Main, Selected Recent Publications, Selected Publications on Proof,
Annotated Bibliography for Proof in Mathematics Education,
See references for 2008,
2007, 2006,
2005, 2004, 2003,
2002, 2001, 2000,
1999, 1998, 1997,
1996, 1995, 1994,
1993, 1992, 1991,
1990, 1989, 1988,
1987, 1986, pre-1986.
(See 2008 annotated bibliography)
Brown, J. (2008). Philosophy of Mathematics: a contemporary
introduction to the world of proofs and pictures. 2nd edition. New York:
Routledge.
Mancosu, P. (2008).Explanation in Mathematics. In E. N. Salta (Ed.), Stanford
Encyclopedia of Philosophy, (Summer 2008 Edition). <http://plato.stanford.edu/archives/sum2008/entries/mathematics-explanation/>.
See references for
2008, 2007,
2006, 2005, 2004,
2003, 2002, 2001,
2000, 1999, 1998,
1997, 1996, 1995,
1994, 1993, 1992,
1991, 1990, 1989,
1988, 1987, 1986,
pre-1986.
(See 2007 annotated bibliography)
Awodey, S., Carus, A. (2007). Carnap's Dream, Godel, Wittgenstein and Logical
Syntax. Sythese, 159(1), 23 - 45.
Burger, E. (2007). Extending the Frontiers of Mathematics: inquiries
into proof and argumentation. Emeryville, CA: Key College Publications.
Byers, W. (2007). How Mathematicians Think: using ambiguity, contradiction
and paradox to create mathematics. Princeton: Princeton University Press.
Cozzoli, D. (2007). Alessandro Piccolomini and the certitude of mathematics. History and Philosophy of Logic, 28(2), 151-171.
Doria, F. (2007). Informal versus formal mathematics. Synthese, 154(3), 401-415.
Giaquinto, M. (2007). Visual Thinking in mathematics: an epistemological
study. Oxford: Oxford University Press.
Havil, J. (2007). Nonplussed!: mathematical proof of implausible ideas.
Princeton: Princeton University Press.
Rav, Y. (2007). A critique of a formalist-mechanist version of the justification of arguments in mathematicians' proof practices. Philosophia Mathematica, 15(3), 291-320.
Sundstrom, T. (2007). Mathematical reasoning: writing and proof. 2nd edition. Upper Saddle River, NJ: Pearson Prentice
Hall.
See references for
2008, 2007,
2006, 2005, 2004,
2003, 2002, 2001,
2000, 1999, 1998,
1997, 1996, 1995,
1994, 1993, 1992,
1991, 1990, 1989,
1988, 1987, 1986,
pre-1986.
(See 2006 annotated bibliography)
Avigad, J. (2006).
Mathematical method and proof. Synthese, 153(1), 105-159.
Azzouni, J. (2006). Tracking reason: Proof,
consequence, and truth. Oxford, UK: Oxford University
Press.
Dawson, J. W. (2006). Why
do mathematicians re-prove theorems? Philosophia Mathematica, 14, 269-286.
Donnelly, S. (2006). Introduction to the archives of Imre Lakatos, 1922-1974. Perspectives on Science, 14(3), 347-353.
Franklin, J. (2006). Artifice and the natural
world: Mathematics, logic, technology. Cambridge: Cambridge
University Press.
Gurka, D. (2006). A missing link: The influence of Lszl Kalmr's empirical view on Lakatos' philosophy of mathematics. Perspectives on Science, 14(3), 263-281.
Jha, S. R. (2006a). Hungarian studies in Lakatos' philosophies of mathematics and science - Editor's introduction. Perspectives on Science, 14(3), 257-262.
Jha, S. R. (2006b). The bid to transcend Popper, and the Lakatos-Polanyi connection. Perspectives on Science, 14(3), 318-346.
Kiss, O. (2006). Heuristic, methodology or logic of discovery? Lakatos on patterns of thinking. Perspectives on Science, 14(3), 302-317.
