Relationships between constructive, predicative, and classical systems of analysis (2009)
Both the constructive and predicative approaches to mathemat-ics arose during the period of what was felt to be a foundational crisis in the early part of this century. Each critiqued an essential...
Penrose’s Gödelian argument (2008)
Penrose Redux, Solomon Feferman
In his book Shadows of the Mind: A search for the missing science of consciousness [SM below], Roger Penrose has turned in another bravura performance, the kind we have come to expect ever since The...
Deciding the Undecidable: Wrestling with Hilbert’s Problems (2008)
was to have lasting fame and importance. Hilbert was at that point a rapidly rising star, if not superstar, in mathematics, and before long he was to be ranked with Henri Poincaré as one of the two...
Enriched stratified systems for the foundations of category (2008)
This is the fourth in a series of intermittent papers on the foundations of category theory stretching back over more than thirty-five years. The first three were “Set-theoretical foundations of...
The Impact of the Incompleteness Theorems (2008)
On Mathematics, Solomon Feferman
In addition to this being the centenary of Kurt Gödel’s birth, January marked 75 years since the publication (1931) of his stunning incompleteness theorems. Though widely known in one form or...
Does reductive proof theory have a viable rationale (2008)
The goals of reduction and reductionism in the natural sciences are mainly explanatory in character, while those in mathematics are primarily foundational. In contrast to global reductionist programs...
What is predicativity? While the term 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...
The Gödel Editorial Project: A synopsis (2008)
that started over twenty years earlier. What I mainly want to do here is trace, from the vantage point of my personal involvement, the at some times halting and at other times intense development of...
(7th Scandinavian Logic Symposium, Uppsala (2008)
Bug (v.t.): to bother, annoy, pester � to prey on, worry
From PSA 1992, vol. 2 (1993), pp. 442–455 (with corrections) Why a little bit goes a long way:
1993]. What rests on what? The proof-theoretic analysis of mathematics (2008)
Whenever a subject is organized systematically for expository or foundational purposes (or both), one must deal with the question: What rests on what? The way in which this is answered in the case of...
2. What examples from your work (or the work of others) illustrate the use of mathematics for philosophy? 3. What is the proper role of philosophy of mathematics in relation to logic, foundations of...
Typical ambiguity: trying to have your cake and eat it too (2008)
Solomon Feferman, John Heywood
Would ye both eat your cake and have your cake?
For Per Lindström My route to arithmetization (2008)
I had the pleasure of renewing my acquaintance with Per Lindström at the meeting of
Poincaré famously compared the logician’s understanding of mathematics to the understanding we would have of chess if we were only to know its rules. ”To understand the game, ” Poincaré...
Jeremy Avigad, Solomon Feferman
2. The Dialectica interpretation of arithmetic..................... 5 3. Consequences and benefits of the interpretation.................. 15 4. Models of T, type structures, and...
Proof Theory Since 1960 (2008)
Hilbert's program modi ed. The background to the development of proof theory since 1960 is contained in the article (MATHEMATICS, FOUNDATIONS OF), Vol. 5, pp. 208-209. Brie y, Hilbert's...
Harmonious Logic Harmonious Logic: Craig’s Interpolation Theorem and its Descendants (2008)
For Bill Craig, with great appreciation for his fundamental contributions to our subject, and for his perennially open, welcoming attitude and fine personality that enhances every encounter....
The significance of Hermann Weyl's Das Kontinuum (2007)
Das Kontinuum, Solomon Feferman
In his 1918 monograph "Das Kontinuum", Hermann Weyl initiated a program for the arithmetical foundations of mathematics. In the years following, this was overshadowed by the foundational...
Proof Theory Since 1960 (2007)
ould unquestionably be formalized. These obstacles led workers in proof theory to modify H.P. in two kinds of ways. The first was to seek reductions of various formal systems S to more constructive...
The unfolding of non-nitist arithmetic (2007)
Solomon Feferman, Thomas Strahm
The unfolding of schematic formal systems is a novel concept which was initiated in Feferman [6]. This paper is mainly concerned with the proof-theoretic analysis of various unfolding systems for...
Gödel, Nagel, minds and machines (2007)
Solomon Feferman, Ernest Nagel
imbroglio about the possible inclusion of Gödel’s original work on incompleteness in the book, Gödel’s Proof, then being written by Nagel with James R. Newman. What led to the conflict were...
Tarski's influence on computer science (2006)
The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision...
Are There Absolutely Unsolvable Problems? Godel's Dichotomy (2006)
This is a critical analysis of the first part of Gödel's 1951 Gibbs lecture on certain philosophical consequences of the incompleteness theorems. Gödel's discussion is framed in terms of a...
Are There Absolutely Unsolvable Problems? Godel's Dichotomy{dagger} (2006)
This is a critical analysis of the first part of Gödel's 1951 Gibbs lecture on certain philosophical consequences of the incompleteness theorems. Gödel's discussion is framed in terms of a...
Are There Absolutely Unsolvable Problems? Godel's Dichotomy{dagger} (2006)
This is a critical analysis of the first part of Gödel's 1951 Gibbs lecture on certain philosophical consequences of the incompleteness theorems. Gödel's discussion is framed in terms of a...
