Hi Carrie,Cool paper! I wonder if there's a better way of augmenting the aims of accepting to help Wright out (I'm thinking of the last paragraph on p44). What if we say that the act of accepting aims both at probable truth and at providing a useful premiss for reasoning that results in true beliefs? That way the usefulness provision allows facts about dominance to be relevant to whether an act of accepting fulfils its aims, without just identifying the aims with the pursuit of valuable cognitive projects. It seems to me less ad hoc, because I think I do try to have beliefs that are going to be useful in reasoning: I ignore lots of useless information, and try to remember useful information, and the weight I place on usefulness is not trumped by considerations of reliability. Other potential examples: pre-calculus belief in infinitesimals, and Quinean belief in sets because of indispensibility arguments (though that's a controversial interpretation).I think your response to this kind of point would involve the crossword analogy. But I don't find your treatment of that example completely persuasive. It seems that it might well be 'good solving' to put in an answer I think dubious if that might help me to get the other clues - and that isn't even a case where I know that it can't hurt. There's an important difference between cases where good epistemic consequences result from reasoning from a belief, and where they result from some non-rational process, as in the case where the goddess will give me true beliefs at some later stage (there may be an analogy with the distinction between causal and evidential decision theory when responding to Newcomb's problem). Similarly, it makes a difference whether accepting S contributes to my larger cognitive projects by helping me survive long enough to carry out those projects, or by acting as a key premiss of the reasoning that those projects involve. So my suggestion really is more restricted than the one you allow on p44, which seems to allow in both kinds of contribution (in the previous sentence) as part of the aim of accepting.
Hi Daniel, Thanks for that - I think it is an interesting suggestion. The 'usefulness' terminology worries me though - especially when you cite things like indispensability arguments as examples of what you mean. That leads one to suspect that what's doing the work is something akin to inference to the best explanation, which is normally taken to be of epistemic value just because it is taken to lead to probably-true beliefs ...
Hmm, it hadn't really occurred to me that indispensibility arguments were IBE. Do platonists think that mathematical objects explain the phenomena? Did Quine? (I just asked Ben and he says he thinks that Quine didn't, but maybe some platonists do...)
I take it the version of IBE in the neighbourhood here is that the best explanation of why mathematics is so useful in the physical sciences is because it is true. Put like that, I for one find this a slightly different thought to indispensibility arguments - at least in their pretty canonical Putnam/Quine formulations (though perhaps even if they are different thoughts, they stand or fall together - the succes of Field's program looks like it would undermine both, for example. I'd want to think that through much more carefully though).
Without having looked back at the literature, i'd have thought that indispensibility arguments and IBE are tied thus:Our reason to believe physical science is that it's the theory that gives best explanation of empirical data (i.e., by IBE). But physical science (as standardly formulated) embeds bits of mathematics---e.g. real analysis. So reason to believe these theories as a whole just is reason to believe the relevant bits of mathematics. Then the Field says: the theory that best explains empirical theory is nominalised, mathematics-free science. So the theory that IBE tells us to believe doesn't commit us to abstracta. If that's the right way to think about it, then Daniel's worry about whether mathematical objects explain things doesn't arise. Objects don't explain stuff, theories explain stuff! And the indispensibility debate is over whether the theory that IBE tells us to believe is mathematically committal.
Of course, one form of indispensability argt would just be an argt that we are (in fact) committed to mathematical objects, because we are committed to our best scientific theory which indispensably quantifies over them.But that doesn't tell us anything about what we *should* believe or be committed to.I think the interesting forms of IA rely on IBE in pretty much the way Robbie says.
Carrie, Robbie,Sure, that sounds right.
I think that Putnam and Quine maybe run the indispensability argument in different ways. What Robbie says sounds like Putnam, whereas the possibility that Carrie dismisses as uninteresting seems more Quinean.The natural response to Carrie's question 'Why should we believe our best theory?' is that believing our best theory allows us to infer true beliefs about future phenomena (that's what makes it the best theory). That's a reason for believing your best theory that doesn't depend on the (controversial) claim that theories are explanatory.In the scientific realism debate, the 'no miracles' argument is at least often voiced as the claim that because (say) the existence of electrons is the best explanation of the data, we should believe in electrons. In that area, the claim that the truth of scientific theory is explanatory is common ground between the realist and anti-realist, because it's part of science, not philosophy, that the existence of electrons (which is entailed by scientific theory) explains the data. That's what makes the argument so strong (though perhaps not so interesting).But anti-Platonists need not accept that mathematical objects explain the data (even if they accept that quantification over those objects is indispensable - not all anti-Platonists are like Field), and so they need not accept that Platonism explains the data either. Such an explanatory claim is no part of either science or mathematics. Thus IBE does not strengthen the indispensability argument for Platonism. I think that Quine's version of the argument (or at least the one which I incautiously attribute to him) is better than Putnam's.(This is all a pretty long-winded attempt to defend what was meant as an aside to my comments on Carrie's paper...)
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