Livingston, E. (2006).The context of Proving. Social Studies of Science, 36 (1), 39-68.
Lombardi, H. (2006). Structures algbriques dynamiques,
espaces topologiques sans points et programme de Hilbert. Annals of Pure
and Applied Logic, 137(1-3), 256-290.
Mt, A. (2006). ērpd Szab and Imre Lakatos, or the relation between history and philosophy of mathematics. Perspectives on Science, 14(3), 282-301.
Panjvani,
C. (2006). Wittgenstein and the concept of strong mathematical
verificationism. Philosophy Quarterly, 56(224),406-425.
Samian, A. L. (2006). 'Phenomena' in Newton's
mathematical experience. Dordrecht: Springer.
See references for 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986, pre-1986.
(See 2005 annotated bibliography)
Aberdein, A. (2005). The uses of argument in mathematics. In D. Hitchcock
(Ed.), The uses of argument: Proceedings of a conference at McMaster
university, 18-21 May 2005 (pp. 1-10).
Hamilton: Media Production.
Baker, A. (2005). Are there genuine mathematical
explanations of physical phenomena? Mind: A Quarterly Review of Philosophy, 114(454), 223-238.
Chemla, K.
(2005). The interplay between proof and algorithm in 3rd century China: The
operation as prescription of computation and the operation as argument. In P.
Mancosu, K. F. Jærgensen & S. A. Pedersen (Eds.), Visualization,
explanation and reasoning styles in mathematics (Synthese library, volume 327) (pp. 123-145). Dordrecht: Springer.
De Waal, C. (2005). Why metaphysics needs logic and
mathematics doesn't: Mathematics, logic, and metaphysics in Peirce's
classification of the sciences. Transactions of the Charles S. Peirce
Society: A Quarterly Journal in American Philosophy, 41(2), 283-297.
Fine, K. (2005). Prcis. Philosophical Studies: An
International Journal for Philosophy in the Analytic Tradition, 122(3), 305-313.
Giaquinto, M.
(2005). Mathematical activity. In P. Mancosu, K. F. Jærgensen & S. A.
Pedersen (Eds.), Visualization, explanation and reasoning styles in
mathematics (Synthese library, volume 327)
(pp. 75-87). Dordrecht: Springer.
Kuipers, T. A. F. (2005). Mathematics and
explication: Reply to Jean Paul Van Bendegem.
New York: Rodopi NY.
Leng, M. (2005). Platonism and anti-Platonism: Why
worry? International Studies in the Philosophy of Science, 19(1), 65-84.
Mancosu, P.
(2005). Visualization in logic and mathematics. In P. Mancosu, K. F. Jærgensen
& S. A. Pedersen (Eds.), Visualization, explanation and reasoning styles
in mathematics (Synthese library, volume 327)
(pp. 13-30). Dordrecht: Springer.
Mancosu, P. &
Hafner, J. (2005). The varieties of mathematical explanation. In P. Mancosu, K.
F. Jærgensen & S. A. Pedersen (Eds.), Visualization, explanation and
reasoning styles in mathematics (Synthese library, volume 327) (pp. 215-250). Dordrecht: Springer.
Mancosu, P., Jærgensen, K. F., & Pedersen, S. A.
(Eds.). (2005). Visualization, explanation and reasoning styles in
mathematics (Synthese library, volume 327).
Dordrecht: Springer.
Paseau, A. (2005). What the foundationalist filter
kept out. Studies in History and Philosophy of Science, 36A(1), 191-201.
Shapiro, S.
(2005). Logical consequence, proof theory, and model theory. In S. Shapiro
(Ed.), The Oxford handbook of philosophy of mathematics and logic (pp. 651-670). Oxford: Oxford University Press.
Sieg, W., & Field, C. (2005). Automated search for
Gdel's proofs. Annals of Pure and Applied Logic, 133(1-3), 319-338.
Tappenden, J.
