Aberdein A. (2006). The informal logic of mathematical proof. In Hersh R., editor. 18 Unconventional Essays on the Nature of Mathematics. New York: Springer, pp. 56–70.
Avigad J. (2006). Mathematical method and proof. Synthese, 153(1), 105–159.
Avigad J. (2008). Understanding proofs. In Mancosu P., editor. The Philosophy of Mathematical Practice. Oxford: Oxford University Press, pp. 317–353.
Azzouni J. (2004). The derivation-indicator view of mathematical practice. Philosophia Mathematica, 12(3), 81–105.
Azzouni J. (2009). Why do informal proofs conform to formal norms?
Foundations of Science, 14(1–2), 9–26.
Azzouni J. (2013). The relationship of derivations in artificial languages to ordinary rigorous mathematical proof. Philosophia Mathematica, 21(2), 247–254.
Barnes J. (2007). Truth, etc. Oxford: Oxford University Press.
Bonnay D. (2006). Qu’est-ce qu’une Constante Logique? Ph.D. Thesis, Université Paris I.
Bonnay D. (2008). Logicality and invariance. Bulletin of Symbolic Logic, 14(1), 29–68.
Bourbaki N. (1970). Théorie des Ensembles. Paris: Hermann.
Bundy A., Atiyah M., Macintyre A., & MacKenzie D. (2005). The nature of mathematical proof [special issue]. Philosophical Transactions of the Royal Society A, 363(1835), 2329–2461.
Bundy A., Jamnik M., & Fugard A. (2005). What is a proof?
Philosophical Transactions of the Royal Society A, 363(1835), 2377–2391.
Burgess J. P. (2015). Rigor and Structure. Oxford: Oxford University Press.
Cellucci C. (2008). Why proof? What is a proof? In Lupacchini R. and Corsi G., editors. Deduction, Computation, Experiment: Exploring the Effectiveness of Proof. Milan: Springer, pp. 1–27.
Church A. (1956). Introduction to Mathematical Logic, Vol. 1. Princeton: Princeton University Press.
Corcoran J. (1973). Gaps between logical theory and mathematical practice. In Bunge M., editor. The Methodological Unity of Science. Dordrecht: Reidel, pp. 23–50.
Curry H. B. (1950). A Theory of Formal Deducibility. Notre Dame Mathematical Lectures, Number 6. Notre Dame, Indiana: University of Notre Dame.
Detlefsen M. (1992a). Poincaré against the logicians. Synthese, 90(3), 349–378.
Detlefsen M. (editor) (1992b). Proof, Logic and Formalization. London: Routledge.
Detlefsen M. (2009). Proof: Its nature and significance. In Gold B. and Simons R. A., editors. Proof and Other Dilemmas: Mathematics and Philosophy. Washington, D.C.: The Mathematical Association of America.
Dutilh Novaes C. (2011). The different ways in which logic is (said to be) formal. History and Philosophy of Logic, 32(4), 303–332.
Feferman S. (1979). What does logic have to tell us about mathematical proofs?
The Mathematical Intelligencer, 2(1), 20–24.
Feferman S. (1999). Logic, logics, and logicism. Notre Dame Journal of Formal Logic, 40(1), 31–54.
Feferman S. (2012). And so on…: Reasoning with infinite diagrams. Synthese, 186(1), 371–386.
Frege G. (1893/1964). The Basic Laws of Arithmetic: Exposition of the System. Berkeley: University of California Press.
Frege G. (1897/1984). On Mr. Peano’s conceptual notation and my own. In McGuiness B., editor. Collected Papers on Mathematics, Logic, and Philosophy. New York: Basil Blackwell, pp. 234–248.
Frege G. (1979). Posthumous Writings. Chicago: University of Chicago Press.
Gödel K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38(1), 173–198.
Gödel K. (193?/1995a). Undecidable diophantine propositions. In Feferman S., Dawson J. W. Jr., Goldfarb W., Parsons C., and Solovay R. M., editors. Collected Works, Vol. III: Unpublished Essays and Lectures. Oxford: Oxford University Press, pp. 164–175.
Gödel K. (1995b). The present situation in the foundations of mathematics. In Feferman S., Dawson J. W. Jr., Goldfarb W., Parsons C., and Solovay R. M., editors. Collected Works, Vol. III: Unpublished Essays and Lectures. Oxford: Oxford University Press, pp. 45–53.
