Results for 'Axiom_of_reducibility'

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  1.  16
    The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility.Edwin D. Mares - 2007 - Notre Dame Journal of Formal Logic 48 (2):237-251.
    This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.
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  2.  4
    The Axiom of Reducibility.Russell Wahl - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1).
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  3.  18
    Report on Some Investigations Concerning the Consistency of the Axiom of Reducibility.John Myhill - 1951 - Journal of Symbolic Logic 16 (1):35-42.
  4.  3
    Review: John Myhill, Report on Some Investigations Concerning the Consistency of the Axiom of Reducibility. [REVIEW]W. V. Quine - 1951 - Journal of Symbolic Logic 16 (3):217-218.
  5.  1
    On the Axiom of Reducibility.C. H. Langford & W. V. Quine - 1937 - Journal of Symbolic Logic 2 (1):60.
  6.  1
    Review: W. V. Quine, On the Axiom of Reducibility. [REVIEW]C. H. Langford - 1937 - Journal of Symbolic Logic 2 (1):60-60.
  7. Quiné W. V.. On the Axiom of Reducibility. Mind, N.S., Vol. 45 , Pp. 498–500.C. H. Langford - 1937 - Journal of Symbolic Logic 2 (1):60.
  8. Was the Axiom of Reducibility a Principle of Logic?Bernard Linsky - 1990 - Russell: The Journal of Bertrand Russell Studies 10 (2):125.
     
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  9. Was the Axiom of Reducibility a Principle of Logic?Bernard Linsky - 1990 - Russell: The Journal of Bertrand Russell Studies 10 (2).
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  10. Report on Some Investigations Concerning the Consistency of the Axiom of Reducibility.John Myhill - 1951 - Journal of Symbolic Logic 16 (3):217-218.
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  11. A Refutation of an Unjustified Attack on the Axiom of Reducibility.John Myhill - 1979 - In Bertrand Russell & George Washington Roberts (eds.), Bertrand Russell Memorial Volume. Humanities Press. pp. 81--90.
     
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  12.  45
    On the Axiom of Reducibility.W. V. Quine - 1936 - Mind 45 (180):498-500.
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  13.  5
    Towards Finishing Off the Axiom of Reducibility.Philippe de Rouilhan - 1996 - Philosophia Scientiae 1 (3):17-35.
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  14.  4
    Russell’s Method of Analysis and the Axioms of Mathematics.Lydia Patton - 2017 - In Sandra Lapointe Christopher Pincock (ed.), Innovations in the History of Analytical Philosophy. London: Palgrave-Macmillan. pp. 105-126.
    In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, Russell’s (...)
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  15.  19
    Universal Sets for Pointsets Properly on the N Th Level of the Projective Hierarchy.Greg Hjorth, Leigh Humphries & Arnold W. Miller - 2013 - Journal of Symbolic Logic 78 (1):237-244.
    The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.
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  16.  4
    Hilbert and the Emergence of Modern Mathematical Logic.Gregory H. Moore - 1997 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1):65-90.
    Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness of propositional logic -results traditionally credited to Bernays and Post. These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its soundness and completeness: a (...)
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  17.  49
    The Definability of the Set of Natural Numbers in the 1925 Principia Mathematica.Gregory Landini - 1996 - Journal of Philosophical Logic 25 (6):597 - 615.
    In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Godel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility cannot (...)
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  18.  13
    Russell's Substitutional Theory of Classes and Relations.Gregory Landini - 1987 - History and Philosophy of Logic 8 (2):171-200.
    This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a version or modification of the substitutional (...)
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  19.  63
    Hilbert and the Emergence of Modern Mathematical Logic.Gregory H. Moore - 1997 - Theoria 12 (1):65-90.
    Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional logic -results traditionally credited to Bernays (1918) and Post (1921). These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its (...)
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  20.  14
    The Metaphysical Axioms and Ethics of Charles Hartshorne.George Allan - 1986 - Review of Metaphysics 40 (2):271 - 304.
    Hartshorne's "neoclassical metaphysics" rests implicitly on five metaphysical axioms: discontinuity, Asymmetry, Sociality, Creativity, And dipolar divinity. The first four axioms entail ethical norms crucial to democracy: non-Reducibility of individual to community, Primacy of present achievement over potential future value, Non-Reducibility of communal to individual, The importance of risk. The fifth axiom undercuts these norms, However. The notion of God as guarantor of achieved value should be dropped from hartshorne's philosophy to make it ethically consistent.
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  21.  13
    Amending Frege's "Grundgesetze der Arithmetik" to the Memory of Nhê (1925-2001).Fernando Ferreira - 2005 - Synthese 147 (1):3 - 19.
    Frege's "Grundgesetze der Arithmetik" is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege's Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the "Grundgesetze" is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...)
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  22. The Interpretation of Set Theory in Mathematical Predication Theory.Harvey M. Friedman - unknown
    This paper was referred to in the Introduction in our paper [Fr97a], “The Axiomatization of Set Theory by Separation, Reducibility, and Comprehension.” In [Fr97a], all systems considered used the axiom of Extensionality. This is appropriate in a set theoretic context.
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  23.  66
    Amending Frege's Grundgesetze der Arithmetik.Fernando Ferreira - 2005 - Synthese 147 (1):3-19.
    Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...)
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  24.  15
    Predicative Logic and Formal Arithmetic.John P. Burgess & A. P. Hazen - 1998 - Notre Dame Journal of Formal Logic 39 (1):1-17.
    After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell's Principia Mathematica with the axiom of infinity but without the axiom of reducibility.
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  25.  57
    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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  26.  31
    A Short Step Between Democracy and Dictatorship.Antonio Quesada - 2012 - Theory and Decision 72 (2):149-166.
    When preferences are defined over two alternatives and societies are variable, the group formed by the relative majority rule, the unanimity rule, the dictatorial rules, and the strongly dictatorial rules is characterized in terms of five axioms: unanimity, reducibility, substitutability, exchangeability, and parity. This result is used to provide characterizations of each of these rules by postulating separating axioms, that is, an axiom and its negation. Such axioms identify traits specifically differentiating a type of rule from the other types. For (...)
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