How Discrete Patterns Emerge from Algorithmic Fine-Tuning: A Visual Plea for Kroneckerian Finitism

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13 décembre 2009

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HAL-SHS : histoire, philosophie et sociologie des sciences et des techniques

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info:eu-repo/semantics/altIdentifier/doi/10.1007/s11245-009-9067-2

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philosophy of mathematics finitism arithmetization elliptic functions Kronecker

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Knowledge--Philosophy Mental philosophy

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Ivahn Smadja, « How Discrete Patterns Emerge from Algorithmic Fine-Tuning: A Visual Plea for Kroneckerian Finitism », HAL-SHS : histoire, philosophie et sociologie des sciences et des techniques, ID : 10.1007/s11245-009-9067-2

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This paper sets out to adduce visual evidence for Kroneckerian finitism by making perspicuous some of the insights that buttress Kronecker's conception of arithmetization as a process aiming at disclosing the arithmetical essence enshrined in analytical formulas, by spotting discrete patterns through algorithmic fine-tuning. In the light of a fairly tractable case study, it is argued that Kronecker's main tenet in philosophy of mathematics is not so much an ontological as a methodological one, inasmuch as highly demanding requirements regarding mathematical understanding prevail over mere preemptive reductionism to whole numbers.

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