Solomon Feferman--Papers and Slides in PDF Format
(Caveat lector: published versions of the following may
contain some changes.)
of unsolvability associated with classes of formalized
theories, J. Symbolic Logic 22 (1957) 161-175.
first order properties of products of algebraic systems (with
R. L. Vaught), Fundamenta Mathematicae 47 (1959),
of metamathematics in a general setting, Fundamenta
Mathematicae 49 (1960),35-92.
recursive progressions of axiomatic theories, J. Symbolic
Logic 27 (1962), 259-316.
along paths in progressions of theories (with C. Spector),
J. Symbolic Logic 27 (1962), 383-390.
of recursive functions by means of hierarchies,
Transactions Amer. Math. Soc. 104 (1962), 101-122.
of predicative analysis, J. Symbolic Logic 29 (1964),
applications of the notions of forcing and generic sets,
Fundamenta Mathematicae 56 (1965), 325-345.
of predicative analysis, II. Representation of ordinals, J.
Symbolic Logic 33 (1968), 193-220.
- Persistent and invariant formulas for outer extensions, Compositio Mathematica 20 (1968), 29-52.
notes on abstract model theory. I. Properties invariant on the
range of definable relations between structures, Fundamenta
Mathematicae 82 (1974) 153-165.
notes on abstract model theory. II. Languages for which the set of
valid sentences is semi-invariantly implicitly definable,
Fundamenta Mathematicae 89 (1975) 111-130.
- A language and axioms for explicit mathematics, in Algebra and Logic (J. N. Crossley, ed.), Lecture Notes in Mathematics 450 (1975), 87-139.
- Categorical foundations and foundations of category theory, in R.E. Butts and J. Hintikka, eds., Logic, Foundations of Mathematics, and Computability Theory, Reidel, Dordrecht (1977) 149-169.
- Recursion in total functionals of finite type, Compositio Mathematica 35 (1977), 3-22.
- Recursion theory and set theory: A marriage of convenience, in Generalized Recursion Theory II (J. E. Fenstad, et al., eds.), North-Holland (1978), 55-98.
- Constructive theories of functions and classes, in Logic Colloquium '78 (M. Boffa, et al., eds.), North-Holland (1979), 159-224.
principles, the bar rule, and autonomously iterated comprehension
schemes in analysis (with G. Jäger), J. Symbolic Logic
48 (1983), 63-70.
useful type-free theories, I, J. Symbolic Logic 49
- A theory of variable types, Rivista Columbiana de Matemáticas XIX (1985), 95-105.
program relativized: Proof-theoretical and foundational
reductions, J. Symbolic Logic 53 (1988), 364-384.
- Finitary inductively
presented logics, in Logic Colloquium '88 (R. Ferro, et
al., eds.), North-Holland, Amsterdam (1989) 191-220; reprinted in What is a Logical System? (D. S. Gabbay, ed.), Clarendon Press, Oxford (1994), 297-328.
on incompleteness, J. Symbolic Logic 56 (1991),
- The development of programs
for the foundations of mathematics in the first third of the 20th
century. (1993). Appears in translation as "Le scuole de
filosofia della matematica" in Storia della scienza (S.
Petruccioli, ed.) Istituto della Enciclopedia Italiana, 10 v.,
2001-2004, v. VIII (2004) 112-121.
- Systems of explicit mathematics with non-constructive mu-operator, Part I (with G. Jäger), Annals of Pure and Applied Logic 65 (1993), 243-263.
- Systems of explicit mathematics with non-constructive mu-operator, Part II (with G. Jäger), Annals of Pure and Applied Logic 79 (1996), 37-52.
- What rests on what? The
proof-theoretic analysis of mathematics, in Philosophy of
Mathematics Part I (J. Czermak, ed.) Proc. of the 15th
International Wittgenstein Symposium, Verlag
Hölder-Pichler-Tempsky, Vienna (1993) 141-171; reprinted as
Ch. 10 in In the Light of
Logic, Oxford Univ. Press, New York (1998)
- Why a little bit goes a long way:
Logical foundations of scientifically applicable mathematics,
in PSA 1992, Vol. II, 442-455, 1993. Reprinted as Chapter
14 in In the Light of Logic,
- Predicative foundations of
arithmetic (with G. Hellman), J. Philosophical Logic 24
- Godel's Dialectica interpretation
and its two-way stretch, in Computational Logic and Proof
Theory (G. Gottlob, et al., eds.), Lecture Notes in Computer
Science 713 (1993) 23-40; reprinted as Ch. 11 in In
the Light of Logic, 209-225.
