Indeterminacy, coincidence, and “Sourcing Newness” in mathematical research

Synthese 200 (1):1-23 (2022)

Abstract

Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías :434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical facts a coincidence is roughly to suggest that the investigation of connections between these facts isn’t worthwhile. To say of this pair, “That’s no coincidence!” is to suggest just the opposite. I further argue that this perspective on mathematical coincidence, which pays special attention to what mathematical coincidences do, may provide us with a better view of what mathematical coincidences are than extant accounts. I close by reflecting on how understanding mathematical coincidences as generating indeterminacy accords with a conception of mathematical research as ultimately aiming to reduce indeterminacy and complexity to triviality as proposed in Rota Indiscrete thoughts, Birkhäuser, 1997).

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,660

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2022-02-23

Downloads
6 (#1,141,205)

6 months
2 (#259,525)

Historical graph of downloads
How can I increase my downloads?

Similar books and articles

What Are Mathematical Coincidences ?M. Lange - 2010 - Mind 119 (474):307-340.
Deep Metaphysical Indeterminacy.Bradford Skow - 2010 - Philosophical Quarterly 60 (241):851 - 858.
Quantum Indeterminacy.Claudio Calosi & Cristian Mariani - 2021 - Philosophy Compass 16 (4):e12731.
On the Referential Indeterminacy of Logical and Mathematical Concepts.Otávio Bueno - 2005 - Journal of Philosophical Logic 34 (1):65 - 79.
Against Quantum Indeterminacy.David Glick - 2017 - Thought: A Journal of Philosophy 6 (3):204-213.
Must We Know What We Mean?Kuang-Ming Cheng - 2005 - Kriterion - Journal of Philosophy 19 (1):21-33.
Indeterminacy and Interpretation.Günter Abel - 1994 - Inquiry: An Interdisciplinary Journal of Philosophy 37 (4):403 – 419.
Kripkenstein: Rule and Indeterminacy.Xin Sheen Liu - 1998 - The Paideia Archive: Twentieth World Congress of Philosophy 32:67-75.
Can Deflationism Allow for Hidden Indeterminacy?Ken Akiba - 2002 - Pacific Philosophical Quarterly 83 (3):223–234.
Why Even Kim‐Style Psychophysical Laws Are Impossible.Steven G. Daniel - 1999 - Pacific Philosophical Quarterly 80 (3):225-237.

References found in this work

On the Plurality of Worlds.David Lewis - 1986 - Wiley-Blackwell.
After Virtue: A Study in Moral Theory.Alasdair C. MacIntyre - 1983 - University of Notre Dame Press.
The Moral Problem.Michael Smith (ed.) - 1994 - Wiley.
Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.

View all 67 references / Add more references

Citations of this work

No citations found.

Add more citations