PhilSci Archive

Indeterminacy, Coincidence, and "Sourcing Newness" in Mathematical Research

Martin, James V. (2021) Indeterminacy, Coincidence, and "Sourcing Newness" in Mathematical Research. [Preprint]

[img]
Preview
Text
indeterminacy.pdf

Download (288kB) | Preview

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(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 research directions. I suggest that to call a pair of mathematical facts (merely) 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(1997)].


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Martin, James V.james.v.martin@wmich.edu0000-0003-4924-4578
Additional Information: forthcoming in Synthese
Keywords: indeterminacy; mathematical coincidence; mathematical practice
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Values
Depositing User: James Martin
Date Deposited: 10 Nov 2021 16:26
Last Modified: 10 Nov 2021 16:26
Item ID: 19806
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Values
Date: 2021
URI: https://philsci-archive.pitt.edu/id/eprint/19806

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item