- Kreisel's "unwinding" program,
in Kreiseliana (P. Odifreddi, ed.), A. K. Peters Ltd.,
Wellesley (1996) 247-273.
- Deciding the Undecidable:
Wrestling with Hilbert's Problems, Inaugural address, Stanford
Univ., May 13, 1994, published as Ch. 1 in In
the Light of Logic, 3-27.
- Penrose's Gödelian
argument, PSYCHE 2 (1996) 21-32.
Erkenntnis 43 (1995) 295-320.
- Computation on abstract data
types. The extensional approach, with an application to
streams, Annals of Pure and Applied Logic 81 (1996)
- Proof Theory Since 1960,
prepared for the Encyclopedia of Philosophy Supplement,
Macmillan Publishing Co., New York.
- Gödel's program for new
axioms: Why, where, how and what?, in Gödel '96 (P.
Hajek, ed.), Lecture Notes in Logic 6 (1996), 3-22.
- Challenges to predicative
foundations of arithmetic (with G. Hellman), in Between
Logic and Intuition. Essays in Honor of Charles Parsons (G.
Sher and R. Tieszen, eds.), Cambridge Univ. Press, Cambridge
- The unfolding of non-finitist
arithmetic (with T. Strahm), Annals of Pure and Applied
Logic 104 (2000) 75-96.
- Does mathematics need new
axioms?, American Mathematical Monthly 106 (1999)
- My route to
arithmetization, Theoria 63 (1997) 168-181.
- Godel's Functional
("Dialectica") Interpretation (with J. Avigad), in The
Handbook of Proof Theory (S. Buss, ed.), North-Holland Pub.
Co., Amsterdam (1998) 337-405.
- Three conceptual problems
that bug me, Unpublished lecture text for 7th Scandinavian
Logic Symposium, Uppsala, 1996.
- Highlights in Proof
Theory, in Proof Theory (V. F. Hendricks, et al., eds.)
Kluwer Academic Publishers, Dordrecht (2000) 11-31.
- The significance of Hermann
Weyl's Das Kontinuum, ibid., 179-194.
- Relationships between
Constructive, Predicative and Classical Systems of Analysis,
- Mathematical Intuition vs.
Mathematical Monsters, Synthese 125 (2000)
- Ah, Chu, in JFAK. Essays
Dedicated to Johan van Benthem on the Occasion of his Fiftieth
Birthday, Amsterdam Univ. Press, Amsterdam (1999), CD-ROM
- Logic, Logics, and
Logicism, Notre Dame J. of Formal Logic 40 (1999)
- Does reductive proof theory
have a viable rationale?, Erkenntnis 53 (2000)
- Alfred Tarski and a watershed
meeting in logic: Cornell, 1957 , in (J. Hintikka, et al.,
eds.) Philosophy and Logic. In search of the Polish
tradition, Synthese Library vol. 323, Kluwer Acad. Pubs.
- Does mathematics need new
axioms?, (Proceedings of a symposium with H. M. Friedman, P.
Maddy and J. Steel, Bulletin of Symbolic Logic 6 (2000)
- Tarski's conception of
logic, Annals of Pure and Applied Logic 126 (2004) 5-13.
- Tarski's conceptual
analysis of semantical notions, Sémantique et
épistémologie (A. Benmakhlouf, ed.) Editions Le
Fennec, Casablanca (2004) [distrib. J. Vrin, Paris]
79-108. Reprinted in (D. Patterson, ed.) New Essays on Tarski and Philosophy, Oxford Univ. Press (2008), 72-93.
- Notes on Operational Set
Theory I. Generalization of "small" large cardinals in classical
and admissible set theory, draft (Theorem 4(i), p. 5, needs
- Predicativity. In
The Oxford Handbook of Philosophy of Mathematics and Logic (S. Shapiro, ed.), Oxford University Press, Oxford (2005)
- Typical ambiguity. Trying to
have your cake and eat it too. One Hundred Years of
Russell's Paradox (G. Link, ed.), Walter de Gruyter, Berlin
- Some formal systems for the
unlimited theory of functors and categories. Unpublished MS
from 1972-73 referred to in the preceding paper, sec. 8. Uneven
scanning has resulted in some missing symbols that can be restored
according to context, including: p. 18, l.6, S*; p.19, Theorem
3.1, S*, and p.26, l.3, a epsilon* b.
