Foundations of Mathematics

Bernhart, Frank. "Are Mathematical Objects Ontologically Real?: Ideas and Suggestions." In A Second Conference on the Foundations of Mathematics, edited by Brabenec, Robert L. Wheaton, IL: Wheaton College (1979) 80-88.

Brouwer, Luitzen Egbertus Jan. "Intuitionistic Reflections on Formalism." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 490-492.

Brouwer, Luitzen Egbertus Jan. "On the Significance of the Principle of Excluded Middle in Mahtematics, Especially in Function Theory." In From Frege to Gödel: A Sourcebook in Mathematical Logic 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 334-345.

Burali-Forti, Cesare. "A Question on Transfinite Numbers." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1897-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 104-112.

De Koning, Jan. "Can Mathematical Methods Yield Theological Truth?" In An Eighth Conference on Mathematics from a Christian Perspective, edited by Robert L. Brabenec. Wheaton, IL: Wheaton College (1991) 176-190.

De Millo, Richard, Richard Lipton, Alan Perlis. "Social Processes and Proofs of Theorems and Programs." In New Directions in the Philosophy of Mathematics: An Anthology: Revised and Expanded Edition, edited by Thomas Tymoczko. Princeton, NJ: Princeton University Press (1998) 267-285.

Finsler, Paul. "Formal Proofs and Undecidability." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel. (1967) 438-445.

Frege, Gottlob. "Begriffsschrift, a Formula Language, Modeled upon That of Arithmetic, for Pure Thought." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1897-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 1-82.

Gödel, Kurt. "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." In Collected Works, Volume 2. (1931) 144-195.

Gödel, Kurt. "Some Metamathematical Results on Completeness and Consistency, on Formally Undecidable Propositions of Pricipia Mathematica and Related Systems I, and on Completeness and Consistency." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931. edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 592-617.

Gödel, Kurt. "The Completeness of the Axioms of the Function Calculus of Logic." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931. edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 582-591.

Goodman, Nicholas D. "Mathematics as an Objective Science." In New Directions in the Philosophy of Mathematics: An Anthology: Revised and Expanded Edition, edited by Tymoczko, Thomas. Princeton, NJ: Princetion University Press (1998) 79-94.

Grabiner, Judith V. "Is Mathematical Truth Time-dependent?" In New Directions in the Philosophy of Mathematics: An Anthology: Revised and Expanded Edition, edited by Tymoczko, Thomas. Princeton, NJ: Princeton University Press (1998) 201-213.

Hedman, Bruce A. "Cantor's Concept of Infinity." In An Eighth Conference on Mathematics from a Christian Perspective, edited by Robert L. Brabenec. Wheaton, IL: Wheaton College (1991) 61-78.

Herbrand, Jaques. "On the Consistency of Arithmetic." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Linclon, NE: toExcel (1967).

Hersh, Reuben. "Some Proposals for Reviving the Philosophy of Mathematics." In New Directions in the Philosophy of Mathematics: An Anthology, edited by Thomas Tymoczko. Princeton, NJ: Princeton University Press (1998) 9-28.

Hilbert, David. "On the Foundations of Logic and Arithmetic." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 129-138.

Hilbert, David. "On the Infinite." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 367-392.

Hilbert, David. "The Foundations of Mathematics." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 464-479.

Holmes, Arthur F. "Wanted: Christian Perspectives in the Philosophy of Mathematics." In Proceedings of the Third Conference on Mathematics from a Christian Perspective, edited by Brabenec, Robert L. Wheaton, IL: Wheaton College (1977) 39-48.

Hubbard, J.H. "The Henon Mapping in the Complex Domain." In Chaotic Dynamics and Fractals, edited by M. Barnsley et al. Academic Press (1986) 101-111.

Kitcher, Philip. "Mathematical Change and Scientific Change." In New Directions in the Philosophy of Mathematics: An Anthology: Revised and Expanded Edition, edited by Tymoczko, Thomas. Princeton, NJ: Princetion University Press (1998) 215-242.

Komogorov, Andrei Nikolaevich. "On the Principles of Excluded Middle." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 414-437.

König, Julius. "On the Foundations of Set Theory and the Continuum Problem." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 145-149.

Lakatos, Imre. "What Does a Mathematical Proof Prove?" In New Directions in the Philosophy of Mathematics: An Anthology, edited by Thomas Tymoczko. Princeton, NJ: Princeton University Press (1998) 153-162.

