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  1. added 2020-05-27
    What Are Numbers?Joongol Kim - 2013 - Synthese 190 (6):1099-1112.
    This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and (...)
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  2. added 2020-05-19
    A Strengthening of the Caesar Problem.Joongol Kim - 2011 - Erkenntnis 75 (1):123-136.
    The neo-Fregeans have argued that definition by abstraction allows us to introduce abstract concepts such as direction and number in terms of equivalence relations such as parallelism between lines and one-one correspondence between concepts. This paper argues that definition by abstraction suffers from the fact that an equivalence relation may not be sufficient to determine a unique concept. Frege’s original verdict against definition by abstraction is thus reinstated.
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  3. added 2020-05-15
    The Julio César Problem.Fraser MacBride - 2005 - Dialectica 59 (2):223-236.
    One version of the Julius Caesar problem arises when we demand assurance that expressions drawn from different theories or stretches of discourse refer to different things. The counter‐Caesar problem arises when assurance is demanded that expressions drawn from different theories. refer to the same thing. The Julio César problem generalises from the counter‐Caesar problem. It arises when we seek reassurance that expressions drawn from different languages refer to the same kind of things. If the Julio César problem is not resolved (...)
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  4. added 2020-05-15
    The Julius Caesar Objection.Richard Heck - 1997 - In Richard G. Heck (ed.), Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford University Press. pp. 273--308.
    This paper argues that that Caesar problem had a technical aspect, namely, that it threatened to make it impossible to prove, in the way Frege wanted, that there are infinitely many numbers. It then offers a solution to the problem, one that shows Frege did not really need the claim that "numbers are objects", not if that claim is intended in a form that forces the Caesar problem upon us.
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  5. added 2020-05-11
    Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic.Matthias Schirn - 2003 - Erkenntnis 59 (2):203 - 232.
    In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar (...)
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  6. added 2020-05-07
    Abstraction and Identity.Roy T. Cook & Philip A. Ebert - 2005 - Dialectica 59 (2):121–139.
    A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
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  7. added 2020-05-07
    The Julio César Problem.Fraser MacBride - 2005 - Dialectica 59 (2):223–236.
    One version of the Julius Caesar problem arises when we demand assurance that expressions drawn from different theories or stretches of discourse refer to different things. The counter‐Caesar problem arises when assurance is demanded that expressions drawn from different theories . refer to the same thing. The Julio César problem generalises from the counter‐Caesar problem. It arises when we seek reassurance that expressions drawn from different languages refer to the same kind of things . If the Julio César problem is (...)
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  8. added 2020-05-05
    Julius Caesar and the Numbers.Nathan Salmón - 2018 - Philosophical Studies 175 (7):1631-1660.
    This article offers an interpretation of a controversial aspect of Frege’s The Foundations of Arithmetic, the so-called Julius Caesar problem. Frege raises the Caesar problem against proposed purely logical definitions for ‘0’, ‘successor’, and ‘number’, and also against a proposed definition for ‘direction’ as applied to lines in geometry. Dummett and other interpreters have seen in Frege’s criticism a demanding requirement on such definitions, often put by saying that such definitions must provide a criterion of identity of a certain kind. (...)
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  9. added 2020-05-05
    Solving the Caesar Problem Without Categorical Sortals.Nikolaj Jang Pedersen - 2009 - Erkenntnis 71 (2):141-155.
    The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y , the number of X ’s is the same as the number of Y ’s just in case there is a 1–1 correspondence between X and Y . The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik , emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of (...)
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  10. added 2020-05-05
    The Julius Caesar Objection : More Problematic Than Ever.Fraser MacBride - 2006 - In Identity and Modality. Oxford University Press. pp. 174.
    This paper investigates the meta-ontological problem, what is the Julius Caesar objection? I distinguish epistemic, metaphysical and semantic versions. I argue that neo-Fregean and supervaluationist solutions to the Caesar objection fails because, amongst other flaws, they fail to determine which version of the problem is in play.
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  11. added 2020-05-05
    The Caesar Problem in its Historical Context: Mathematical Background.Jamie Tappenden - 2005 - Dialectica 59 (2):237–264.
    The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.
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  12. added 2020-05-05
    Caesar From Frege's Perspective.Gary Kemp - 2005 - Dialectica 59 (2):179-199.
    I attempt to explain Frege's handling of the Julius Caesar issue in terms of his more general philosophical commitments. These only became fully explicit in his middle-period writings, but his earlier moves are best explained, I suggest, if we suppose them to be implicit in his earlier thinking. These commitments conditionally justify Frege in rejecting Hume's Principle as either a definition or axiom but in accepting Axiom V. However, the general epistemological picture they constitute has serious problems in accounting for (...)
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  13. added 2020-05-05
    Hale on Caesar.Peter Sullivan & Michael Potter - 1997 - Philosophia Mathematica 5 (2):135--52.
    Crispin Wright and Bob Hale have defended the strategy of defining the natural numbers contextually against the objection which led Frege himself to reject it, namely the so-called ‘Julius Caesar problem’. To do this they have formulated principles (called sortal inclusion principles) designed to ensure that numbers are distinct from any objects, such as persons, a proper grasp of which could not be afforded by the contextual definition. We discuss whether either Hale or Wright has provided independent motivation for a (...)
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  14. added 2020-05-04
    Julius Caesar and Basic Law V.Richard G. Heck - 2005 - Dialectica 59 (2):161–178.
    This paper dates from about 1994: I rediscovered it on my hard drive in the spring of 2002. It represents an early attempt to explore the connections between the Julius Caesar problem and Frege's attitude towards Basic Law V. Most of the issues discussed here are ones treated rather differently in my more recent papers "The Julius Caesar Objection" and "Grundgesetze der Arithmetik I 10". But the treatment here is more accessible, in many ways, providing more context and a better (...)
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  15. added 2020-05-04
    What is Frege's Julius Caesar Problem?Dirk Greimann - 2003 - Dialectica 57 (3):261-278.
    This paper aims to determine what kind of problem Frege's famous “Julius Caesar problem” is. whether it is to be understood as the metaphysical problem of determining what kind of things abstract objects like numbers or value‐courses are, or as the epistemological problem of providing a means of recognizing these objects as the same again, or as the logical problem of providing abstract sortal concepts with a sharp delimitation in order to fulfill the law of excluded middle, or as the (...)
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  16. added 2020-05-03
    Frege on Referentiality and Julius Caesar in Grundgesetze Section 10.Bruno Bentzen - 2019 - Notre Dame Journal of Formal Logic 60 (4):617-637.
    This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It (...)
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