PhilSci Archive

Fractal Patterns in Reasoning

Atkinson, David and Peijnenburg, Jeanne (2011) Fractal Patterns in Reasoning. [Preprint]

[img]
Preview
PDF
Download (209Kb) | Preview

    Abstract

    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.


    Export/Citation:EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
    Social Networking:

    Item Type: Preprint
    Keywords: Probabilistic justification, regress, many dimensions, Mandelbrot fractal
    Subjects: General Issues > Confirmation/Induction
    Depositing User: David Atkinson
    Date Deposited: 21 Dec 2011 10:23
    Last Modified: 21 Dec 2011 10:23
    Item ID: 8961
    URI: http://philsci-archive.pitt.edu/id/eprint/8961

    Actions (login required)

    View Item

    Document Downloads