The necessity of mathematics

Journal article


Yli-Vakkuri, Juhani and Hawthorne, John. (2020). The necessity of mathematics. Noûs. 54(3), pp. 549 - 577. https://doi.org/10.1111/nous.12268
AuthorsYli-Vakkuri, Juhani and Hawthorne, John
Abstract

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.

Year2020
JournalNoûs
Journal citation54 (3), pp. 549 - 577
PublisherWiley-Blackwell Publishing, Inc.
ISSN1468-0068
Digital Object Identifier (DOI)https://doi.org/10.1111/nous.12268
Scopus EID2-s2.0-85053474222
Page range549 - 577
Research GroupDianoia Institute of Philosophy
Publisher's version
File Access Level
Controlled
Place of publicationUnited States of America
Permalink -

https://acuresearchbank.acu.edu.au/item/8896y/the-necessity-of-mathematics

Restricted files

Publisher's version

  • 125
    total views
  • 0
    total downloads
  • 2
    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

Doncaster pandas and Caesar's armadillo : Scepticism and via negativa knowledge
Spectre, Levi and Hawthorne, John Patrick. (2024). Doncaster pandas and Caesar's armadillo : Scepticism and via negativa knowledge. Philosophy and Phenomenological Research. 108(2), pp. 360-373. https://doi.org/10.1111/phpr.12974
LF : A foundational higher-order logic
Goodsell, Zachary and Yli-Vakkuri, Tuomo Juhani. (2024). LF : A foundational higher-order logic. PsyArXiv Preprints. 1, pp. 1-21. https://doi.org/10.48550/arXiv.2401.11050
Absolutism and its Limits
Hawthorne, John Patrick, Isaacs, Yoaav and Littlejohn, Clayton. (2023). Absolutism and its Limits. Journal of Moral Philosophy. 105(20), pp. 170-189. https://doi.org/10.1163/17455243-20233831
The safety conception of knowledge
Hawthorne, John Patrick and Dietz, Christina. (2023). The safety conception of knowledge. In Externalism about Knowledge pp. 150-185 Oxford University Press. https://doi.org/10.1093/oso/9780198866749.003.0007
Evidence, experience and decision
Hawthorne, John Patrick. (2023). Evidence, experience and decision. Philosophical Studies: an international journal for philosophy in the analytic tradition. 180(8), pp. 2491-2502. https://doi.org/10.1007/s11098-023-01930-w
Challenges for an experimentalist's skepticism about cases
Strohminger, Margot and Yli-Vakkuri, Juhani. (2023). Challenges for an experimentalist's skepticism about cases. In In Vaidya, Anand and Prelević, Duško (Ed.). Epistemology of modality and philosophical methodology pp. 338-358 Routledge. https://doi.org/10.4324/9781003002192-19
Counterpart theory and counterfactuals
Hawthorne, John and Yli-Vakkuri, Juhani. (2023). Counterpart theory and counterfactuals. In In Bennett, Karen and Zimmerman, Dean W. (Ed.). Oxford studies in metaphysics ; volume 13 pp. 129-165 Oxford University Press. https://doi.org/10.1093/oso/9780192886033.003.0005
Inheritance : Professor Procrastinate and the logic
Blumberg, Kyle and Hawthorne, John. (2023). Inheritance : Professor Procrastinate and the logic. Philosophy and Phenomenological Research. 106(1), pp. 84-106. https://doi.org/10.1111/phpr.12846
Intensionalism and propositional attitudes
Yli-Vakkuri, Juhani and Hawthorne, John. (2022). Intensionalism and propositional attitudes. In In Kriegel, Uriah (Ed.). Oxford studies in philosophy of mind ; volume 2 pp. 114-174 Oxford University Press. https://doi.org/10.1093/oso/9780192856685.003.0005
Non-measurability, imprecise credences, and imprecise chances
Isaacs, Yoaav, Hájek, Alan and Hawthorne, John. (2022). Non-measurability, imprecise credences, and imprecise chances. Mind. 131(523), pp. 894-918. https://doi.org/10.1093/mind/fzab031
