The applicability of mathematics to physical modality

Berenstain, Nora

doi:10.1007/s11229-016-1067-3

Cited by 6 publications

(3 citation statements)

References 42 publications

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“…The difficulty of providing (2), i.e., a naturalist account of how it is that mathematical entities are able to explain empirical facts, is twofold. On the one hand, the reason why mathematical facts are able to explain worldly facts is often thought to be by MENP supporters that mathematical facts are modally stronger than physical facts (Lange, 2013b), or that mathematical facts provide modal information about empirical facts (Berenstain, 2017). But if one provides this kind of reasons, one just begs the question.…”

Section: Menp and Naturalismmentioning

confidence: 99%

Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

Sterpetti

2021

Found Sci

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This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists.

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Section: Menp and Naturalismmentioning

confidence: 99%

Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

Sterpetti

2021

Found Sci

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“…Indeed, advocates of SR may strengthen their argument by noting experimentally confirmed consequences of the theory not predicted by the theory's author. Again, this is the sort of indispensability argument for realism about mathematical entities (Berenstain 2017), committing us not only to the existence of abstract mathematical entities but to a metaphysical structural relation ("Mathematics").…”

Section: The World Structurementioning

confidence: 99%

Some Philosophical Remarks on the Concept of Structure: Framing Michał Heller’s Perspective

Oleksowicz

2021

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Perceiving objects in a structural or relational way in the ontology of physics and mathematics, as opposed to the classical way, shows how the concept of structure remains crucial for contemporary philosophy of physics and philosophy of science. In this paper, a particular emphasis is placed on certain philosophical concepts proposed by Michał Heller, concerning the context of the structural understanding of theories and the world. The first aim is to provide a general critical survey of the main assumptions of structural realism (SR). The second aim is to interpret Heller's philosophy of structure in accordance with the principal tenets of SR, illuminating certain criticisms of Heller's approach. Having analyzed Heller's approach, a question arises concerning the type of dependence on structuralism in the philosophy of physics and the philosophy of mathematics, in addition to certain metaphysical assumptions regarding the concept of structure. It is argued that Heller's SR conflates the adoption of mathematical structures in theories (the case of the realism-anti-realism debate) with the debate on mathematical explanations and the explanatory role of mathematical constraints.

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“…More precisely, Leng notes that the kind of mathematics employed in science can be embedded within a suitable version of set theory (Leng suggests ZFC with urelements, which 10 For additional cases in which mathematics is alleged to play such an explanatory role within science, see (Baker 2017a;2017b), (Berenstain 2017), (Colyvan 1999;, (Lyon and Colyvan 2008), and (Lyon 2012).…”

Section: Leng's Fictionalismmentioning

confidence: 99%

Mathematical surrealism as an alternative to easy-road fictionalism

Boyce

2019

Philos Stud

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Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as "mathematical surrealists" by contrast appeal to facts about the intrinsic character of the concrete world, not to explain why our best mathematically imbued scientific theories and explanations are acceptable in spite of having false components, but in order to replace those theories and explanations with parasitic, nominalistically acceptable alternatives. I argue that easy-road fictionalism is viable only if mathematical surrealism is and that the latter constitutes a superior nominalist strategy. Two advantages of mathematical surrealism are that it neither begs the question concerning the explanatory role of mathematics in science nor requires rejecting the cogency of inference to the best explanation.

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The applicability of mathematics to physical modality

Cited by 6 publications

References 42 publications

Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

Some Philosophical Remarks on the Concept of Structure: Framing Michał Heller’s Perspective

Mathematical surrealism as an alternative to easy-road fictionalism

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