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# Frege: Value-Ranges

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1. Stipulations Missing Axioms in Frege's Grundgesetze der Arithmetik.Gregory Landini - forthcoming - History and Philosophy of Logic:1-36.
Frege's Grundgesetze der Arithmetik offers a conception of cpLogic as the study of functions. Among functions are included those that are concepts, i.e. characteristic functions whose values are the logical objects that are the True/the False. What, in Frege's view, are the objects the True/the False? Frege's stroke functions are themselves concepts. His stipulation introducing his negation stroke mentions that it yields [...]. But curiously no accommodating axiom is given, and there is no such theorem. Why is it that some (...)

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2. Logic and Sets.Marta Vlasáková - forthcoming - Logic and Logical Philosophy:1.
The notion of the extension of a concept has been used in logic for a long time. It is usually considered to be closely connected to the intuitive notion of a set and thus seems as though it should be embedded into set theory. However, there are significant differences between this “logical” concept of set and the notion of set (class) as defined via standard axiomatic systems of set theory; it may, therefore, be quite misleading to consider the two concepts (...)

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3. Frege’s View of the Context Principle After 1890.Krystian Bogucki - 2022 - Grazer Philosophische Studien 99 (1):1-29.
The aim of this article is to examine Frege’s view of the context principle in his mature philosophical doctrine. Here, the author argues that the context principle is embodied in the contextual explanation of value-ranges presented in Basic Laws of Arithmetic. The contextual explanation of value-ranges plays essentially the same role as the context principle in The Foundations of Arithmetic. It is supposed to show how a reference to natural numbers is possible. Moreover, the author argues against the view that (...)

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4. Extensions, Numbers and Frege’s Project of Logic as Universal Language.Nora Grigore - 2020 - Axiomathes 30 (5):577-588.
Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...)
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5. Extensions, Numbers and Frege’s Project of Logic as Universal Language.Nora Grigore - 2020 - Axiomathes 30 (5):577-588.
Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...)
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6. Extensions, Numbers and Frege’s Project of Logic as Universal Language.Nora Grigore - 2020 - Axiomathes 30 (5):577-588.
Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...)
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7. Frege's Cardinals and Neo-Logicism.Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):60-90.
Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding (...)

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8. Concepts, Extensions, and Frege's Logicist Project.Matthias Schirn - 2006 - Mind 115 (460):983-1006.
Although the notion of logical object plays a key role in Frege's foundational project, it has hardly been analyzed in depth so far. I argue that Marco Ruffino's attempt to fill this gap by establishing a close link between Frege's treatment of expressions of the form ‘the concept F’ and the privileged status Frege assigns to extensions of concepts as logical objects is bound to fail. I argue, in particular, that Frege's principal motive for introducing extensions into his logical theory (...)

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9. Frege’s Permutation Argument Revisited.Kai Frederick Wehmeier & Peter Schroeder-Heister - 2005 - Synthese 147 (1):43-61.
In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument), by means of which he intends to show that an arbitrary value-range may be identified with the True, and any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identifiability thesis, following Schroeder-Heister (1987)). As far as we are aware, there is no consensus in the literature as to (i) the proper interpretation of the permutation (...)

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10. Tackling Three of Frege's Problems: Edmund Husserl on Sets and Manifolds. [REVIEW]Claire Ortiz Hill - 2002 - Axiomathes 13 (1):79-104.
Edmund Husserl was one of the very first to experience the direct impact of challenging problems in set theory and his phenomenology first began to take shape while he was struggling to solve such problems. Here I study three difficulties associated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and 'Russell's paradox'.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory and to develop (...)

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11. To Err is Humeant.Mark Wilson - 1999 - Philosophia Mathematica 7 (3):247-257.
George Boolos, Crispin Wright, and others have demonstrated how most of Frege's treatment of arithmetic can be obtained from a second-order statement that Boolos dubbed ‘Hume's principle’. This note explores the historical evidence that Frege originally planned to develop a philosophical approach to numbers in which Hume's principle is central, but this strategy was abandoned midway through his Grundlagen.

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12. O principio do contexto nas Grundgesetze de Frege.Matthias Schirn - 1996 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (3):177-201.
Pretendo usar o exemplo dos nomes de percursos de valores como prova de que, contrariamente ao que Michael Resnik e Michael Dummett sustentam, Frege nunca abandonou o seu princípio do contexto: “Apenas no contexto de uma sentenya tem uma palavra significado”. Em particular, pretendo mostrar que a prova da completude com relação ao significado, que Frege tentou introduzir na linguagem formal das Grundgesetze der Arithmetik, baseia-se em uma aplicação do principio do contexto, e que, em consequencia, tambem nomes de percursos (...)
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13. Frege y los nombres de cursos de valores.Matthias Schirn - 1995 - Theoria 10 (1):109-133.
Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik (Volume I, 1893, Volume 11, 1903). More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this (...)
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14. Frege y los nombres de cursos de valores.Matthias Schirn - 1994 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 9 (2):109-133.
Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik. More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this problem in connection with the introduction (...)
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15. Frege Y Los Nombres de Cursos de Valores.Matthias Schirn - 1994 - Theoria 9 (2):109-133.
Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik (Volume I, 1893, Volume 11, 1903). More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this (...)

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16. Frege's Theory of Concepts and Objects and the Interpretation of Second-Order Logic.William Demopoulus & William Bell - 1993 - Philosophia Mathematica 1 (2):139-156.
This paper casts doubt on a recent criticism of Frege's theory of concepts and extensions by showing that it misses one of Frege's most important contributions: the derivation of the infinity of the natural numbers. We show how this result may be incorporated into the conceptual structure of Zermelo- Fraenkel Set Theory. The paper clarifies the bearing of the development of the notion of a real-valued function on Frege's theory of concepts; it concludes with a brief discussion of the claim (...)

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17. Los Wertverläufe de Frege y la teoría de conjuntos.Raúl Orayen - 1988 - Análisis Filosófico 8 (1):1.
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18. A Model-Theoretic Reconstruction of Frege's Permutation Argument.Peter Schroeder-Heister - 1987 - Notre Dame Journal of Formal Logic 28 (1):69-79.

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19. Grundgesetze, Section 10.Adrian W. Moore & Andrew Rein - 1986 - In L. Haaparanta & J. Hintikka (eds.), Frege Synthesized. D. Reidel Publishing Co.. pp. 375--384.

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20. Frege's Double Correlation Thesis and Quine's Set Theories NF and ML.Nino B. Cocchiarella - 1985 - Journal of Philosophical Logic 14 (1):1 - 39.

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21. Frege Structures and the Notions of Truth and Proposition.P. Aczel - 1980 - In J. Barwise, H. J. Keisler & K. Kunen (eds.), The Kleene Symposium. North-Holland.

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22. Hätte Frege ohne Wertverlaufsfunktion auskommen können?Peter Hinst - 1975 - In Christian Thiel (ed.), Frege und die moderne Grundlagenforschung: Symposium, gehalten in Bad Homburg im Dezember 1973. Meisenheim am Glan: Hain. pp. 33-51.
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23. Wertverlauf.Ignacio Angelelli - 1967 - In Studies on Gottlob Frege and Traditional Philosophy. Dordrecht: Springer. pp. 205-223.
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24. Dos problemas en la doctrina de Frege.Thomas M. Simpson - 1967 - Critica 1 (1):101-116.