Magicicada, Mathematical Explanation and Mathematical Realism

Rizza, Davide

doi:10.1007/s10670-010-9261-z

Cited by 28 publications

(12 citation statements)

References 19 publications

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“…Whether the cases described are ones in which the mathematics is genuinely explanatorily indispensable remains contested. It has been disputed by Melia (2000), Leng (2002), Pincock (2004a), Saatsi (2011), and Rizza (2011), and defended by Lyon and Colyvan (2008), Baker (2009), Colyvan (2010), and Lyon (2012). I do not explicitly offer a defense of premise 2 here, though I do elucidate the specific explanatory indispensability at evidence in each of the cases discussed.…”

Section: Scientific Realism and The Indispensability Argumentmentioning

confidence: 99%

The applicability of mathematics to physical modality

Berenstain

2016

Synthese

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This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The view presented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal structure of the physical world. The no-miracles argument is the primary motivation for scientific realism. It is a presupposition of this argument that unobservable entities are explanatory only when they determine the empirical phenomena they explain. I argue that mathematical entities should also be seen as explanatory only when they determine the empirical facts they explain, namely, the modal structure of the physical world. Thus, scientific realism commits us to a metaphysical determination relation between mathematics and physical modality that has not been previously recognized. The requirement to account for the metaphysical dependence of modal physical structure on mathematics limits the class of acceptable solutions to the applicability problem that are available to the scientific realist.

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Section: Scientific Realism and The Indispensability Argumentmentioning

confidence: 99%

The applicability of mathematics to physical modality

Berenstain

2016

Synthese

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“…Some have tried to show that the mathematical component is in fact dispensable. 12 Saatsi (2007), Daly and Langford (2009), Rizza (2011). explanatory. 13 Others have accepted the indispensability of the mathematics for the overall explanation, but claimed that the mathematical component is not itself 11 Clearly a parallel constraint may be formulated for 13-year cicadas, in which the ecosystem limits potential periods to the range from 12 to 15 years.…”

Section: Prime Periods Minimize Intersection (Compared To Non-prime Pmentioning

confidence: 99%

Explanation in Biology

Braillard¹,

Malaterre

2015

History, Philosophy and Theory of the Life Sciences

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“…In my view, even if we assume that in their practices scientists appeal to mathematical explanations, nevertheless this is not sufficient to elucidate the notion of mathematical explanation. 14 For an alternative account to Baker's and Baron's interpretation of the cicada case study, see Rizza (2011). The history of science offers a number of cases in which provisional mathematical explanation holds as long as a causal explanation is to be found. 15 Explaining a phenomenon is a matter of understanding how the phenomenon is causally produced (Strevens 2008, p. 3).…”

Section: Which Explanatory Role For Mathematics?mentioning

confidence: 99%

Which explanatory role for mathematics in scientific models? Reply to “The Explanatory Dispensability of Idealizations”

Bianchi

2015

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In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron's distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron's non-causal notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron's argument that idealizations do not help to carry the explanatory load at least for two reasons: (1) mathematics is not independent of idealizations in modelling and (2) idealizations help mathematics to carry the explanatory load of a model in different degrees.

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Magicicada, Mathematical Explanation and Mathematical Realism

Cited by 28 publications

References 19 publications

The applicability of mathematics to physical modality

The applicability of mathematics to physical modality

Explanation in Biology

Which explanatory role for mathematics in scientific models? Reply to “The Explanatory Dispensability of Idealizations”

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