Topoi 29 (1):61-75 (2010)

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.
Keywords Philosophy of mathematics  Finitism  Arithmetization  Kronecker
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DOI 10.1007/s11245-009-9067-2
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The Genesis of Ideal Theory.Harold M. Edwards - 1980 - Archive for History of Exact Sciences 23 (4):321-378.
Purity as an Ideal of Proof.Michael Detlefsen - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 179-197.

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