On Probabilities and Confirmation Holism

According to a theory of knowledge called confirmation holism, we believe facts on the basis of their being part of a larger body of knowledge that we believe in total. For example, my belief in Sweden is a part of my knowledge of geography and history as a whole. I would have to doubt much of what I know of the nations and history of the world to disbelieve in Sweden.

One problem that's been advanced against such confirmation holism is the idea that we must have to assign each fact we know a probability, and then, by the laws of probability, don't we calculate the odds of our entirety of holistic conjunction of facts just as the product of the individual probabilities? For example, if we believe each fact of a 500-fact conjunction with p = 0.95, does this make our degree of belief in the 500-conjunct equal to (0.95)^500, or just 0.0000000000073?

But, of course, we DON'T calculate the probabilities of the whole this way! The multiplication rule for the conjunct of two probabilities assumes that those probabilities are independent! . And, in the case of confirmation holism, that is exactly what we would deny.

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