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2012 Fractal Patterns in Reasoning
David Atkinson, Jeanne Peijnenburg
Notre Dame J. Formal Logic 53(1): 15-26 (2012). DOI: 10.1215/00294527-1626500


This paper is the third and final one in a sequence of three. All three papers emphasize that a proposition can be justified by an infinite regress, on condition that epistemic justification is interpreted probabilistically. The first two papers showed this for one-dimensional chains and for one-dimensional loops of propositions, each proposition being justified probabilistically by its precursor. In the present paper we consider the more complicated case of two-dimensional nets, where each "child" proposition is probabilistically justified by two "parent" propositions. Surprisingly, it turns out that probabilistic justification in two dimensions takes on the form of Mandelbrot's iteration. Like so many patterns in nature, probabilistic reasoning might in the end be fractal in character.


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David Atkinson. Jeanne Peijnenburg. "Fractal Patterns in Reasoning." Notre Dame J. Formal Logic 53 (1) 15 - 26, 2012.


Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1238.03018
MathSciNet: MR2925266
Digital Object Identifier: 10.1215/00294527-1626500

Primary: 60A99

Rights: Copyright © 2012 University of Notre Dame


Vol.53 • No. 1 • 2012
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