Mathematical explanation and epistemology: Please mind the gap

Journal article

Baron, Sam. (2016). Mathematical explanation and epistemology: Please mind the gap. Ratio. 29(2), pp. 149 - 167. https://doi.org/10.1111/rati.12101
AuthorsBaron, Sam
Abstract

This paper draws together two strands in the debate over the existence of mathematical objects. The first strand concerns the notion of extra‐mathematical explanation: the explanation of physical facts, in part, by facts about mathematical objects. The second strand concerns the access problem for platonism: the problem of how to account for knowledge of mathematical objects. I argue for the following conditional: if there are extra‐mathematical explanations, then the core thesis of the access problem is false. This has implications for nominalists and platonists alike. Platonists can make a case for epistemic access to mathematical objects by providing evidence in favour of the existence of extra‐mathematical explanations. Nominalists, by contrast, can use the access problem to cast doubt on the idea that mathematical objects play a substantive role in scientific explanation.

Year2016
JournalRatio
Journal citation29 (2), pp. 149 - 167
PublisherBlackwell Publishing Ltd
ISSN0034-0006
Digital Object Identifier (DOI)https://doi.org/10.1111/rati.12101
Scopus EID2-s2.0-84964961675
Page range149 - 167
Research GroupDianoia Institute of Philosophy
Publisher's version
File Access Level
Controlled
Place of publicationUnited Kingdom
Permalink -

https://acuresearchbank.acu.edu.au/item/8qv16/mathematical-explanation-and-epistemology-please-mind-the-gap

Log in to edit

Restricted files

Publisher's version

  • 92
    total views
  • 0
    total downloads
  • 0
    views this month
  • 0
    downloads this month
These values are for the period from 19th October 2020, when this repository was created.