Reply to Bourget and Mendelovici
Yli-Vakkuri, Tuomo Juhani and Hawthorne, John Patrick. (2022). Reply to Bourget and Mendelovici. Inquiry. pp. 1-11. https://doi.org/10.1080/0020174X.2022.2129485
Desire
Blumberg, Kyle and Hawthorne, John. (2022). Desire. Philosophers' Imprint. 22(8), pp. 1-17. https://doi.org/10.3998/phimp.2116
A new hope
Blumberg, Kyle and Hawthorne, John. (2022). A new hope. Journal of Philosophy. 119(1), pp. 5-32. https://doi.org/10.5840/jphil202211911
Being in a position to know
Yli-Vakkuri, Juhani and Hawthorne, John. (2022). Being in a position to know. Philosophical Studies. 179, pp. 1323-1339. https://doi.org/10.1007/s11098-021-01709-x
Knowledge from multiple experiences
Goldstein, Simon and Hawthorne, John. (2022). Knowledge from multiple experiences. Philosophical Studies. 179(4), pp. 1341-1372. https://doi.org/10.1007/s11098-021-01710-4
Counterfactual contamination
Goldstein, Simon and Hawthorne, John. (2022). Counterfactual contamination. Australasian Journal of Philosophy. 100(2), pp. 262-278. https://doi.org/10.1080/00048402.2021.1886129
The epistemic use of ‘ought’
Hawthorne, John Patrick. (2021). The epistemic use of ‘ought’. In Conditionals, Probability & Paradox: Themes from the Philosophy of Dorothy Edgington pp. 164-173 Oxford University Press. https://doi.org/10.1093/oso/9780198712732.003.0010
Solving a paradox of evidential equivalence
Dorr, Cian, Hawthorne, John and Isaacs, Yoaav. (2021). Solving a paradox of evidential equivalence. Mind. 130(520), pp. 1159-1182. https://doi.org/10.1093/mind/fzaa022
The rationality of epistemic akrasia
Hawthorne, John, Isaacs, Yoaav and Lasonen-Aarnio, Maria. (2021). The rationality of epistemic akrasia. Philosophical Perspectives. 35(1), pp. 206-228. https://doi.org/10.1111/phpe.12144
Wanting what’s not best
Blumberg, Kyle and Hawthorne, John. (2021). Wanting what’s not best. Philosophical Studies. 179(4), pp. 1275-1296. https://doi.org/10.1007/s11098-021-01707-z
The bounds of possibility : Puzzles of modal variation
Dorr, Cian, Hawthorne, John and Yli-Vakkuri, Juhani. (2021). The bounds of possibility : Puzzles of modal variation Oxford University Press. https://doi.org/10.1093/oso/9780192846655.001.0001
Scotus on universals
Hawthorne, John. (2021). Scotus on universals. In In Pasnau, Robert (Ed.). Oxford studies in medieval philosophy : Volume 4 pp. 64-77 Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198786368.003.0003
Reply to Speaks
Yli-Vakkuri, Juhani and Hawthorne, John. (2021). Reply to Speaks. Philosophical Studies. 178(9), pp. 3061-3065. https://doi.org/10.1007/s11098-020-01553-5
Reply to Pietroski
Yli-Vakkuri, Juhani and Hawthorne, John. (2021). Reply to Pietroski. Philosophical Studies. 178(9), pp. 3055-3059. https://doi.org/10.1007/s11098-020-01552-6
Reply to Byrne
Yli-Vakkuri, Juhani and Hawthorne, John. (2021). Reply to Byrne. Philosophical Studies. 178(9), pp. 3049-3054. https://doi.org/10.1007/s11098-020-01551-7
Graded epistemic justification
Hawthorne, John and Logins, Artūrs. (2020). Graded epistemic justification. Philosophical Studies. 178(6), pp. 1845-1858. https://doi.org/10.1007/s11098-020-01512-0
Indexicality, de re belief, and narrow content : A reply to Sawyer
Yli-Vakkuri, Juhani and Hawthorne, John. (2020). Indexicality, de re belief, and narrow content : A reply to Sawyer. Inquiry. pp. 1-11. https://doi.org/10.1080/0020174X.2020.1831852
Knowledge, practical adequacy and stakes
