Editing Foundations of mathematics (section)

== References ==
* [[Jeremy Avigad|Avigad, Jeremy]] (2003) ''[https://www.andrew.cmu.edu/user/avigad/Papers/elementary.pdf Number theory and elementary arithmetic]'', Philosophia Mathematica Vol. 11, pp.&nbsp;257–284
* [[Howard Eves|Eves, Howard]] (1990), ''Foundations and Fundamental Concepts of Mathematics Third Edition'', Dover Publications, INC, Mineola NY, {{ISBN|0-486-69609-X}} (pbk.) cf §9.5 Philosophies of Mathematics pp.&nbsp;266–271. Eves lists the three with short descriptions prefaced by a brief introduction.
* Goodman, N.D. (1979), "[https://www.jstor.org/stable/2320581 Mathematics as an Objective Science]", in Tymoczko (ed., 1986).
* [[Wilbur Dyre Hart|Hart, W.D.]] (ed., 1996), ''The Philosophy of Mathematics'', Oxford University Press, Oxford, UK.
* [[Reuben Hersh|Hersh, R.]] (1979), "Some Proposals for Reviving the Philosophy of Mathematics", in (Tymoczko 1986).
* [[David Hilbert|Hilbert, D.]] (1922), "Neubegründung der Mathematik. Erste Mitteilung", ''Hamburger Mathematische Seminarabhandlungen'' 1, 157–177. Translated, "The New Grounding of Mathematics. First Report", in (Mancosu 1998).
* Katz, Robert (1964), ''Axiomatic Analysis'', D. C. Heath and Company.
* {{cite book | author=Kleene, Stephen C. | title=Introduction to Meta-Mathematics| publisher=North-Holland Pub. Co | location=Amsterdam NY| orig-year=1952 | year=1991 | edition=Tenth impression 1991 | isbn=0-7204-2103-9| author-link=Stephen Kleene}}
: In Chapter III ''A Critique of Mathematic Reasoning, §11. The paradoxes'', Kleene discusses [[Intuitionism]] and [[Formalism (mathematics)|Formalism]] in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Extraordinary writing by an extraordinary mathematician.
* Mancosu, P. (ed., 1998), ''From Hilbert to Brouwer. The Debate on the Foundations of Mathematics in the 1920s'', Oxford University Press, Oxford, UK.
* [[Hilary Putnam|Putnam, Hilary]] (1967), "Mathematics Without Foundations", ''Journal of Philosophy'' 64/1, 5–22. Reprinted, pp.&nbsp;168–184 in W.D. Hart (ed., 1996).
* —, "What is Mathematical Truth?", in Tymoczko (ed., 1986).
* {{cite journal|author=Sudac, Olivier|title=The prime number theorem is PRA-provable|date=Apr 2001|journal=Theoretical Computer Science|volume=257|issue=1–2|pages=185–239|doi=10.1016/S0304-3975(00)00116-X|doi-access=}}
* [[Anne Sjerp Troelstra|Troelstra, A. S.]] (no date but later than 1990), [https://web.archive.org/web/20060209210015/http://staff.science.uva.nl/~anne/hhhist.pdf "A History of Constructivism in the 20th Century"], A detailed survey for specialists: §1 Introduction, §2 Finitism & §2.2 Actualism, §3 Predicativism and Semi-Intuitionism, §4 Brouwerian Intuitionism, §5 Intuitionistic Logic and Arithmetic, §6 Intuitionistic Analysis and Stronger Theories, §7 Constructive Recursive Mathematics, §8 Bishop's Constructivism, §9 Concluding Remarks. Approximately 80 references.
* [[Thomas Tymoczko|Tymoczko, T.]] (1986), "Challenging Foundations", in Tymoczko (ed., 1986).
* —,(ed., 1986), ''[https://books.google.com/books?id=a-M9DwAAQBAJ&dq=%22New+Directions+in+the+Philosophy+of+Mathematics%22&pg=PR9 New Directions in the Philosophy of Mathematics]'', 1986. Revised edition, 1998.
* van Dalen D. (2008), "Brouwer, Luitzen Egbertus Jan (1881–1966)", in Biografisch Woordenboek van Nederland. URL:http://www.inghist.nl/Onderzoek/Projecten/BWN/lemmata/bwn2/brouwerle [2008-03-13]
* [[Hermann Weyl|Weyl, H.]] (1921), "Über die neue Grundlagenkrise der Mathematik", ''Mathematische Zeitschrift'' 10, 39–79. Translated, "On the New Foundational Crisis of Mathematics", in (Mancosu 1998).
* [[Raymond Louis Wilder|Wilder, Raymond L.]] (1952), ''Introduction to the Foundations of Mathematics'', John Wiley and Sons, New York, NY.