- Series Information
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Notes on the Contributors
- Philosophy of Mathematics and Its Logic: Introduction
- A Priority and Application: Philosophy of Mathematics in the Modern Period
- Later Empiricism and Logical Positivism
- Wittgenstein on Philosophy of Logic and Mathematics
- The Logicism of Frege, Dedekind, and Russell
- Logicism in the Twenty‐first Century
- Logicism Reconsidered
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism Reconsidered
- Structuralism Reconsidered
- Mathematics—Application and Applicability
- Logical Consequence, Proof Theory, and Model Theory
- Logical Consequence From a Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
Abstract and Keywords
While the term predicativity suggests that there is a single idea involved, what the history will show is that there are a number of ideas of predicativity which may lead to different logical analyses. This article uncovers these only gradually. A central question is then what, if anything, unifies them. Though early discussions are often muddy on the concepts and their employment, in a number of important respects they set the stage for the further developments, and so this article gives them special attention. Note that, ahistorically, modern logical and set-theoretical notation are used throughout, as long as it does not conflict with original intentions.
Solomon Feferman is Professor of Mathematics and Philosophy and the Patrick Suppes Professor of Humanities and Sciences, Emeritus, at Stanford University. He is the author of numerous articles on logic and the foundations of mathematics and of In the Light of Logic (Oxford University Press, 1998), editor in chief of the Collected Works of Kurt Gödel (vols. I–V, Oxford University Press, 1986–2003), and author with Anita B. Feferman of Truth and Consequences: The Life and Logic of Alfred Tarski (forthcoming). Feferman received the Rolf Schock Prize for Logic and Philosophy for 2003.
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