Putnam uses Skolem's theorem (every consistent first-order theory has a model whose domain is the integers or some subset thereof) to argue that the meanings of our sentences are indeterminate.
If considerations of elegance CAN make something a more natural candidate for the meaning of a given word (e.g. someone with behavior that doesn't distinguish between plus and quus means plus), then the mere existence of some (clumsly and arbitrary) Skolem model doesn't pose a problem for our meaning something definite - since the Skolem model's interpretation of expressions like "all possible subsets" will be much less elegant than the natural one.
If considerations of elegance CAN'T make something a more natural candidate for the meaning of a given word, then Putnam is wrong to assume that even the meanings of the first order logical connectives which his perverse Skolem model captures are pinned down. For why think that we mean 'or' rather than a quus like version of 'or' that starts behaving like `and' in sentences longer than a billion words long?
Wednesday, November 24, 2010
Sunday, November 21, 2010
Old Evidence and Apologies
If the problem of old evidence for Bayesian epistemology is just the following, then I don't think it's a problem:
Sometimes it seems like we should change our probabilities based on discovering logical consequences of a theory, but Bayesian updating only involves changing probabilities when you make a new observation.
For (it seems to me) this objection has the same ultimate structure as the following, surely bad, objection:
Sometimes it seems like we should apologize, but obeying so-and-so's moral theory involves never wronging anyone - and hence never apologizing.
If old evidence E is logically incompatible with hypothesis H, then Bayesianism says that you should *already* have ruled out all the worlds where H is true, and changed your probabilities accordingly, whenever you observed that E. So, I see no problem for the Bayesian epistemologist in saying that when you discover that you have failed to update in the way required by the theory (by not noticing a logical incompatibility), you should fix the mistake and change your probabilities accordingly.
[Compare this with the following popular intuition in ethics: you should promise to visit your grandmother and then visit her, but given that you aren't going to visit you shouldn't promise to visit her.]
Sometimes it seems like we should change our probabilities based on discovering logical consequences of a theory, but Bayesian updating only involves changing probabilities when you make a new observation.
For (it seems to me) this objection has the same ultimate structure as the following, surely bad, objection:
Sometimes it seems like we should apologize, but obeying so-and-so's moral theory involves never wronging anyone - and hence never apologizing.
If old evidence E is logically incompatible with hypothesis H, then Bayesianism says that you should *already* have ruled out all the worlds where H is true, and changed your probabilities accordingly, whenever you observed that E. So, I see no problem for the Bayesian epistemologist in saying that when you discover that you have failed to update in the way required by the theory (by not noticing a logical incompatibility), you should fix the mistake and change your probabilities accordingly.
[Compare this with the following popular intuition in ethics: you should promise to visit your grandmother and then visit her, but given that you aren't going to visit you shouldn't promise to visit her.]
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