Bandu On I B E In Mathematics
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What is it?
An argument pointing out apparent flaws in Baker’s example (investigation into the prime-numbered nature of the life cylces of cicadas) of a mathematical explanation of a scientific fact. In so doing, Bandu points out a more general problem for IBE-based arguments for the existence of mathematical entities: the assumption that the truth of the explanandum already implies the existence of the entities it involves. If these include mathematical entities, then the argument begs the question against the nominalist (this observation is due to Leng, not Bandu). Furthermore, if one doesn’t accept the truth of the explanandum, one cannot use IBE.
Where can it be found?
Bandu, S., Inference to the best explanation and mathematical realism, Sythese (2008) 160:13-20.
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What do I think? - Does one have to accept that asserting the truth of a statement (i.e. the scientific explanandum in this case) involves accepting that the entities involved in that statement exist? — I guess what I’m asking here if there are either non-realist conceptions of truth or a version of IBE that doesn’t require this strict truth assertion. — Perhaps something along the lines of putting the explanandum is a sort of metaphorical way as per Yablo? - If correct, what this in effect means is that the indispensability argument will only work if one is able to find an explanans involving an inseparable mathematical component for a purely non-mathematical, scientific explanandum. - Overall, I think I probably need to step back and work from the ground up on the IBE literature in order to get a clear idea of the ocntext here.
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