David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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In Bob Hale & Crispin Wright (eds.), The Reason's Proper Study. Oxford University Press. 307-333 (2001)
This paper is a reply to George Boolos's three papers (Boolos (1987a, 1987b, 1990a)) concerned with the status of Hume's Principle. Five independent worries of Boolos concerning the status of Hume's Principle as an analytic truth are identified and discussed. Firstly, the ontogical concern about the commitments of Hume's Principle. Secondly, whether Hume's Principle is in fact consistent and whether the commitment to the universal number by adopting Hume's Principle might be problematic. Also the so-called `surplus content' worry is discussed, which points out that the conceptual resources to grasp Hume's Principle vastly outstrip the conceptual resources employed in arithmetical reasoning. And lastly whether Hume's Principle is in bad company with other unsuccessful implicit definitions. In the last section, an account towards our entitlement to Hume&'s Principle is sketched.
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Sean Walsh (2014). Logicism, Interpretability, and Knowledge of Arithmetic. Review of Symbolic Logic 7 (1):84-119.
Joshua Schechter & David Enoch (2006). Meaning and Justification: The Case of Modus Ponens. Noûs 40 (4):687 - 715.
Sean Walsh (2012). Comparing Peano Arithmetic, Basic Law V, and Hume's Principle. Annals of Pure and Applied Logic 163 (11):1679-1709.
Øystein Linnebo (2009). Bad Company Tamed. Synthese 170 (3):371 - 391.
Øystein Linnebo (2009). Introduction. Synthese 170 (3):321-329.
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