The nature of innovation and advancement in mathematics : A philosophical investigation
Degree GrantorUniversity of Canterbury
This paper seeks a philosophical explanation as to why certain mathematical settings seem more accommodating to certain theorems, especially when this is a new setting formulated after the theorem. I will emphasise the distinction between the formal language of mathematical symbolism and its informal counterpart, conceived as & metalangauge. This distinction is characterised using the intension/ extension distinction, borrowed from the study of natural languages. The same natural language distinction is then applied to the notion of logical consequence, in order to clarify the conceptual relationships between old and new settings. It will turn out that a semantic conception of mathematical truth best explains the foregoing conclusions while at the same time avoiding the pitfalls of traditional Platonism.
SubjectsField of Research::01 - Mathematical Sciences::0101 - Pure Mathematics
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