PhilSci Archive

The Formulation and Justification of Mathematical Definitions Illustrated By Deterministic Chaos

Werndl, Charlotte (2009) The Formulation and Justification of Mathematical Definitions Illustrated By Deterministic Chaos. [Preprint]

[img]
Preview
PDF - Draft Version
Download (100Kb) | Preview

    Abstract

    The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification are widespread in mathematics. After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. I then go on to criticize Lakatos’s account of proof-generated definitions—the main account in the literature on this issue—as being limited and also misguided: as for topological definitions of chaos, in nearly all mathematical fields various kinds of justification are found and are also reasonable.


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

    Item Type: Preprint
    Keywords: definitions in mathematics; justification of definitions; Lakatos; chaos; mathematical reasoning
    Subjects: Specific Sciences > Physics > Classical Physics
    Specific Sciences > Mathematics
    Depositing User: Charlotte Werndl
    Date Deposited: 30 Jun 2011 07:29
    Last Modified: 30 Jun 2011 07:29
    Item ID: 8687
    URI: http://philsci-archive.pitt.edu/id/eprint/8687

    Actions (login required)

    View Item

    Document Downloads