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

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

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
Categories (categorize this paper)
DOI 10.1007/s11245-009-9067-2
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,066
Through your library

References found in this work BETA

Purity as an Ideal of Proof.Michael Detlefsen - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 179-197.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

The Fine-Tuning Argument.M. C. Bradley - 2001 - Religious Studies 37 (4):451-466.
Astrophysical Fine Tuning, Naturalism, and the Contemporary Design Argument.Mark A. Walker & M. Milan - 2006 - International Studies in the Philosophy of Science 20 (3):285 – 307.
Should We Care About Fine-Tuning?Jeffrey Koperski - 2005 - British Journal for the Philosophy of Science 56 (2):303-319.
Fine-Tuning and the Infrared Bull’s-Eye.John T. Roberts - 2012 - Philosophical Studies 160 (2):287-303.
The Fine-Tuning Argument.Neil A. Manson - 2009 - Philosophy Compass 4 (1):271-286.


Added to PP index

Total views
131 ( #53,842 of 2,236,359 )

Recent downloads (6 months)
17 ( #42,000 of 2,236,359 )

How can I increase my downloads?


My notes

Sign in to use this feature