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  1. added 2020-05-22
    Hume = Small Hume.Jeffrey Ketland - 2002 - Analysis 62 (1):92–93.
    We can modify Hume’s Principle in the same manner that George Boolos suggested for modifying Frege’s Basic Law V. This leads to the principle Small Hume. Then, we can show that Small Hume is interderivable with Hume’s Principle.
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  2. added 2019-05-12
    Is Hume's Principle Analytic?Crispin Wright - 1999 - Notre Dame Journal of Formal Logic 40 (1):6-30.
    One recent `neologicist' claim is that what has come to be known as "Frege's Theorem"–the result that Hume's Principle, plus second-order logic, suffices for a proof of the Dedekind-Peano postulate–reinstates Frege's contention that arithmetic is analytic. This claim naturally depends upon the analyticity of Hume's Principle itself. The present paper reviews five misgivings that developed in various of George Boolos's writings. It observes that each of them really concerns not `analyticity' but either the truth of Hume's Principle or our entitlement (...)
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  3. added 2019-04-08
    Finitude and Hume’s Principle.Richard Heck - 1997 - Journal of Philosophical Logic 26 (6):589-617.
    The paper formulates and proves a strengthening of 'Frege's Theorem', which states that axioms for second-order arithmetic are derivable in second-order logic from Hume's Principle, which itself says that the number of Fs is the same as the number of Gs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. 'Finite Hume's Principle' also suffices (...)
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  4. added 2018-12-09
    Frege's Cardinals Do Not Always Obey Hume's Principle.Gregory Landini - 2017 - History and Philosophy of Logic 38 (2):127-153.
    Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's ‘no-classes’ theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theory of cardinal numbers as objects set out in Frege's Grundgesetze. (...)
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  5. added 2018-12-09
    Hume’s Principle, Beginnings.Albert Visser - 2011 - Review of Symbolic Logic 4 (1):114-129.
    In this note we derive Robinson???s Arithmetic from Hume???s Principle in the context of very weak theories of classes and relations.
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  6. added 2018-12-09
    Hume on Deduction.Charles Echelbarger - 1987 - Philosophy Research Archives 13:351-365.
    In this paper, the author discusses the feasibility of constructing a Humean model of the psychological realities of categorical propositions and syllogistic deduction by employing only Hume’s kinds of “ideas” and kinds of mental operations on ideas which Hume explicitly or implicitly postulated in his theory of discursive thinking.
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  7. added 2016-07-12
    Why, in 1902, Wasn't Frege Prepared to Accept Hume's Principle as the Primitive Law for His Logicist Program?Kazuyuki Nomoto - 2000 - Annals of the Japan Association for Philosophy of Science 9 (5):219-230.
  8. added 2016-05-02
    In Good Company? On Hume’s Principle and the Assignment of Numbers to Infinite Concepts.Paolo Mancosu - 2015 - Review of Symbolic Logic 8 (2):370-410.
    In a recent article, I have explored the historical, mathematical, and philosophical issues related to the new theory of numerosities. The theory of numerosities provides a context in which to assign numerosities to infinite sets of natural numbers in such a way as to preserve the part-whole principle, namely if a set A is properly included in B then the numerosity of A is strictly less than the numerosity of B. Numerosities assignments differ from the standard assignment of size provided (...)
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  9. added 2016-05-02
    Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171-227.
    In this paper, I shall discuss several topics related to Frege's paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege's notion of evidence and its interpretation by Jeshion, the introduction (...)
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  10. added 2016-05-02
    Axiom V and Hume's Principle in Frege's Foundational Project.Matthias Schirn - 1995 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 30 (66):7-20.
  11. added 2016-05-02
    How Far Can Hume is-Ought Thesis Be Generalized,(Vol 20, Pg 37, 1991).G. Schurz - 1995 - Journal of Philosophical Logic 24 (6):667-668.
  12. added 2016-05-02
    Tesi di Hume E Sistemi di Logica Deontica.Sergio Galvan - 1988 - Epistemologia 11 (2):183.
  13. added 2016-05-02
    What is Hume's Doctrine of Negation.Robert W. Burch - 1976 - International Logic Review 7:236-242.
  14. added 2015-01-24
    The Contemporary Interest of an Old Doctrine.William Demopoulos - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:209 - 216.
    We call Frege's discovery that, in the context of second-order logic, Hume's principle-viz., The number of Fs = the number of Gs if, and only if, F a G, where F a G (the Fs and the Gs are in one-to-one correspondence) has its usual, second-order, explicit definition-implies the infinity of the natural numbers, Frege's theorem. We discuss whether this theorem can be marshalled in support of a possibly revised formulation of Frege's logicism.
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  15. added 2015-01-14
    Hume on Deduction.Charles Echelbarger - 1987 - Philosophy Research Archives 13:351-365.
    In this paper, the author discusses the feasibility of constructing a Humean model of the psychological realities of categorical propositions and syllogistic deduction by employing only Hume’s kinds of “ideas” and kinds of mental operations on ideas which Hume explicitly or implicitly postulated in his theory of discursive thinking.
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  16. added 2015-01-11
    Hume, Precursor of Modern Empiricism: An Analysis of His Opinions on Meaning, Metaphysics, Logic, and Mathematics.Farhang Zabeeh - 1960 - The Hague: M. Nijhoff.
