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  1.  31
    Is Hume’s Principle Analytic?Eamon Darnell & Aaron Thomas-Bolduc - forthcoming - Synthese:1-17.
    The question of the analyticity of Hume's Principle is central to the neo-logicist project. We take on this question with respect to Frege's definition of analyticity, which entails that a sentence cannot be analytic if it can be consistently denied within the sphere of a special science. We show that HP can be denied within non-standard analysis and argue that if HP is taken to depend on Frege's definition of number, it isn't analytic, and if HP is taken to be (...)
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    Takeuti's Well-Ordering Proof: Finitistically Fine?Eamon Darnell & Aaron Thomas-Bolduc - 2018 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics The CSHPM 2017 Annual Meeting in Toronto, Ontario. Birkhäuser Basel.
    If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form. The paper begins with a historically informed discussion of (...)
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  3. Research in History and Philosophy of Mathematics: The Cshpm 2017 Annual Meeting in Toronto, Ontario.Amy Ackerberg-Hastings, Marion W. Alexander, Zoe Ashton, Christopher Baltus, Phil Bériault, Daniel J. Curtin, Eamon Darnell, Craig Fraser, Roger Godard, William W. Hackborn, Duncan J. Melville, Valérie Lynn Therrien, Aaron Thomas-Bolduc & R. S. D. Thomas (eds.) - 2018 - Springer Verlag.
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  4. Takeuti’s Well-Ordering Proof: Finitistically Fine?Eamon Darnell & Aaron Thomas-Bolduc - 2018 - In Amy Ackerberg-Hastings, Marion W. Alexander, Zoe Ashton, Christopher Baltus, Phil Bériault, Daniel J. Curtin, Eamon Darnell, Craig Fraser, Roger Godard, William W. Hackborn, Duncan J. Melville, Valérie Lynn Therrien, Aaron Thomas-Bolduc & R. S. D. Thomas (eds.), Research in History and Philosophy of Mathematics: The Cshpm 2017 Annual Meeting in Toronto, Ontario. Springer Verlag. pp. 167-180.
    If one of Gentzen’s consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert’s program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen’s second proof can be finitistically justified. In particular, the focus is on Takeuti’s purportedly finitistically acceptable proof of the well ordering of ordinal notations in Cantor normal form.The paper begins with a historically informed discussion of finitism and its limits, before (...)
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  5. Takeuti’s Well-Ordering Proof: Finitistically Fine?Eamon Darnell & Aaron Thomas-Bolduc - 2018 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics the Cshpm 2017 Annual Meeting in Toronto, Ontario. Birkhäuser. pp. 167-180.
    If one of Gentzen’s consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert’s program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen’s second proof can be finitistically justified. In particular, the focus is on Takeuti’s purportedly finitistically acceptable proof of the well ordering of ordinal notations in Cantor normal form.The paper begins with a historically informed discussion of finitism and its limits, before (...)
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