(2005). Proof style and understanding in mathematics I: Visualization,
unification and axiom choice. In P. Mancosu, K. F. Jærgensen & S. A.
Pedersen (Eds.), Visualization, explanation and reasoning styles in
mathematics (Synthese library, volume 327)
(pp. 147-214). Dordrecht: Springer.
Tieszen, R. (2005). Phenomenology, logic, and the philosophy
of mathematics. Cambridge: Cambridge University
Press.
Van Bendegem, J.
P. (2005). Proofs and arguments: The special case of mathematics. In R. Festa,
A. Aliseda & J. Peijnenburg (Eds.), Cognitive structures in scientific
inquiry: Essays in debate with Theo Kuipers: Volume 2 (Poznan Studies, volume
84) (pp. 157-169). New York: Rodopi NY.
See references for 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986, pre-1986.
(See 2004 annotated bibliography)
Ahnert,
T. (2004). Newtonianism in early enlightenment Germany, c. 1720 to 1750:
Metaphysics and the critique of dogmatic philosophy. Studies in History and
Philosophy of Science, 35A(3), 471-491.
Avigad,
J. (2004). Forcing in proof theory. Bulletin of Symbolic Logic, 10(3), 305-333.
Azzouni,
J. (2004). The derivation-indicator view of mathematical practice.
Philosophia Mathematica, 12(2), 81-105.
Berardi,
S. (2004). Krivine's intuitionistic proof of classical completeness (for
countable languages). Annals of Pure and Applied Logic, 129(1-3), 93-106.
Bourdeau,
M. (2004). Prsentation: Intuitionnisme et philosophie. Revue Internationale
de Philosophie, 58(230), 383-400.
Brown,
J. R. (2004). Peeking into Plato's heaven. Philosophy of Science, 71(5), 1126-1138.
Cozzo,
C. (2004). Wittgenstein e l'oggettivit della dimostrazione. Rivista di Filosofia,
95(1), 63-92.
Gattei,
S. (2004). Karl Popper's philosophical breakthrough. Philosophy of Science,
71(4), 448-466.
Glanzberg,
M. (2004). Truth, reflection, and hierarchies. Synthese: An International
Journal for Epistemology, Methodology and Philosophy of Science, 142(3), 289-315.
Magnani,
L. (2004). Conjectures and manipulations: Computational modeling and the
extra-theoretical dimension of scientific discovery. Minds and Machines:
Journal for Artificial Intelligence, 14(4), 507-537.
Ranta,
A., & Cooper, R. (2004). Dialogue systems as proof editors. Journal of
Logic, Language and Information, 13(2), 225-240.
Ravetz,
J. R. (2004). An Hungarian tragedy. Inquiry: An Interdisciplinary Journal of
Philosophy, 47(4), 413-422.
Redhead,
M. (2004). Mathematics and the mind. British Journal for the Philosophy of
Science, 55(4), 731-737.
Stadler,
F. (2004). Induction and deduction in the sciences (Vienna circle institute
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2007,
2006, 2005, 2004,
2003, 2002, 2001,
2000, 1999, 1998,
1997, 1996, 1995,
1994, 1993, 1992,
1991, 1990, 1989,
1988, 1987, 1986,
pre-1986.
(See 2003 annotated bibliography)
Alvarez, C. (2003). Two ways
of reasoning and two ways of arguing in geometry: Some remarks concerning the
application of figures in Euclidean geometry. Synthese, 134, 289-323.
Andrews,
P. B. (2003). An introduction to mathematical logic and type theory: To
truth through proof. Dordrecht: Kluwer Academic Publishers.
Billinge,
H. (2003). Did Bishop have a philosophy of mathematics? Philosophia
Mathematica, 11(2), 176-194.
Brown,
J. R. (2003). Philosophy of mathematics: An introduction to the world of
proofs and pictures. New York: Routledge.
Cooke,
E. F. (2003). Peirce, fallibilism, and the science of mathematics.
Philosophia Mathematica, 11(2), 158-175.