  17. added 2015-01-06
    Hume's "Dialectic".Dorothy P. Coleman - 1984 - Hume Studies 10 (2):139-155.
  18. added 2014-04-02
    Hume's Foundational Project in the Treatise.Miren Boehm - 2016 - European Journal of Philosophy 24 (1):55-77.
    In the Introduction to the Treatise Hume very enthusiastically announces his project to provide a secure and solid foundation for the sciences by grounding them on his science of man. And Hume indicates in the Abstract that he carries out this project in the Treatise. But most interpreters do not believe that Hume's project comes to fruition. In this paper, I offer a general reading of what I call Hume's ‘foundational project’ in the Treatise, but I focus especially on Book (...)
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  19. added 2014-03-26
    Hume's Inductive Logic.Alberto Mura - 1998 - Synthese 115 (3):303-331.
    This paper presents a new account of Hume’s “probability of causes”. There are two main results attained in this investigation. The first, and perhaps the most significant, is that Hume developed – albeit informally – an essentially sound system of probabilistic inductive logic that turns out to be a powerful forerunner of Carnap’s systems. The Humean set of principles include, along with rules that turn out to be new for us, well known Carnapian principles, such as the axioms of semiregularity, (...)
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  20. added 2014-01-19
    Comments on 'Hume's Master Argument'.Charles Pigden - 2010 - In Hume on Is and Ought. Palgrave-Macmillan. pp. 128-142.
    This is a commentary on Adrian Heathcote’s interesting paper ‘Hume’s Master Argument’. Heathcote contends that No-Ought-From-Is is primarily a logical thesis, a ban on Is/Ought inferences which Hume derives from the logic of Ockham. NOFI is thus a variation on what Heathcote calls ‘Hume’s Master Argument’, which he also deploys to prove that conclusions about the future (and therefore a-temporal generalizations) cannot be derived by reason from premises about the past, and that conclusions about external objects or other minds cannot (...)
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  21. added 2013-11-26
    Three Interviews.Miro Brada - manuscript
    To support my Phd theses and results of my grant research in 1999, I asked 1) prominent chemist Antonín Holý, author of substances to treat hepatitis and HIV, about the indivisibility of the art and science (published in Slovak Narodna Obroda and Czech blisty,cz), 2) the distinguished economist William Baumol about the alternative activities (published in Slovak Nove Slovo, Czech Respekt and blisty.cz), 3) Nobel Laureate Clive Granger about the significance of the economics (published in 2004 in Czech weekly Tyden). (...)
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  22. added 2013-11-25
    A Humean Temporal Logic.Donald L. M. Baxter - 2000 - The Proceedings of the Twentieth World Congress of Philosophy 2000 (Analytic Philosophy and Logic):209-216.
    Hume argues that the idea of duration is just the idea of the manner in which several things in succession are arrayed. In other words, the idea of duration is the idea of successiveness. He concludes that all and only successions have duration. Hume also argues that there is such a thing as a steadfast object—something which co-exists with many things in succession, but which is not itself a succession. Thus, it seems that Hume has committed himself to a contradiction: (...)
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  23. added 2013-09-04
    Certainty, Necessity, and Knowledge in Hume's Treatise.Miren Boehm - 2013 - In Stanley Tweyman (ed.), David Hume, A Tercentenary Tribute [the version in PhilPapers is the accurate, final version of the paper].
    Hume appeals to different kinds of certainties and necessities in the Treatise. He contrasts the certainty that arises from intuition and demonstrative reasoning with the certainty that arises from causal reasoning. He denies that the causal maxim is absolutely or metaphysically necessary, but he nonetheless takes the causal maxim and ‘proofs’ to be necessary. The focus of this paper is the certainty and necessity involved in Hume’s concept of knowledge. I defend the view that intuitive certainty, in particular, is certainty (...)
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  24. added 2013-09-04
    The Concept of Body in Hume’s Treatise.Miren Boehm - 2013 - ProtoSociology:206-220.
    Hume’s views concerning the existence of body or external objects are notoriously difficult and intractable. The paper sheds light on the concept of body in Hume’s Treatise by defending three theses. First, that Hume’s fundamental tenet that the only objects that are present to the mind are perceptions must be understood as methodological, rather than metaphysical or epistemological. Second, that Hume considers legitimate the fundamental assumption of natural philosophy that through experience and observation we know body. Third, that many of (...)
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  25. added 2013-09-04
    Filling the Gaps in Hume’s Vacuums.Miren Boehm - 2012 - Hume Studies 38 (1):79-99.
    The paper addresses two difficulties that arise in Treatise 1.2.5. First, Hume appears to be inconsistent when he denies that we have an idea of a vacuum or empty space yet allows for the idea of an “invisible and intangible distance.” My solution to this difficulty is to develop the overlooked possibility that Hume does not take the invisible and intangible distance to be a distance at all. Second, although Hume denies that we have an idea of a vacuum, some (...)
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  26. added 2013-08-18
    Hume on Intuitive and and Demonstrative Inference.Robert A. Imlay - 1975 - Hume Studies 1 (2):31-47.