Export as

Related outputs

On Drugs
Baron, Samuel, Linton, Sara and O'Malley, Maureen A.. (2023). On Drugs. The Journal of Medicine and Philosophy. 48(6), pp. 551-564. https://doi.org/10.1093/jmp/jhad035
Moving ego versus moving time : investigating the shared source of future-bias and near-bias
Baron, Samuel, Everett, Brigitte C., Latham, Andrew J., Miller, Kristie, Tierney, Hannah and Oh, Jordan Veng Thang. (2023). Moving ego versus moving time : investigating the shared source of future-bias and near-bias. Synthese : an international journal for epistemology, methodology and philosophy of science. 202(3), pp. 1-33. https://doi.org/10.1007/s11229-023-04286-0
Trouble on the horizon for presentism
Baron, Samuel and Bihan, Baptiste Le. (2023). Trouble on the horizon for presentism. Philosophers' Imprint. 23(1), pp. 1-19. https://doi.org/10.3998/phimp.823
Non-dynamism and temporal disturbances
Baron, Samuel, Latham, Andrew J. and Varga, Somogy. (2023). Non-dynamism and temporal disturbances. Synthese: an international journal for epistemology, methodology and philosophy of science. 202(2), pp. 1-13. https://doi.org/10.1007/s11229-023-04253-9
Causal theories of spacetime
Baron, Samuel and Le Bihan, Baptiste. (2023). Causal theories of spacetime. Nous. pp. 1-23. https://doi.org/10.1111/nous.12449
Presentism and representation : Saying it without words
Baron, Sam, Miller, Kristie and Tallant, Jonathan. (2023). Presentism and representation : Saying it without words. Synthese. 201(2), p. Article 36. https://doi.org/10.1007/s11229-022-03987-2
Explainable AI and causal understanding : Counterfactual approaches considered
Baron, Sam. (2023). Explainable AI and causal understanding : Counterfactual approaches considered. Minds and Machines. 33(2), pp. 347-377. https://doi.org/10.1007/s11023-023-09637-x
Spacetime quietism in quantum gravity
Baron, Samuel and Bihan, Baptiste Le. (2022). Spacetime quietism in quantum gravity. In The Foundations of Spacetime Physics: Philosophical Perspectives pp. 155-175 Routledge. https://doi.org/10.4324/9781003219019-9
The harmony of grounding
Baron, Sam, Miller, Kristie and Tallant, Jonathan. (2022). The harmony of grounding. Philosophical Studies. 179(11), pp. 3421-3446. https://doi.org/10.1007/s11098-022-01819-0
Spacetime : Function and approximation
Baron, Sam. (2022). Spacetime : Function and approximation. Synthese. 200(2), p. Article 170. https://doi.org/10.1007/s11229-022-03498-0
Quantum gravity and mereology : Not so simple
Baron, Sam and Le Bihan, Baptiste. (2022). Quantum gravity and mereology : Not so simple. The Philosophical Quarterly. 72(1), pp. 19-40. https://doi.org/10.1093/pq/pqab016
TIME, AND TIME AGAIN
Baron, Sam and Lin, Yi-Cheng. (2022). TIME, AND TIME AGAIN. The Philosophical Quarterly. 72(2), pp. 259-282. https://doi.org/10.1093/pq/pqab040
Much ado about aboutness
Baron, Sam, Chua, Reginald Mary, Miller, Kristie and Norton, James. (2022). Much ado about aboutness. Inquiry. 65(3), pp. 298-326. https://doi.org/10.1080/0020174X.2019.1592705
Counterfactuals of ontological dependence
Baron, Sam. (2022). Counterfactuals of ontological dependence. Journal of the American Philosophical Association. 8(2), pp. 278-299. https://doi.org/10.1017/apa.2019.39
Metaphysical explanation : The Kitcher picture
Baron, Sam and Norton, James. (2021). Metaphysical explanation : The Kitcher picture. Erkenntnis. 86(1), pp. 187-207. https://doi.org/10.1007/s10670-018-00101-2
Parts of spacetime
Baron, Sam. (2021). Parts of spacetime. American Philosophical Quarterly. 58(4), pp. 387-397. https://doi.org/10.2307/48619322
Unification and mathematical explanation in science
Baron, Samuel. (2021). Unification and mathematical explanation in science. Synthese. 199(3-4), pp. 7339-7363. https://doi.org/10.1007/s11229-021-03118-3
What's so spatial about time anyway?
Baron, Sam and Evans, Peter W.. (2021). What's so spatial about time anyway? The British Journal for the Philosophy of Science. 72(1), pp. 159-183. https://doi.org/10.1093/bjps/axy077
Eliminating spacetime
Baron, Sam. (2021). Eliminating spacetime. Erkenntnis. https://doi.org/10.1007/s10670-021-00402-z
Temporal fictionalism for a timeless world
Baron, Sam, Miller, Kristie and Tallant, Jonathan. (2021). Temporal fictionalism for a timeless world. Philosophy and Phenomenological Research. 102(2), pp. 281-301. https://doi.org/10.1111/phpr.12637
It’s one thing to rule them all and another thing to bind them
