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Full-Text Articles in Logic and Foundations
What Is A Number?, Nicholas Radley
What Is A Number?, Nicholas Radley
HON499 projects
This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.
A Foundation For Arithmetic, Kevin Halasz
A Foundation For Arithmetic, Kevin Halasz
Summer Research
This paper contains a proof of Frege's Theorem: the statement, first discovered by George Boolos, that Gottlob Frege's failed proof of the analyticity of arithmetic could be slightly altered so as to provide an axiomitization of arithmetic with just one proposition. After an expository treatment of the mathematical work in Frege's 'Foundations of Arithmetic,' the work in which Frege presented his failed proof, a novel, and particularly succinct, proof of the Theorem is provided.
A Philosophical Examination Of Proofs In Mathematics, Eric Almeida
A Philosophical Examination Of Proofs In Mathematics, Eric Almeida
Undergraduate Review
No abstract provided.