Re: Beliefs and probabilities 2

Opening post.

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.

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  1. First of all, many thanks for the flattering review you wrote for my and Raymond
    Bradley’s _Possible Worlds_.

    Now, about your thesis (with various subsequent qualifications)that S believes that p implies that S believes that the probability of p is >0.5. I think that this thesis is refuted by a rather simple counter-example. Young children (and under-
    educated adults) lack the concept of probability. For example, my three-year-old
    grandson believes that there is a toy firetruck in his bedroom. (Actually there are several.) But surely he does not believe that the probability of there being a toy firetruck in his bedroom is greater than 0.5 [or 50%]. He is incapable of having this latter belief because he has no concept of probability at all and none of decimals (or percentages) and likely will not for another few years.

    Over the years I have found that a great many claims in epistemology are refuted by looking at the actual beliefs of young children and uneducated and unsophisticated

    Then, too, some epistemologists ascribe propositional beliefs to some animals (where propositional beliefs are not to be construed as linguistic). But they would not want to to ascribe concomitant or implied probabilistic beliefs to those animals, even less numerically qualified probabilities.

    Norman Swartz, Professor Emeritus
    Department of Philosophy
    Simon Fraser University

  2. Hi Norman Swartz,

    I’m extremely honored that you choose to comment on my ‘blog’. I didn’t know you knew about it. Perhaps you didn’t but just googled the title of your book “Possible worlds” which I have mentioned a lot lately. The reason being of course that I was reading it and I had some (a lot?) of thoughts along the way.

    I think that you’re counter-example is good. However I’m not sure that one lacking a certain concept precludes one from having beliefs about it. Consider an analogy with knowledge: Some people probably lack a concept of truth but still they are able to know things even though the concept of truth is involved in the concept knowledge. The cases are not entirely similar as the concept of truth is only a part of the concept of knowledge, not as in the other case where the concept of probability is the only concept needed. I will have to think more about it.

    I think that you may be right about the thing with epistemology and children/unsophisticated people. I’ll keep that in mind when I try to come up with counter-examples in the future.

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