- What kind of logic is
"Independence Friendly" logic?, in The
Philosophy of Jaakko Hintikka (Randall E. Auxier and Lewis
Edwin Hahn, eds.); Library of Living Philosophers vol. 30, Open
Court (2006), 453-469.
- Comments on
"Predicativity as a philosophical position" by G. Hellman,
Review Internationale de Philosophie (special issue,
Russell en héritage. Le centenaire des Principles,
Ph. de Rouilhan, ed.) 229 (no. 3, 2004), 313-323.
- The Gödel
editorial project: a synopsis Bull. Symbolic Logic 11
(2005) 132-149; reprinted in Kurt Gödel. Essays for his Centennial (S. Feferman, C. Parsons and S. G. Simpson, eds.), Lecture Notes in Logic 33 (2010), Assoc. for Symbolic Logic, Cambridge University Press, 2010.
- Enriched stratified systems for the
foundations of category theory, in What is Category Theory?
(G. Sica, ed.), Polimetrica, Milano (2006), 185-203; reprinted in (G. Sommaruga, ed.), Foundational Theories of Classical and Constructive Mathematics, Springer, Dordrecht (2011), 127-143.
- Tarski's influence on
computer science, invited lecture for LICS 2005, Chicago, June
28, 2005. Has appeared in Logical
Methods in Computer Science, vol. 2 issue 3 (2006).
- Review of Incompleteness. The
proof and paradox of Kurt Gödel, by Rebecca
Goldstein, London Review of Books, vol. 28, no. 3 (9
- The impact of Gödel's incompleteness
theorems on mathematics, Notices American
Mathematical Society 53 no. 4 (April 2006), 434-439.
- Are there absolutely unsolvable
problems? Gödel's dichotomy, Philosophia Mathematica,
Series III vol. 14 (2006), 134-152.
- Turing's thesis,
Notices American Mathematical Society 53 no. 10 (Nov.
2006), reprinted in Alan Turing's Systems of Logic. The Princeton Thesis (A. W. Appel, ed.), Princeton Univ. Press, 13-26.
- The nature and significance of
Gödel's incompleteness theorems, lecture for the
Princeton Institute for Advanced Study Gödel Centenary
Program, Nov. 17, 2006.
- Lieber Herr Bernays! Lieber Herr
Gödel! Gödel on finitism, constructivity and Hilbert's
, in Kurt Gödel and the Foundations of Mathematics. Horizons of Truth (M. Baaz, et al., eds.) Cambridge University Press (2011), 111-133.
- Lieber Herr Bernays! Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program, preprint of the preceding in Dialectica 62 (2008), 179-203. (With some editorial differences.)
- Harmonious logic: Craig's
interpolation theorem and its descendants, transparencies for
the lecture at Interpolations--A Conference in Honor of William
Craig, UC Berkeley, 13 May 2007.
- Harmonious logic: Craig's interpolation theorem and its descendants, Synthese 164, no. 3 (2008), 341-357.
- Axioms for determinateness and
truth, The Review of Symbolic Logic, 1 no. 2 (2008), 204-217.
- Philosophy of mathematics: 5
questions, in Philosophy of Mathematics: 5 Questions
(V. F. Hendricks and H. Leitgeb, eds.), Automatic Press/VIP
- Gödel, Nagel, minds and
machines, Ernest Nagel Lecture, Columbia University, Sept. 27,
2007; J. Philosophy CVI, nr. 4, April 2009, 201-219.
- The Proof Theory of Classical and Constructive Inductive Definitions: A 40 year saga, slides for an invited talk at the Pohlersfest, Münster 18 July 2008.
- Conceptual structuralism and the continuum, slides for talk Phil Math Intersem 2010 Université Paris 7-Diderot, 6/08/10 (revision of slides for talk at VIIIth International Ontology Congress, San Sebastián, 10/01/08).
- Conceptions of the continuum, slides for talk at Barcelona Workshop on the Foundations of Mathematics, October 6, 2008.
- And so on ...: Reasoning with infinite diagrams, slides for talk at Workshop on Diagrams in Mathematics, Paris, October 9, 2008, and Logic Seminar, Stanford, February 24, 2009.
- What's definite? What's not? Slides for talk at Harvey Friedman 60th birthday conference, Ohio State U., May 16, 2009.
- On the strength of some semi-constructive theories, in Proof, Categories and Computation: Essays in honor of Grigori Mints, (S. Feferman and W. Sieg, eds.), College Publications, London (2010), 109-129; reprinted in Logic, Construction, Computation (U. Berger, et al., eds.)(H. Schwichtenberg Festschrift volume), Ontos Verlag, Frankfurt (2012), 201-225.
