One of the upshots of a number of my posts on the limitations of probability theory is that there are events that are probabilistically incomparable—neither can be said to be more likely than the other. (For instance, this post.) But an objective chance at a good is good, and better the greater the chance and worse the lower the chance. Chances p and q at the same good G will, then, be incommensurably good when the chances p and q are incomparable. Hence, if there are incomparable objective chances, there can be incommensurable goods. But it's plausible that there can be incomparable chances (see the post I linked to above, for instance). So there can be incommensurable goods.
2 comments:
I don't think it follows from the premises you give that "Chances p and q at the same good G will, then, be incommensurably good when the chances p and q are incomparable". Your premises do not imply that the good of an objective chance at a good always varies with its objective chance. The premise "The goodness of an objective chance at a good is the goodness of the good multiplied by its objective chance of occurring", if applied to incomparable chances at a good, would give you the conclusion you want, but this premise isn't derivable from your premises. Your premise just says that if an objective chance at a good is higher than another objective chance at that good, then the good of the first objective chance is better than that of the second. The premise doesn't tell you how to rank incomparable chances at a good.
yeah: what I should say is that if the good is fixed, the value of the chance is greater iff the probability is higher and equal iff the probability is equal.
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