Menzel, Christopher. "God and Mathematical Objects." In Mathematics in a Postmodern Age: A Christian Perspective, edited by Russell W. Howell and W. James Bradley. Grand Rapid: Wm. B. Eerdmans (2001) 65-97.
Dilemma of abstract objects. Are they created? Are they eternal? Are mathematical models and abstract objects the products of God's thoughts and concepts? God is rathional and conceives of all possible well-formed thoughts and objects.

Murdoch, John E. "Infinity and Continuity." In The Cambridge History of Later Medieval Philosophy from the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100-1600, edited by N. Kretzmann, A. Kenney, J. Pinborg, E. Stump. Cambridge: Cambridge University Press (1982) 564-591.

Murdock, James. "Arrogance and Humility in the Philosophy of Mathematics." In A Fourth Conference on Mathematics from a Christian Perspective, edited by Robert L. Brabenec. Wheaton, IL: Wheaton College (1983) 49-74.

Neuhouser, David L. "Beauty in Mathematics: some theological implications." In A Seventh Conference on Mathematics from a Christian Perspective, edited by Chase, Gene B. Messiah College (1989) 57-63.

Neuhouser, David. "Reality and Imagination in Mathematics and Religion." In A Third Conference on Mathematics from a Christian Perspective, edited by Robert L. Brabenec. Wheaton, IL: Wheaton College (1981) 99-112.

Peano, Giuseppe. "The Principles of Arithmetic, Presented by a New Method." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-19, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 83-97.

Peat, F. David. "Mathematics and Science: Mathematics and the Language of Nature." In Mathematics and Science, edited by Ronald E. Mickens, Teaneck, NJ: Word Scientific (1990) 154-172.

Perciante, Terence H. "Intuitionism." In A Second Conference on the Foundations of Mathematics, edited by Robert L. Brabenec. Wheaton, IL: Wheaton College (1979) 69-73.

Putnam, Hilary. "What Is Mathematical Truth?" In New Directions in the Philosophy of Mathematics: An Anthology: Revised and Expanded Edition, edited by Tymoczko, Thomas. Princeton, NJ: Princeton University Press (1998) 49-65.

Resnick, Michael D. "Proof as a Source of Truth." In New Directions in the Philosophy of Mathematics: An Anthology, edited by Thomas Tymoczko. Princeton, NJ: Princeton University Press (1998) 317-336.

Richard, Jules. "The Principles of Mathematics and the Problem of Sets." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 142-144.

Thurston, William P. "On Proof and Progress in Mathematics." In New Directions in the Philosophy of Mathematics: An Anthology, edited by Thomas Tymoczko. Princeton, NJ: Princeton University Press (1998) 337-355.

Tymoczko, Thomas. "The Four-color Problem and its Philosophical Significance." In New Directions in the Philosophy of Mathematics: An Anthology: Revised and Expanded Edition, edited by Tymoczko, Thomas. Princeton, NJ: Princeton University Press (1998) 243-266.

Von Neumann, John. "On the Introduction of Transfinite Numbers." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoort. Lincoln, NE: toExcel (1967) 346-354.

Warner, John W. "Infinity and Reality." In A Christian Perspective on the Foundations of Mathematics, edited by Robert L. Brabenec. Wheaton, IL: Wheaton College (1977) 127-140.

Weyl, Hermann. "Philosophie Der Mathematik Und Naturwissenschaft." In Hanbuch Der Philosophie, edited by R. Oldenbourg. (1927).

Whitehead, Alfred North, Bertrand Russell. "Incomplete Symbols: Descriptions." In From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879-1931, edited by J. Heijenoortf. Lincoln, NE: toExcel (1967) 216-223.

Whitney, Gordon E. "The Significance of Formally Undecideable Propositions for the Use of Classical Logic in Theological Arguments." In A Fifth Conference on Mathematics from a Christian Perspective, edited by Robert L. Brabenec. King's College (1985) 65-70.

Wilder, Raymond. "The Cultural Basis of Mathematics." In New Directions in the Philosophy of Mathematics: An Anthology, edited by Tymoczko, Thomas. Princeton, NJ: Princeton University Press (1998) 185-199.

Zwier, Paul. "A Comparative Study of Christian Mathematical Realism and its Humanistic Alternatives." In A Fourth Conference on Mathematics from a Christian Perspective, edited by Brabenec, Robert L. Wheaton, IL: Wheaton College (1983) 75-85.