- The proof theory of classical and constructive inductive definitions. A 40 year saga, 1968-2008, in (R. Schindler, ed.) Ways of Proof Theory, Ontos Verlag, Frankfurt (2010), 7-30.
- Operational set theory and small large cardinals, Information and Computation 207 (2009), 971-979.
- Modernism in mathematics, review of Plato's Ghost by Jeremy Gray (Princeton U. Press, 2008), American Scientist 97 no. 5 (Sept-Oct 2009), 417.
- Conceptions of the continuum, Intellectica 51 (2009/1), 169-189.
- The unfolding of finitist arithmetic (with Thomas Strahm), The Review of Symbolic Logic 3 (2010), 665-689.
- Set-theoretical invariance criteria for logicality, Notre Dame J. of Formal Logic 51 (2010), 3-20.
- Gödel's incompleteness theorems, free will and mathematical thought, in Free Will and Modern Science (R. Swinburne, ed.), OUP for the British Academ (2011), 102-122.
- Foundations of category theory: What remains to be done, slides for contributed talk at ASL 2011 meet, UC Berkeley, March 24, 2011.
- Axiomatizing Truth: How and Why , slides for invited lecture at Pillars of Truth Conference, Princeton University, April 8-10, 2011.
- Axiomatizing truth: Why and how, in Logic, Construction, Computation (U. Berger, et al., eds.)(H. Schwichtenberg Festschrift volume), Ontos Verlag, Frankfurt (2012) 185-200.
- About and around computing over the reals, to appear in Computability: Gödel, Church, Turing and Beyond (J. Copeland, C. Posy and O. Shagrir, eds), MIT Press.
- Which quantifiers are logical?: A combined semantical and inferential criterion, slides for talk Aug 08, 2011, ESSLLI Workshop on Logical Constants, Ljubljana.
- Which quantifiers are logical? A combined semantical and inferential criterion, text for preceding talk; to appea in Synthese..
- Is the Continuum Hypothesis a definite mathematical problem?, Draft of paper for the lecture to the Philosophy Dept., Harvard University, Oct. 5, 2011 in the EFI project series.
- Is the Continuum Hypothesis a definite mathematical problem?, slides for the preceding talk.
- Turing's 'Oracle': From absolute to relative computability--and back, slides for Logic Seminar talk, Stanford, April 10, 2012.
- About and around computing over the reals, slides for Logic Seminar talk, Stanford, April 17, 2012.
- And so on... Reasoning with infinite diagrams, Synthese 186, no. 1 (2012), 371-386.
- Review of Curtis Franks The Autonomy of Mathematical Knowledge. Hilbert's program revisited, Philosophia Mathematica. Series III, 20 no.3 (2012), 387-400.
- On rereading van Heijenoort's Selected Essays, Logica Universalis 6 no. 3-4 (2012), 535-552.
- Introduction to Foundations of Explicit Mathematics (book in progress by S. Feferman, G. Jäger, S.Strahm, with the assistnace of U. Buchholtz), draft 7/19/12.
- Three Problems for Mathematics; Lecture 1: Bernays, Gödel, and Hilbert's consistency program, slides for inaugural Paul Bernays Lectures, ETH, Zurich, Sept. 11, 2012.
- Three Problems for Mathematics: Lecture 2: Is the Continuum Hypothesis a definite mathematical problem?, slides for inaugural Paul Bernays Lectures, ETH, Zurich, Sept. 12, 2012.
- Three Problems for Mathematics; Lecture 3: Foundations of Unlimited Category Theory, slides for inaugural Paul Bernays Lectures, ETH, Zurich, Sept. 12, 2012.
- What's special about mathematical proofs?, Remarks for the Williams Symposium on Proof, University of Pennsylvania, Nov. 9, 2012.
- Foundations of unlimited category theory: What remains to be done, The Review of Symbolic Logic 6 (2013), 6-15.
- Why isn't the Continuum Problem on the Millennium ($1,000,000) Prize list?, slides for CSLI Workshop on Logic, Rationality and Intelligent Interaction, Stanford, June 1, 2013.
- How a little bit goes a long way: Predicative foundations of analysis, unpublished notes dating from 1977-1981, with a new introduction.
- Theses for computation and recursion on concrete and abstract structures, to appear in a Turing Centennial volume for Birkhäuser edited by G. Sommaruga and T. Strahm.