many of them we hold. But is there any actual reason to make this change to one’s web of belief if it is not better in any way to the traditionally held beliefs about these things? No. I advocate instead conservatism about changing one’s mind upon discovering that some large change in one’s web of beliefs would result in a consistent and coherent belief set that is just as good as the one one has.