Anderson, Charity and Hawthorne, John. (2019). Knowledge, practical adequacy and stakes. In In Gendler, Tamar Szabó and Hawthorne, John (Ed.). Oxford studies in epistemology, Volume 6 pp. 234-257 Oxford University Press. https://doi.org/10.1093/oso/9780198833314.003.0010
Pragmatic Encroachment and Closure
Anderson, Charity and Hawthorne, John. (2019). Pragmatic Encroachment and Closure. In In B. Kim and M. McGrath (Ed.). Pragmatic Encroachment in Epistemology pp. 107 - 115 Routledge. https://doi.org/10.4324/9781315168197
Knowledge of objective modality
Strohminger, Margot and Yli-Vakkuri, Juhani. (2019). Knowledge of objective modality. Philosophical Studies. 176(5), pp. 1155 - 1175. https://doi.org/10.1007/s11098-018-1052-4
Operator arguments revisited
Fritz, Peter, Hawthorne, John and Yli-Vakkuri, Juhani. (2019). Operator arguments revisited. Philosophical Studies. 176(11), pp. 2933 - 2959. https://doi.org/10.1007/s11098-018-1158-8
Possible Patterns
Russell, Jeffrey Sanford and Hawthorne, John. (2018). Possible Patterns. In In K. Bennett and D. W. Zimmerman (Ed.). Oxford Studies in Metaphysics pp. 149 - 193 Oxford University Press. https://doi.org/10.1093/oso/9780198828198.003.0005
Narrow content
Yli-Vakkuri, Juhani and Hawthorne, John. (2018). Narrow content Oxford University Press. https://doi.org/10.1093/oso/9780198785965.001.0001
Reflections on the Ideology of Reasons
Hawthorne, John and Magidor, Ofra. (2018). Reflections on the Ideology of Reasons. In In D. Star (Ed.). The Oxford Handbook of Reasons and Normativity pp. 113 - 142 Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199657889.013.6
Fine-tuning Fine-tuning
Hawthorne, John and Isaacs, Yoaav. (2018). Fine-tuning Fine-tuning. In In M. A. Bentone, J. Hawthorne and D. Rabinowitz (Ed.). Knowledge, Belief, and God: New Insights in Religious Epistemology pp. 136 - 168 Oxford University Press. https://doi.org/10.1093/oso/9780198798705.003.0008
Narrow content and ur-content
Yli-Vakkuri, Juhani and Hawthorne, John. (2018). Narrow content and ur-content. In Narrow Content pp. 72 - 105 Oxford University Press. https://doi.org/10.1093/oso/9780198785965.003.0004
Quasi-internalism
Yli-Vakkuri, Juhani and Hawthorne, John. (2018). Quasi-internalism. In Narrow Content pp. 158 - 175 Oxford University Press. https://doi.org/10.1093/oso/9780198785965.003.0006
Rationality and narrow content
Yli-Vakkuri, Juhani and Hawthorne, John. (2018). Rationality and narrow content. In Narrow Content pp. 130 - 157 Oxford University Press. https://doi.org/10.1093/oso/9780198785965.003.0005
Moderate modal skepticism
Strohminger, Margot and Yli-Vakkuri, Juhani. (2018). Moderate modal skepticism. In In M. A. Benton, J. Hawthorne and D. Rabinowitz (Ed.). Knowledge, Belief, and God: New Insights in Religious Epistemology pp. 302 - 321 Oxford University Press. https://doi.org/10.1093/oso/9780198798705.003.0016
Truth-conditionality
Yli-Vakkuri, Juhani and Hawthorne, John. (2018). Truth-conditionality. In Narrow Content pp. 63 - 97 Oxford University Press. https://doi.org/10.1093/oso/9780198785965.003.0003
Semantic externalism without thought experiments
Yli-Vakkuri, Juhani. (2018). Semantic externalism without thought experiments. Analysis. 78(1), pp. 81 - 89. https://doi.org/10.1093/analys/anx127
What is narrow content?
Yli-Vakkuri, Juhani and Hawthorne, John. (2018). What is narrow content? In Narrow Content pp. 1 - 46 Oxford University Press. https://doi.org/10.1093/oso/9780198785965.003.0002
Knowledge and false belief
Hawthorne, John. (2017). Knowledge and false belief. In In Borges, Rodrigo, de Almeida, Claudio and Klein, Peter D. (Ed.). Explaining knowledge : New essays on the gettier problem pp. 325-344 Oxford University Press. https://doi.org/10.1093/oso/9780198724551.003.0020
