Semantic Realism: Why Mathematicians Mean What They Say
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Description: Article by Elaine Landry presented at the 20th World Congress of Philosophy. She argues that if we distinguish between semantic realism and ontological realism, then we can be Platonists and Formalists at the same time. (It is fair to warn readers that her definition of semantic realism is an odd one).
20th WCP: Semantic Realism: Why Mathematicians Mean What They Say Semantic Realism: Why Mathematicians Mean What They Say I argue that if we distinguish between ontological realism and semantic realism, then we no longer have to choose between platonism and formalism. If we take category theory as the language of mathematics, then a linguistic analysis of the content and structure of what we say in and about mathematical theories allows us to justify the inclusion of mathematical concepts and theories as legitimate objects of philosophical study. Insofar as this analysis relies on a distinction between ontological and semantic realism, it relies also on an implicit distinction between mathematics as a descriptive science and mathematics as a descriptive discourse. It is this latter distinction which gives rise to the tension between the mathematician
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