Corfield, D. (2003). Towards
a philosophy of real mathematics. Cambridge, UK: Cambridge University Press.
Dosen, K. (2003). Identity of proofs based on normalization and
generality. Bulletin of Symbolic Logic, 9(4),
477-503.
Dubucs,
J. (2003). Preuves, fondements et certificats. Philosophia Scientiae, 7(1), 167-198.
Fallis,
D. (2003). Intentional gaps in mathematical proofs. Synthese: An
International Journal for Epistemology, Methodology and Philosophy of Science,
134(1-2), 45-69.
Fichot,
J. (2003). Truth, proofs and functions. Synthese: An International Journal
for Epistemology, Methodology and Philosophy of Science, 137(1-2), 43-58.
Hale, M. (2003). Essentials
of mathematics: Introduction to theory, proof, and the professional culture (Resource Materials Series). Mathematical
Association of America, Washington, DC.
Landesman,
C. (2003). Reason and arithmetic. Philosophical Forum, 34(3-4), 317-327.
Longo,
G. (2003). Proofs and programs. Synthese: An International Journal for
Epistemology, Methodology and Philosophy of Science, 134(1-2), 85-117.
Panza,
M. (2003). Mathematical proofs. Synthese: An International Journal for
Epistemology, Methodology and Philosophy of Science, 134(1-2), 119-158.
Peressini,
A. (2003). Proof, reliability, and mathematical knowledge. Theoria: A
Swedish Journal of Philosophy, 69(3), 211-232.
Piccinini,
G. (2003). Alan Turing and the mathematical objection. Minds and Machines:
Journal for Artificial Intelligence, 13(1), 23-48.
Szab,
L. E. (2003). Formal systems as physical objects: A physicalist account of mathematical
truth. International Studies in the Philosophy of Science, 17(2), 117-125.
Van
Bendegem, J. P. (2003). Thought experiments in mathematics: Anything but proof.
Philosophica (Belgium), 72, 9-33.
Womach,
C., & Farach, M. (2003). Randomization, persuasiveness and rigor in proofs.
Synthese: An International Journal for Epistemology, Methodology and Philosophy
of Science, 134(1-2), 71-84.
Zach,
R. (2003). The practice of finitism: Epsilon calculus and consistency proofs in
Hilbert's program. Synthese: An International Journal for Epistemology,
Methodology and Philosophy of Science, 137(1-2), 211-259.
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2003, 2002, 2001,
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1997, 1996, 1995,
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1991, 1990, 1989,
1988, 1987, 1986,
pre-1986.
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Alcolea Banegas, J. (2002). La
demostracin matemtica: Problemtica actual. Contrastes: Revista
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Dove, I. (2002). Can pictures
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Fallis, D. (2002). Response
to: "What is the goal of proof?" by A. Lercher. Logique et Anal,
N.S. 45, 397-398.
Fallis, D. (2002a). What do
mathematicians want? Probabilistic proofs and the epistemic goals of
mathematicians. Logique et Anal, N.S. 45, 373-388.
Kahle, R. (2002b). Mathematical
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Journal for Epistemology, Methodology and Philosophy of Science, 133(1-2), 237-255.
Lercher, A. (2002). What is
the goal of proof? Logique et Anal, N.S. 45, 389-395.
Mancosu, P. (2002). On the
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Sieg, W. (2002). Beyond
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Weber, E. and Verhoeven, L.
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Bronkhorst, J. (2001). Panini
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Cupillari, A. (2001). The
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Fitelson, B. and Wos, L.
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Ganeri, J. (2001).Objectivity
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Kadvany, J. (2001). Imre
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Antonelli, A. and May, R.
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Berg, J. (2000). From
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Aigner, M., &
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Balaguer, M.
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Corfield, D.
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Main, Selected Recent Publications, Selected Publications on Proof,
Annotated Bibliography for Proof in Mathematics Education,
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