Tallant, Jonathan and Baron, Sam. (2021). It’s one thing to rule them all and another thing to bind them. Synthese. 198, pp. 105-115. https://doi.org/10.1007/s11229-018-01983-z
Explanation impossible
Baron, Sam and Colyvan, Mark. (2021). Explanation impossible. Philosophical Studies. 178, pp. 559-576. https://doi.org/10.1007/s11098-020-01445-8
A Counterfactual Approach to Explanation in Mathematic
Baron, Sam, Colyvan, Mark and Ripley, David. (2020). A Counterfactual Approach to Explanation in Mathematic. Philosophia Mathematica. 28(1), pp. 1-34. https://doi.org/10.1093/philmat/nkz023
Purely physical explananda : Bistability in perception
Baron, Sam. (2020). Purely physical explananda : Bistability in perception. In In Falguera, José L. and Martinez Vidal, Concha (Ed.). Abstract objects : For and against pp. 17-34 Springer. https://doi.org/10.1007/978-3-030-38242-1_2
A counterfactual approach to explanation in mathematics
Baron, Sam, Colyvan, Mark and Ripley, David. (2020). A counterfactual approach to explanation in mathematics. Philosophia Mathematica. 28(1), pp. 1-34. https://doi.org/10.1093/philmat/nkz023
The curious case of spacetime emergence
Baron, Sam. (2020). The curious case of spacetime emergence. Philosophical Studies. 177, pp. 2207-2226. https://doi.org/10.1007/s11098-019-01306-z
Presentism, continuous time-travel and the phenomenology of passage
Baron, Sam and Braddon-Mitchell, David. (2020). Presentism, continuous time-travel and the phenomenology of passage. Erkenntnis. https://doi.org/10.1007/s10670-020-00217-4
Grounding at a distance
Baron, Sam, Miller, Kristie and Tallant, Jonathan. (2020). Grounding at a distance. Philosophical Studies. 177, pp. 3373-3390. https://doi.org/10.1007/s11098-019-01374-1
Counterfactual scheming
Baron, Sam. (2020). Counterfactual scheming. Mind. 129(514), pp. 535 - 562. https://doi.org/10.1093/mind/fzz008
Deflating deflationary truthmaking
Asay, Jamin and Baron, Sam. (2020). Deflating deflationary truthmaking. The Philosophical Quarterly. 70(278), pp. 1 - 21. https://doi.org/10.1093/pq/pqz036
The end of mystery
Baron, Sam and Colyvan, Mark. (2019). The end of mystery. American Philosophical Quarterly. 56(3), pp. 247-264. https://doi.org/10.2307/48570634
Non-naturalistic moral explanation
Baron, Samuel, Colyvan, Mark, Miller, Kristie and Rubin, Michael. (2019). Non-naturalistic moral explanation. Synthese. https://doi.org/10.1007/s11229-019-02341-3
Mathematical explanation by law
Baron, Sam. (2019). Mathematical explanation by law. The British Journal for the Philosophy of Science. 70(3), pp. 683-717. https://doi.org/10.1093/bjps/axx062
Empirical incoherence and double functionalism
Baron, Sam. (2019). Empirical incoherence and double functionalism. Synthese. 199, pp. 413-439. https://doi.org/10.1007/s11229-019-02462-9
Infinite lies and explanatory ties: Idealization in phase transitions
Baron, Sam. (2019). Infinite lies and explanatory ties: Idealization in phase transitions. Synthese. 196(5), pp. 1939 - 1961. https://doi.org/10.1007/s11229-018-1678-y
How to endure presentism
Baron, Sam. (2019). How to endure presentism. Inquiry. 62(6), pp. 659 - 673. https://doi.org/10.1080/0020174X.2018.1487883
An introduction to the philosophy of time
Baron, Sam and Miller, Kristie. (2018). An introduction to the philosophy of time Polity Press.
Time, physics, and philosophy : It's all relative
Baron, Sam. (2018). Time, physics, and philosophy : It's all relative. Philosophy Compass. 13(1), pp. 1-14. https://doi.org/10.1111/phc3.12466
A formal apology for metaphysics
Baron, Sam. (2018). A formal apology for metaphysics. Ergo. 5(39), pp. 1030-1060. https://doi.org/10.3998/ergo.12405314.0005.039
Do not revise Ockham's Razor without necessity
Baron, Sam and Tallant, Jonathan. (2018). Do not revise Ockham's Razor without necessity. Philosophy and Phenomenological Research. 96(3), pp. 596 - 619. https://doi.org/10.1111/phpr.12337
How mathematics can make a difference
Baron, Sam, Colyvan, Mark and Ripley, David. (2017). How mathematics can make a difference. Philosophers' Imprint. 17(3), pp. 1 - 19.
Back to the unchanging past
Baron, Sam. (2017). Back to the unchanging past. Pacific Philosophical Quarterly. 98(1), pp. 129 - 147. https://doi.org/10.1111/papq.12127
Feel the flow
Baron, Sam. (2017). Feel the flow. Synthese. 194(2), pp. 609 - 630. https://doi.org/10.1007/s11229-015-0964-1
Time enough for explanation
Baron, Sam and Colyvan, Mark. (2016). Time enough for explanation. Journal of Philosophy. 113(2), pp. 61-88. https://doi.org/10.5840/jphil201611324
