Responses by Tim McGrew to questions I raised in an e-mail concerning the multiplication rule:
In order for an argument to be a ʽgoodʼ one, the confidence we have in the truth of the conclusion must be greater than .5, otherwise we canʼt claim to know the conclusion (I think this is uncontroversial).
The trouble is that "good argument" is not sufficiently well defined for us to say whether it must meet this criterion. An argument that nails down the probability of the conclusion at .51 -- no higher and no lower -- meets the criterion you named; but is it really, for just that reason, a "better" argument than one that shows that the conclusion has a probability of at least .4 and perhaps much more?
In order for an argument to be a ʽgoodʼ one, the confidence we have in the truth of the conclusion must be greater than .5, otherwise we canʼt claim to know the conclusion (I think this is uncontroversial).
The trouble is that "good argument" is not sufficiently well defined for us to say whether it must meet this criterion. An argument that nails down the probability of the conclusion at .51 -- no higher and no lower -- meets the criterion you named; but is it really, for just that reason, a "better" argument than one that shows that the conclusion has a probability of at least .4 and perhaps much more?