ETD

A Possibly Correct Theory of Mathematics

Public Deposited

The abstract, platonic theory of numbers is typically taken to provide metaphysical justification for mathematical statements like “1+1=2”. For the anti-realist theory of mathematical fictionalism, a central task is finding equally compelling metaphysical justification; for instance, what distinguishes “1+1=2” from “1+1=3” if not the full-blooded existences of abstract numbers? Statements of the former kind are clearly “correct”, to some extent, while statements like the latter are likewise “incorrect”. In this paper, after briefly outlining mathematical fictionalism, I examine the most integral features of mathematics which any philosophy of mathematics need satisfy. After doing so, I survey the most influential fictionalist attempts to provide metaphysical distinction between the correct and incorrect mathematical statements. As I will show, however, none of these current responses are particularly satisfying for a philosophy of mathematics. I conclude by developing my own fictionalist theory which is in-line with the most necessary and important intuitions and conceptions about mathematics, which also neatly sorts between the metaphysically correct and incorrect mathematical statements.


MLA citation style (9th ed.)

Marks, James David. A Possibly Correct Theory of Mathematics. . 2023. dickinson.hykucommons.org/concern/etds/2c885fec-b8fe-4768-83c0-0faf9a1906da.

APA citation style (7th ed.)

M. J. David. (2023). A Possibly Correct Theory of Mathematics. https://dickinson.hykucommons.org/concern/etds/2c885fec-b8fe-4768-83c0-0faf9a1906da

Chicago citation style (CMOS 17, author-date)

Marks, James David. A Possibly Correct Theory of Mathematics. 2023. https://dickinson.hykucommons.org/concern/etds/2c885fec-b8fe-4768-83c0-0faf9a1906da.

Note: These citations are programmatically generated and may be incomplete.

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