D'Alessandro, William (2022) Unrealistic Models in Mathematics. [Preprint]
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Abstract
Models are indispensable tools of scientific inquiry, and one of their main uses is to improve our understanding of the phenomena they represent. How do models accomplish this? And what does this tell us about the nature of understanding? While much recent work has aimed at answering these questions, philosophers' focus has been squarely on models in empirical science. I aim to show that pure mathematics also deserves a seat at the table. I begin by presenting two cases: Cramér’s random model of the prime numbers and the function field model of the integers. These cases show that mathematicians, like empirical scientists, rely on unrealistic models to gain understanding of complex phenomena. They also have important implications for some much-discussed theses about scientific understanding. First, modeling practices in mathematics confirm that one can gain understanding without obtaining an explanation. Second, these cases undermine the popular thesis that unrealistic models confer understanding by imparting counterfactual knowledge.
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Item Type: | Preprint | ||||||
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Keywords: | models, modeling, unrealistic models, understanding, explanation, mathematical practice, number theory | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Practice General Issues > Explanation Specific Sciences > Mathematics General Issues > Models and Idealization |
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Depositing User: | Dr. William D'Alessandro | ||||||
Date Deposited: | 02 Oct 2022 16:57 | ||||||
Last Modified: | 02 Oct 2022 16:57 | ||||||
Item ID: | 21225 | ||||||
DOI or Unique Handle: | 10.3998/phimp.1712 | ||||||
Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Practice General Issues > Explanation Specific Sciences > Mathematics General Issues > Models and Idealization |
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Date: | 2022 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/21225 |
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