Monism : The islands of plurality
Baron, Sam and Tallant, Jonathan. (2016). Monism : The islands of plurality. Philosophy and Phenomenological Research. 93(3), pp. 583-606. https://doi.org/10.1111/phpr.12270
Metaphysics as fairness
Baron, Sam. (2016). Metaphysics as fairness. Synthese. 193(7), pp. 2237 - 2259. https://doi.org/10.1007/s11229-015-0842-x
The explanatory dispensability of idealizations
Baron, Sam. (2016). The explanatory dispensability of idealizations. Synthese. 193(2), pp. 365 - 386. https://doi.org/10.1007/s11229-014-0517-z
Explaining mathematical explanation
Baron, Sam. (2016). Explaining mathematical explanation. The Philosophical Quarterly. 66(264), pp. 458 - 480. https://doi.org/10.1093/pq/pqv123
The priority of the now
Baron, Sam. (2015). The priority of the now. Pacific Philosophical Quarterly. 96(3), pp. 325-348. https://doi.org/10.1111/papq.12030
Female under-representation among philosophy majors : A map of the hypotheses and a survey of the evidence
Dougherty, Tom, Baron, Samuel and Miller, Kristie. (2015). Female under-representation among philosophy majors : A map of the hypotheses and a survey of the evidence. Feminist Philosophy Quarterly. 1(1), p. Article 4. https://doi.org/10.5206/fpq/2015.1.4
Why is there female under-representation among philosophy majors? Evidence of a pre-university effect
Baron, Sam, Dougherty, Tom and Miller, Kristie. (2015). Why is there female under-representation among philosophy majors? Evidence of a pre-university effect. Ergo. 2(14), pp. 330-365. https://doi.org/10.3998/ergo.12405314.0002.014
A bump on the road to presentism
Baron, Sam. (2015). A bump on the road to presentism. American Philosophical Quarterly. 52(4), pp. 345 - 356.
Our concept of time
Baron, Samuel and Miller, Kristie. (2015). Our concept of time. In In B. Mölder, V. Arstila and P. Øhrstrøm (Ed.). Philosophy and psychology of time pp. 29 - 52 Springer International Publishing. https://doi.org/10.1007/978-3-319-22195-3_3
Et tu, brute?
Baron, Sam. (2015). Et tu, brute? In In C. Daly (Ed.). The Palgrave handbook of philosophical methods pp. 258 - 281 Palgrave Macmillan. https://doi.org/10.1057/9781137344557_11
Temporal experience, temporal passage and the cognitive sciences
Baron, Sam, Cusbert, John, Farr, Matt, Kon, Maria and Miller, Kristie. (2015). Temporal experience, temporal passage and the cognitive sciences. Philosophy Compass. 10(8), pp. 560 - 571. https://doi.org/10.1111/phc3.12244
Why do female students leave philosophy? The story from Sydney
Dougherty, Tom, Baron, Samuel and Miller, Kristie. (2015). Why do female students leave philosophy? The story from Sydney. Hypatia. 30(2), pp. 467 - 474. https://doi.org/10.1111/hypa.12150
Tensed truthmaker theory
Baron, Sam. (2015). Tensed truthmaker theory. Erkenntnis. 80(5), pp. 923 - 944. https://doi.org/10.1007/s10670-014-9689-7
Causation sans time
Baron, Sam and Miller, Kristie. (2015). Causation sans time. American Philosophical Quarterly. 52(1), pp. 27 - 40.
What is temporal error theory?
Baron, Sam and Miller, Kristie. (2015). What is temporal error theory? Philosophical Studies. 172(9), pp. 2427 - 2444. https://doi.org/10.1007/s11098-014-0419-4
The hard road to presentism
Asay, Jamin and Baron, Sam. (2014). The hard road to presentism. Pacific Philosophical Quarterly. 95(3), pp. 314 - 335. https://doi.org/10.1111/papq.12029
Animal interrupted, or why accepting Pascal's Wager might be the last thing you ever do
Baron, Sam and Van Dyke, Christina. (2014). Animal interrupted, or why accepting Pascal's Wager might be the last thing you ever do. The Southern Journal of Philosophy. 52(S1), pp. 109 - 133. https://doi.org/10.1111/sjp.12069
Optimisation and mathematical explanation: Doing the Lévy Walk
Baron, Sam. (2014). Optimisation and mathematical explanation: Doing the Lévy Walk. Synthese. 191(3), pp. 459 - 479. https://doi.org/10.1007/s11229-013-0284-2
Can indispensability-driven platonists be (serious) presentists?
Baron, Sam. (2014). Can indispensability-driven platonists be (serious) presentists? Theoria. 80(2), pp. 153 - 173. https://doi.org/10.1111/theo.12031
Groundless truth
Baron, Sam, Miller, Kristie and Norton, James. (2014). Groundless truth. Inquiry. 57(2), pp. 175 - 195. https://doi.org/10.1080/0020174X.2013.855652
Causation in a timeless world
Baron, Sam and Miller, Kristie. (2014). Causation in a timeless world. Synthese. 191(12), pp. 2867 - 2886. https://doi.org/10.1007/s11229-014-0427-0