How discrete patterns emerge from algorithmic fine-tuning: A visual plea for kroneckerian finitism

Topoi 29 (1):61-75 (2009)
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Abstract

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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Purity as an ideal of proof.Michael Detlefsen - 2008 - In Paolo Mancosu, The Philosophy of Mathematical Practice. Oxford, GB: Oxford University Press. pp. 179-197.
The genesis of ideal theory.Harold M. Edwards - 1980 - Archive for History of Exact Sciences 23 (4):321-378.

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