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How can physics account for mathematical truth?

Szabo, Laszlo E. (2010) How can physics account for mathematical truth? [Preprint]

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    If physicalism is true, everything is physical. In other words, everything supervenes on, or is necessitated by, the physical. Accordingly, if there are logical/mathematical facts, they must be necessitated by the physical facts of the world. In this paper, I will sketch the first steps of a physicalist philosophy of mathematics; that is, how physicalism can account for logical and mathematical facts. We will proceed as follows. First we will clarify what logical/mathematical facts actually are. Then, we will discuss how these facts can be accommodated in the physicalist ontology. This might sound like immanent realism (as in Mill, Armstrong, Kitcher, or Maddy), according to which the mathematical concepts and propositions reflect some fundamental features of the physical world. Although, in my final conclusion I will claim that mathematical and logical truths do have contingent content in a sophisticated sense, and they are about some peculiar part of the physical world, I reject the idea, as this thesis is usually understood, that mathematics is about the physical world in general. In fact, I reject the idea that mathematics is about anything. In contrast, the view I am proposing here will be based on the strongest formalist approach to mathematics.

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    Item Type: Preprint
    Keywords: physicalism, mathematical truth, formalism, formal system, physical theory, empiricism
    Subjects: General Issues > Theory/Observation
    General Issues > Logical Positivism/Logical Empiricism
    General Issues > Laws of Nature
    Specific Sciences > Mathematics
    General Issues > Reductionism/Holism
    General Issues > Structure of Theories
    Specific Sciences > Physics
    Depositing User: Laszlo E. Szabo
    Date Deposited: 07 May 2010
    Last Modified: 01 Jul 2012 00:24
    Item ID: 5338

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