Abstract
A Benacerraf–Field challenge is an argument intended to show that common realist theories of a given domain are untenable: such theories make it impossible to explain how we’ve arrived at the truth in that domain, and insofar as a theory makes our reliability in a domain inexplicable, we must either reject that theory or give up the relevant beliefs. But there’s no consensus about what would count here as a satisfactory explanation of our reliability. It’s sometimes suggested that giving such an explanation would involve showing that our beliefs meet some modal condition, but realists have claimed that this sort of modal interpretation of the challenge deprives it of any force: since the facts in question are metaphysically necessary and so obtain in all possible worlds, it’s trivially easy, even given realism, to show that our beliefs have the relevant modal features. Here I show that this claim is mistaken—what motivates a modal interpretation of the challenge in the first place also motivates an understanding of the relevant features in terms of epistemic possibilities rather than metaphysical possibilities, and there are indeed epistemically possible worlds where the facts in question don’t obtain.
Highlights
For us to be correct in our beliefs about some part of the world is for it to be the case that, in the relevant domain, our beliefs by and large coincide with the facts
A straightforward causal explanation is available in the case of my beliefs about the weather: I came to my belief that it’s raining by observing the rain
We’re thinking about epistemically possible worlds.24. This is plausible enough, I think, but we can make our motivation for an epistemic analysis more definitive by providing a case that makes it very clear that the worlds relevant to whether we should take the truth of our beliefs to be lucky in an epistemically problematic way are epistemically possible worlds rather than metaphysically possible ones
Summary
For us to be correct in our beliefs about some part of the world is for it to be the case that, in the relevant domain, our beliefs by and large coincide with the facts. There can’t, on any naturalistically respectable theory of how our cognitive faculties work, be a connection of any sort between mind-independent abstract objects and our having the mathematical beliefs we do It seems that, given platonism, no explanation is going to be available, even in principle, of why our mathematical beliefs coincide with the facts. Between our beliefs and the facts is modally robust in any sense that could reasonably be required—after all, if there are no worlds where the facts differ, believing what we believe guarantees that we aren’t going to go wrong, in which case no reasonable modal conception can deliver the verdict that standard mind-independence theories make our reliability inexplicable The problem with this objection—call it the objection from necessity—is that it relies on the assumption that the worlds across which modal robustness is to be evaluated, for the purposes of the Benacerraf–Field challenge, are the metaphysically possible worlds, and there’s good reason to think this assumption is false. Adherence is analogous to Safety but is instead meant to rule out nearby false negatives—i.e., worlds where we falsely believe that it’s not true that p.9 Note that, to make sense of the claim that the main counterfactual formulations of Safety and Adherence are equivalent to the corresponding parenthetical formulations, we must suppose that the counterfactual formulations are to be understood not in accordance with the usual view, on which counterfactuals with true antecedents are trivially true, but in accordance with Nozick’s suggested alternative, on which, for a counterfactual with a true antecedent p to be true, the consequent must be true in the actual world and “in the ‘close’ worlds where p is true”—the consequent must remain true “for some distance out in the p neighborhood of the actual world” (1981, p. 176).
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