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  1. Andrew Arana (2005). Review of S. Feferman's in the Light of Logic. [REVIEW] Mathematical Intelligencer 27 (4).
    We review Solomon Feferman's 1998 essay collection In The Light of Logic (Oxford University Press).
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  2. Solomon Feferman, Relationships Between Constructive, Predicative and Classical Systems of Analysis.
    Both the constructive and predicative approaches to mathematics arose during the period of what was felt to be a foundational crisis in the early part of this century. Each critiqued an essential logical aspect of classical mathematics, namely concerning the unrestricted use of the law of excluded middle on the one hand, and of apparently circular \impredicative" de nitions on the other. But the positive redevelopment of mathematics along constructive, resp. predicative grounds did not emerge as really viable alternatives to (...)
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  3. Richard Heck, Frege Arithmetic and "Everyday Mathematics&Quot;.
    The purpose of this note is to demonstrate that predicative Frege arithmetic naturally interprets some weak but non-trivial arithmetical theories. The weak theories in question are all related to Tarski, Mostowski, and Robinson's R. In saying that the interpretation is "natural", I mean that it relies only upon "definitions" of arithmetical notions that are themselves "natural", that is, that have some claim to be "definitions" in something other than a purely formal sense.
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  4. Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.
    Øystein Linnebo has recently shown that the existence of successors cannot be proven in predicative Frege arithmetic, using Frege’s definitions of arithmetical notions. By contrast, it is shown here that the existence of successor can be proven in ramified predicative Frege arithmetic.
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  5. Richard Heck (1996). The Consistency of Predicative Fragments of Frege's Grundgesetze der Arithmetik. History and Philosophy of Logic 17 (1):209-220.
    As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is (...)
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  6. Geoffrey Hellman (2004). Predicativism as a Philosophical Position. Revue Internationale de Philosophie 3:295-312.
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  7. Thomas Hofweber (2000). Proof-Theoretic Reduction as a Philosopher's Tool. Erkenntnis 53 (1-2):127-146.
    Hilbert’s program in the philosophy of mathematics comes in two parts. One part is a technical part. To carry out this part of the program one has to prove a certain technical result. The other part of the program is a philosophical part. It is concerned with philosophical questions that are the real aim of the program. To carry out this part one, basically, has to show why the technical part answers the philosophical questions one wanted to have answered. Hilbert (...)
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  8. St Iwan (2000). On the Untenability of Nelson's Predicativism. Erkenntnis 53 (1-2):147-154.
    By combining some technical results from metamathematicalinvestigations of systems of Bounded Arithmetic, I will givean argument for the untenability of Nelson's finitistic program,encapsulated in his book Predicative Arithmetic.
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  9. Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.
    Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...)
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  10. Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...)
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  11. Charles Parsons (1990). On Constructive Interpretation of Predicative Mathematics. Garland Pub..
  12. Audrey Yap (2009). Predicativity and Structuralism in Dedekind's Construction of the Reals. Erkenntnis 71 (2):157 - 173.
    It is a commonly held view that Dedekind’s construction of the real numbers is impredicative. This naturally raises the question of whether this impredicativity is justified by some kind of Platonism about sets. But when we look more closely at Dedekind’s philosophical views, his ontology does not look Platonist at all. So how is his construction justified? There are two aspects of the solution: one is to look more closely at his methodological views, and in particular, the places in which (...)
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