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Logic and Foundations of Mathematics

Honors Program Theses

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Why Are They Called Real Numbers If They Aren’T Real, And Other Such Questions?, Rahmat Rashid Jan 2022

Why Are They Called Real Numbers If They Aren’T Real, And Other Such Questions?, Rahmat Rashid

Honors Program Theses

This thesis studies the position of mathematical realism (the position that mathematical objects have ontological status) through history, starting with Pythagoras up until W.V.O Quine, and examining how these positions originate from each other. I hope to see how the position has changed and why, and provide an argument against the strongest of the realist positions, drawing on this extensive background. Finally, I advance my own argument against the strongest arguments for mathematical realism, and propose alternatives to a view of mathematical realism.