Misapprehensions about the fine-tuning argument
Hawthorne, John and Isaacs, Yoaav. (2017). Misapprehensions about the fine-tuning argument. Religious Epistemology. 81, pp. 133 - 155. https://doi.org/10.1017/S1358246117000297
The epistemology of modality
Strohminger, Margot and Yli-Vakkuri, Juhani. (2017). The epistemology of modality. Analysis. 77(4), pp. 825 - 838. https://doi.org/10.1093/analys/anx058
Evil and evidence
Benton, Matthew A., Hawthorne, John and Isaacs, Yoaav. (2016). Evil and evidence. In In Kvanvig, Jonathan (Ed.). Oxford studies in philosophy of religion : Volume 7 pp. 1-31 Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198757702.003.0001
Epistemicism and modality
Yli-Vakkuri, Juhani. (2016). Epistemicism and modality. Canadian Journal of Philosophy. 46(4-5), pp. 803 - 835. https://doi.org/10.1080/00455091.2016.1201878
Higher-order free logic and the prior-Kaplan paradox
Bacon, Andrew, Hawthorne, John and Uzquiano, Gabriel. (2016). Higher-order free logic and the prior-Kaplan paradox. Canadian Journal of Philosophy. 46(4-5), pp. 493 - 541. https://doi.org/10.1080/00455091.2016.1201387
Belief is weak
Hawthorne, John, Rothschild, Daniel and Spectre, Levi. (2016). Belief is weak. Philosophical Studies. 173(5), pp. 1393 - 1404. https://doi.org/10.1007/s11098-015-0553-7
General dynamic trivality theorems
Russell, Jeffrey Sanford and Hawthorne, John. (2016). General dynamic trivality theorems. The Philosophical Review. 125(3), pp. 307 - 339. https://doi.org/10.1215/00318108-3516936
Higher-order free logic and the Prior-Kaplan paradox
Bacon, Andrew, Hawthorne, John and Uzquiano, Gabriel. (2016). Higher-order free logic and the Prior-Kaplan paradox. Canadian Journal of Philosophy. 46(4-5), pp. 493 - 541. https://doi.org/10.1080/00455091.2016.1201387
Vagueness and modality - An ecumenical approach
Litland, Jon Erling and Yli-Vakkuri, Juhani. (2016). Vagueness and modality - An ecumenical approach. Philosophical Perspectives. 30(1), pp. 229 - 269. https://doi.org/10.1111/phpe.12088
Some remarks on imagination and convention
Hawthorne, John. (2016). Some remarks on imagination and convention. Mind and Language. 31(5), pp. 625 - 634. https://doi.org/10.1111/mila.12123
Comments on transient truths: An essay in the metaphysics of propositions (Berit Brogaard)
Hawthorne, John. (2015). Comments on transient truths: An essay in the metaphysics of propositions (Berit Brogaard). Inquiry. 58(6), pp. 617 - 624. https://doi.org/10.1080/0020174X.2015.1077014
Cretan deductions
Fraser, Rachel Elizabeth and Hawthorne, John. (2015). Cretan deductions. Philosophical Perspectives. 29(1), pp. 163 - 178. https://doi.org/10.1111/phpe.12070
Groupthink
Russell, Jeffrey Sanford, Hawthorne, John and Buchak, Lara. (2015). Groupthink. Philosophical Studies. 172(5), pp. 1287 - 1309. https://doi.org/10.1007/s11098-014-0350-8
Semantic plasticity and speech reports
Dorr, Cian and Hawthorne, John. (2014). Semantic plasticity and speech reports. The Philosophical Review. 123(3), pp. 281 - 338. https://doi.org/10.1215/00318108-2683531
Semantic plasticity and speech reports
Dorr, Cian and Hawthorne, John. (2014). Semantic plasticity and speech reports. The Philosophical Review. 123(3), pp. 281 - 338. https://doi.org/10.1215/00318108-2683531
Knowing against the odds
Dorr, Cian, Goodman, Jeremy and Hawthorne, John. (2014). Knowing against the odds. Philosophical Studies. 170(2), pp. 277 - 287. https://doi.org/10.1007/s11098-013-0212-9