Tarski's conceptual analysis of semantical notions”. Sémantique et épistémologie (2004)
Solomon Feferman, Dedicated Robert, L. Vaught
Fellow student, dear friend, colleague
Highlights in Proof Theory (2000)
This is a survey of some of the principal developments in proof theory from its inception in the 1920s, at the hands of David Hilbert, up to the 1960s. Hilbert's aim was to use this as a tool in...
Does Reductive Proof Theory Have A Viable Rationale? (2000)
The goals of reduction and reductionism in the natural sciences are mainly explanatory in character, while those in mathematics are primarily foundational. In contrast to global reductionist programs...
Logic, Logics, and Logicism (1999)
The paper starts with an examination and critique of Tarski's well-known proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which...
A theorem obtained by van Benthem for preservation of formulas under Chu transforms between Chu spaces is strengthened and derived from a general many-sorted interpolation theorem. The latter has...
Does Mathematics Need New Axioms? (1999)
this article I will be looking at the leading question from the point of view of the logician, and for a substantial part of that, from the perspective of one supremely important logician: Kurt...
Logic, Logics, and Logicism (1999)
The paper starts with an examination and critique of Tarski's wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one...
Logic, logics and logicism (1999)
The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which...
THE STUDY OF PROOFS AND ORDINALS. (1998)
The results of a project devoted to the study and characterization of various stratifications of the notions of mathematical proofs and definitions are briefly summarized. (Author)
Gödel's Functional ("Dialectica") Interpretation (1998)
Jeremy Avigad, Solomon Feferman
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 2. The Dialectica interpretation of arithmetic . . . . . . . . . . . . . . . . . . . . . 341 3....
Relationships between Constructive, Predicative and Classical Systems of Analysis (1997)
this article.
Gödel's Dialectica interpretation and its two-way stretch (1997)
this article has appeared in Computational Logic and Proof Theory (Proc. 3
Godel's program for new axioms: Why, where, how and what (1996)
Solomon Feferman, Solomon Feferman
From 1931 until late in his life (at least 1970) Godel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his...
Three Conceptual Problems That Bug Me (1996)
Introduction I will talk here about three problems that have bothered me for a number of years, during which time I have experimented with a variety of solutions and encouraged others to work on...
Challenges to Predicative Foundations of Arithmetic (1996)
Solomon Feferman, Geoffrey Hellman
This paper was written while the first author was a Fellow at the Center for Advanced Study in the Behavioral Sciences (Stanford, CA) whose facilities and support, under grants from the Andrew W....
Questions of definedness are ubiquitous in mathematics. Informally, these involve reasoning about expressions which may or may not have a value. This paper surveys work on logics in which such...
Predicative Foundations of Arithmetic (1995)
Solomon Feferman, Geoffrey Hellman
this paper to show that this appearance is illusory: as will emerge, a predicatively acceptable axiomatization of the natural number system can be formulated, and both the existence of structures of...
Penrose's Gödelian argument (1994)
Solomon Feferman, Penrose Redux
explanation of Schrodingerian quantum mechanics. 1 I am only competent to say something substantive about the first part of the new effort, resting as it does to a considerable extent on a version of...
Systems of explicit mathematics with non-constructive µ-operator. Part I (1993)
Solomon Feferman, Gerhard Jäger
this paper is to present full proofs of these results, in two parts. In this first part we deal only with theories of operations and numbers which may contain the operator. Then, in Part II, we shall...
Godel's Dialectica interpretation and its two-way stretch (1993)
number theory in a quantifier-free theory of functionals of finite type; this subsequently came to be known as Gödel’s functional or Dialectica interpretation. The article itself was written in...
What Rests On What? The Proof-Theoretic Analysis Of Mathematics (1992)
analysis goes beyond concrete analysis by its use of arbitrary spaces of various kinds, e.g. metric spaces, Banach spaces, Hilbert spaces, etc. Moreover, for functional analysis, applications often...
The number systems : foundations of algebra and analysis / by Solomon Feferman (1989)
Incluye bibliografía
Finitary Inductively Presented Logics (1988)
A notion of finitary inductively presented (f.i.p.) logic is proposed here, which includes all syntactically described logics (formal systems) met in practice. A f.i.p. theory FS 0 is set up which is...
Formal consistency proofs and interpretability of theories /--by Solomon Feferman. (1957)
Thesis (Ph. D. in Mathematics)--University of California, Berkeley, June 1957.
Thesis (Ph. D. in Mathematics)--University of California, Berkeley, June 1957.
(From The Autobiography of Julia Robinson by Constance Reid) (1919)
Julia Bowman Robinson, Solomon Feferman, Washington D. C, Julia Bowman Robinson, Solomon Feferman, S A Mathematician, ...
One of my earliest memories is of arranging pebbles in the shadow of a giant saguaro... I think I have always had a basic liking for the natural numbers. To me they are the one real thing. We can...
The Unfolding of Non-Finitist Arithmetic
Solomon Feferman, Thomas Strahm
The unfolding of schematic formal systems is a novel concept which was initiated in Feferman [6]. This paper is mainly concerned with the proof-theoretic analysis of various unfolding systems for...