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  1. added 2020-05-29
    On the Philosophical Interest of Frege Arithmetic.William Demopoulos - 2003 - Philosophical Books 44 (3):220-228.
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  2. added 2020-05-25
    Frege's Result: Frege's Theorem and Related Matters.Hirotoshi Tabata - 2012 - Frontiers of Philosophy in China 7 (3):351-366.
    One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.
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  3. added 2020-05-24
    Richard G. Heck, Jr.: Frege’s Theorem. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-733.
  4. added 2020-05-22
    Frege's Theorem and Foundations for Arithmetic.Edward N. Zalta - Spring 2015 - In Stanford Encyclopedia of Philosophy.
    The principal goal of this entry is to present Frege's Theorem (i.e., the proof that the Dedekind-Peano axioms for number theory can be derived in second-order logic supplemented only by Hume's Principle) in the most logically perspicuous manner. We strive to present Frege's Theorem by representing the ideas and claims involved in the proof in clear and well-established modern logical notation. This prepares one to better prepared to understand Frege's own notation and derivations, and read Frege's original work (whether in (...)
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  5. added 2020-05-22
    Richard G. Heck, Jr. , Frege's Theorem . Reviewed By. [REVIEW]Manuel Bremer - 2012 - Philosophy in Review 32 (4):319-325.
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  6. added 2020-05-22
    Frege's Logic, Theorem, and Foundations for Arithmetic.Edward N. Zalta - 2010 - Stanford Encyclopedia of Philosophy.
  7. added 2020-05-22
    Frege's Theorem and the Peano Postulates.George Boolos - 1995 - Bulletin of Symbolic Logic 1 (3):317-326.
    Two thoughts about the concept of number are incompatible: that any zero or more things have a (cardinal) number, and that any zero or more things have a number (if and) only if they are the members of some one set. It is Russell's paradox that shows the thoughts incompatible: the sets that are not members of themselves cannot be the members of any one set. The thought that any (zero or more) things have a number is Frege's; the thought (...)
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  8. added 2020-05-21
    Frege's Conception of Numbers as Objects.Crispin Wright - 1983 - Aberdeen University Press.
  9. added 2020-05-20
    Frege's Theorem and His Logicism.Hirotoshi Tabata - 2000 - History and Philosophy of Logic 21 (4):265-295.
    As is well known, Frege gave an explicit definition of number (belonging to some concept) in ?68 of his Die Grundlagen der Arithmetik.
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  10. added 2020-05-20
    On the Philosophical Significance of Frege's Theorem.Crispin Wright - 1997 - In Richard G. Heck (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. pp. 201--44.
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  11. added 2020-05-20
    Saving Frege From Contradiction.George Boolos - 1986 - Proceedings of the Aristotelian Society 87:137--151.
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  12. added 2020-05-20
    Frege's Theory of Numbers.Charles Parsons - 1965 - In M. Black (ed.), Philosophy in America. Cornell University Press. pp. 180-203.
  13. added 2020-05-19
    Review of Frege's Theorem[REVIEW]G. Aldo Antonelli - 2012 - International Studies in the Philosophy of Science 26 (2):219-222.
  14. added 2020-05-19
    Frege's Theorem.Richard G. Heck - 2011 - Clarendon Press.
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
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  15. added 2020-05-18
    Frege's Theorem. [REVIEW]P. Ebert - 2014 - Philosophical Quarterly 64 (254):166-169.
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  16. added 2020-05-17
    Frege’s Theorem by Richard G. Heck, Jr. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-732.
  17. added 2020-05-12
    Reading Frege's Grundgesetze.Richard Heck - 2012 - Oxford University Press.
    Richard G. Heck presents a new account of Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, which establishes it as a neglected masterpiece at the center of Frege's philosophy. He explores Frege's philosophy of logic, and argues that Frege knew that his proofs could be reconstructed so as to avoid Russell's Paradox.
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  18. added 2020-05-11
    IX—Saving Frege From Contradiction.George Boolos - 1987 - Proceedings of the Aristotelian Society 87 (1):137-152.
  19. added 2020-05-10
    Why Frege Would Not Be a Neo‐Fregean.Marco Ruffino - 2003 - Mind 112 (445):51-78.
    In this paper, I seek to clarify an aspect of Frege's thought that has been only insufficiently explained in the literature, namely, his notion of logical objects. I adduce some elements of Frege's philosophy that elucidate why he saw extensions as natural candidates for paradigmatic cases of logical objects. Moreover, I argue (against the suggestion of some contemporary scholars, in particular, Wright and Boolos) that Frege could not have taken Hume's Principle instead of Axiom V as a fundamental law of (...)
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  20. added 2020-05-04
    Frege's Theorem and the Peano Postulates.George Boolos - 1995 - Bulletin of Symbolic Logic 1 (3):317-326.
  21. added 2020-05-03
    Frege’s Theorem.Richard Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
    A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.
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  22. added 2020-05-03
    Frege’s Theorem: An Introduction.Richard Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
    A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.
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