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Mathematical Realism and Anti-Literalism

  • PHILOSOPHY·THOUGHT·CULTURE
  • 2011, (12), pp.33~66
  • Publisher : Research Institute for East-West Thought
  • Research Area : Humanities > Other Humanities

LEE JINHEE 1

1아주대학교

Candidate

ABSTRACT

Mark Balaguer argues that fictionalism is the best version of anti-realistic thesis. The most important reason of his argument is that fictionalism, unlike other nominalisms, is based on literalism which says literal meaning of mathematical sentences are platonic. But I don't agree with him. So, in this paper, I shall give a refutation of Balaguer's argument. I will show that literal or intuitive understanding of mathematical sentences does not presuppose platonic semantics. Futhermore, mathematical realism and fictionalism have the same base; it is literalism. Literalism is one of the most compelling arguments for mathematical realism. So my argument against literalism also gives a good reason for denying mathematical realism. This paper consists of three parts. In the first part, I give a general introduction to the fictionalism. In the second part, I present Balaguer's ficitionalism with his explantion of mathematical practices and mathematical truth, especially on his IBP. In the last part, I offer my reason to refute literalism and propose an alternative understanding of literal meaning of mathematical sentences. I split rationalism into two groups in relation to the sustainability of mankind. One is the dominant rationalism that human beings can control environment and may dominate nature from the narrow anthropocentrism, and the other is the ecological rationalism that human beings must make rational choices considered ecological factors for the sake of their sustainability. The ecological irrationality has increased greatly by the dominant rationalism. In other words, the dominant rationalism has only made environmental pollution, climatic change, and natural resource depletion worse. Therefore, the ecological rationalism as the extended rationalism has been made the urgent demand for the solution to ecological problems. The dominant rationalism has failed because it tried dominating nature without full understanding of her. For the sake of the sustainability of mankind, we have to preserve abundant nature, and restore destructed environment and eco-system. The person who fully understands nature can manage her well. The ecological rationalism insists that we have to grasp the complicated organic causation of nature, evaluate the non-instrumental values as well as instrumental values of nature, and consider the welfare of non-human beings as well as human beings. If we managed the earth with the ecological rationality, we could raise the sustainability of mankind.

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This paper was written with support from the National Research Foundation of Korea.
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