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

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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 04:24  
Item ID:  5338  
URI:  http://philsciarchive.pitt.edu/id/eprint/5338 
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