Inference to the best explanation and mathematical realism

Bangu, Sorin

doi:10.1007/s11229-006-9070-8

Cited by 48 publications

(26 citation statements)

References 11 publications

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“…23 So variable sharing of the kind described for mathematical claims may not be assured. Indeed, as Bangu ([2008]) has argued, if mathematical facts do appear in the explanandum of a putative extra-mathematical explanation, then that explanation is left open to the charge that it is actually an intra-mathematical explanation: an explanation of one mathematical fact by another. 24 It follows that in order for the DM theory to correctly handle extra-mathematical explanations as such, an alternative account of relevance is needed.…”

Section: Irrelevancementioning

confidence: 99%

Mathematical Explanation by Law

Baron

2019

The British Journal for the Philosophy of Science

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Call an explanation in which a non-mathematical fact is explained -in part or in whole -by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this paper, a theory of extra-mathematical explanation is developed. The theory is modeled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts.

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Section: Irrelevancementioning

confidence: 99%

Mathematical Explanation by Law

Baron

2019

The British Journal for the Philosophy of Science

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“…In a recent paper (Bangu (2008)) Sorin Bangu has argued that Baker's example is problematic because it begs the question in favour of the mathematical realist by presupposing that an explanandum formulated in mathematical terms (i.e. the prime-numbered length of Magicicada's life-cycle) is true.…”

Section: Baker's Claimmentioning

confidence: 99%

Magicicada, Mathematical Explanation and Mathematical Realism

Rizza

2010

Erkenn

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Baker (2005) claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus cannot be used by the mathematical realist. I also show that, despite this, mathematics keeps playing an important methodological role in the explanation and does not reduce to a merely computational or descriptive framework.

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“…Any hypothesis that acts as an explanation for some E is a potential explanation but only true hypotheses can be actual explanations. Sorin Bangu (2008Bangu ( , 2012 and Mary Leng (2005Leng ( , 2010 suggest that construing explanation factively is question-begging in this context.…”

Section: Introductionmentioning

confidence: 96%

Should scientific realists be platonists?

Busch

Morrison

2015

Synthese

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Enhanced Indispensability Arguments (EIA) claim that Scientific Realists are committed to the existence of mathematical entities due to their reliance on Inference to the Best Explanation (IBE). Our central question concerns this purported parity of reasoning: do people who defend the EIA make an appropriate use of the resources of Scientific Realism (in particular, IBE) to achieve platonism? ( §2) We argue that just because a variety of different inferential strategies can be employed by Scientific Realists does not mean that ontological conclusions concerning which things we should be Scientific Realists about are arrived at by any inferential route which eschews causes ( §3), and nor is there any direct pressure for Scientific Realists to change their inferential methods ( §4). We suggest that in order to maintain inferential parity with Scientific Realism, proponents of EIA need to give details about how and in what way the presence of mathematical entities directly contribute to explanations ( §5).

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Inference to the best explanation and mathematical realism

Cited by 48 publications

References 11 publications

Mathematical Explanation by Law

Mathematical Explanation by Law

Magicicada, Mathematical Explanation and Mathematical Realism

Should scientific realists be platonists?

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