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

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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)].
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Item Type:  Preprint  

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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://philsciarchive.pitt.edu/id/eprint/19806 
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