Naturalism in Mathematics and the Authority of Philosophy

Paseau, Alexander

doi:10.1093/bjps/axi123

Cited by 17 publications

(9 citation statements)

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“…Although I think it is, this would require a separate argument, so I'll ignore this complication here; see Beebee and Dodd 2005 for discussion. 10 See Burgess and Rosen (1997), Maddy (1997Maddy ( , 2005Maddy ( , 2007, Paseau (2005Paseau ( , 2013. For detailed exegesis of Quine's own views, see Hookway (1988) and Hylton (2007).…”

Section: Indispensability and Naturalismmentioning

confidence: 99%

Indispensability, causation and explanation

Bangu

2018

THEORIA

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When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists' endorsement of this causal mathematical nominalism is in tension with another position some (many?) of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival of mathematical nominalism, the mathematical realist position supported by the 'Indispensability Argument' -but I do this indirectly, by showing that the road toward it is not blocked by considerations from causation.Keywords: Indispensability, Causation, Explanation, Nominalism, Realism, Causal Eliminativism.RESUMEN: Al considerar el realismo matemático, algunos realistas científicos lo rechazan y expresan su simpatía por la aproximación opuesta, el nominalismo matemático; es más, muchos justifican esta opción invocando la inercia causal de los objetos matemáticos. El propósito principal de esta nota es mostrar que la adhesión de los realistas científicos a este nominalismo matemático causal entra en tensión con otra posición que algunos (¿muchos?) de ellos también aceptan, la doctrina del naturalismo metodológico. Al subrayar este conflicto, pretendo desequilibrar la balanza a favor de un rival del nominalismo matemático, la posición realista matemática que apoya el 'Argumento de la Indispensabilidad' -pero lo hago indirectamente, mostrando que el camino hacia esta posición no queda bloqueado por consideraciones sobre la causación-.

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Section: Indispensability and Naturalismmentioning

confidence: 99%

Indispensability, causation and explanation

Bangu

2018

THEORIA

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“…19 For criticisms of stronger readings of Moorean arguments, see Paseau (2005), Daly andLiggins (2011), andSider (2013: §2). 20 This is emphasized by Sider (2011: 347), who also does not motivate his concern with 'fundamental language' on the basis of Moorean modesty.…”

Section: Concluding Remarks: Reality Appearance and Metaphysical Strmentioning

confidence: 99%

“…For criticisms of stronger readings of Moorean arguments, see Paseau (), Daly and Liggins (), and Sider (: §2).…”

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confidence: 99%

Against Fundamentality‐Based Metaphysics

Lipman

2016

Nous

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Metaphysical views typically draw some distinction between reality and appearance, endorsing realism about some subject matters and antirealism about others. There are different conceptions of how best to construe antirealist theories. A simple view has it that we are antirealists about a subject matter when we believe that this subject matter fails to obtain. This paper discusses an alternative view, which I will call the fundamentality‐based conception of antirealism. We are antirealists in this sense when we think that the relevant matter fails to be constitutive of fundamental reality. The following discussion will not rely on any particular understanding of fundamental reality, covering conceptions based on grounding, naturalness and truthmaking, to name three salient ones. This paper argues that there are serious issues with fundamentality‐based metaphysics. It will be argued that: (1) the fundamentality‐based approach shapes and restricts our realist and antirealist views in unsatisfying ways, (2) that it is unable to handle the conflicting facts that lie across the envisaged ‘layers’ of the metaphysically structured world, and (3) that the methodological reasons for adopting the fundamentality‐based approach fail. The paper will conclude with a diagnosis of the discussed issues, identifying a common source.

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“…It is a crude induction, and it refutes fictionalism only if it proves too much. (See Leng 2005, Paseau 2005 and Balaguer 2009 for further discussion).…”

Section: Deferentialism 325mentioning

confidence: 99%

Deferentialism

Daly

Liggins

2010

Philos Stud

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There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend-deferentialism, as we will call it-certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism's failings and present our own anti-deferentialist approach to philosophical inquiry.

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Naturalism in Mathematics and the Authority of Philosophy

Cited by 17 publications

References 15 publications

Indispensability, causation and explanation

Indispensability, causation and explanation

Against Fundamentality‐Based Metaphysics

Deferentialism

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