Goethe N. B. & Friend M. (2010). Confronting ideals of proof with the ways of proving of the research mathematician. Studia Logica, 96(2), 273–288.
Goldfarb W. (2001). Frege’s conception of logic. In Floyd J. and Shieh S., editors. Future Pasts: The Analytic Tradition in Twentieth-Century Philosophy. New York: Oxford University Press, pp. 25–41.
Goldfarb W. (2003). Deductive Logic. Indianapolis: Hackett Publishing.
Hales T. (2012). Dense Sphere Packings: A Blueprint for Formal Proofs. London Mathematical Society Lecture Notes Series, Vol. 400. Cambridge: Cambridge University Press.
Hardy G. H. & Wright E. M. (1975). An Introduction to the Theory of Numbers (Fourth Edition). Oxford: Oxford University Press.
Kitcher P. (1981). Mathematical rigor–Who needs it?
Noûs, 15(4), 469–493.
Kitcher P. (1984). The Nature of Mathematical Knowledge. New York: Oxford University Press.
Kleene S. C. (1952). Introduction to Metamathematics. New York: van Nostrand.
Kreisel G. (1967). Informal rigour and completeness proofs. In Lakatos I., editor. Problems in the Philosophy of Mathematics. Amsterdam: North-Holland, pp. 138–186.
Kreisel G. (1970). The formalist-positivist doctrine of mathematical precision in the light of experience. L’Âge de la Science, 3, 17–46.
Kreisel G. (1981). Neglected possibilities of processing assertions and proofs mechanically: Choice of problems and data. In Suppes P., editor. University-Level Computer-Assisted Instruction at Stanford: 1968–1980. Stanford, CA: Stanford University, Institute for Mathematical Studies in the Social Sciences, pp. 131–148.
Larvor B. (2012). How to think about informal proofs. Synthese, 187(2), 715–730.
Leitgeb H. (2009). On formal and informal provability. In Linnebo Ø. and Bueno O., editors. New Waves in Philosophy of Mathematics. New York: Palgrave Macmillan, pp. 263–299.
Lewis D. (1988). Relevant implication. Theoria, 54(3), 161–174.
Lycan W. G. (1989). Logical constants and the glory of truth-conditional semantics. Notre Dame Journal of Formal Logic, 30(3), 390–400.
Mac Lane S. (1986). Mathematics: Form and Function. New York: Springer-Verlag.
MacFarlane J. G. (2000). What does it Mean to Say that Logic is Formal? Ph.D. Thesis, University of Pittsburgh.
MacFarlane J. G. (2002). Frege, Kant, and the logic in logicism. Philosophical Review, 111(1), 25–65.
MacKenzie D. (2001). Mechanizing Proof: Computing, Risk, and Trust. Cambridge, MA: MIT Press.
Marciszewski W. & Murawski R. (1995). Mechanization of Reasoning in a Historical Perspective. Poznaǹ Studies in the Philosophy of the Sciences and the Humanities, Vol. 43. Amsterdam: Rodopi.
Marr D. (1982). Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York: W. H. Freeman and Company.
McGee V. (1996). Logical operations. Journal of Philosophical Logic, 25(6), 567–580.
Myhill J. (1960). Some remarks on the notion of proof. The Journal of Philosophy, 57(14), 461–471.
Poincaré H. (1894). Sur la nature du raisonnement mathématique. Revue de Métaphysique et de Morale, 2, 371–384.
Prawitz D. (2012). The epistemic significance of valid inference. Synthese, 187(3), 887–898.
Prawitz D. (2013). Validity of inferences. In Frauchiger M., editor. Reference, Rationality, and Phenomenology: Themes from Føllesdal. Heusenstamm: Ontos Verlag, pp. 179–204.
Rav Y. (1999). Why do we prove theorems?
Philosophia Mathematica, 7(3), 5–41.
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.
Robinson J. A. (1991). Formal and informal proofs. In Boyer R. S., editor. Automated Reasoning: Essays in Honor of Woody Bledsoe. Automated Deduction Series, Vol. 1. London: Kluwer Academic Publishers, pp. 267–282.
Robinson J. A. (1997). Informal rigor and mathematical understanding. In Gottlob G., Leitsch A., and Mundici D., editors. Computational Logic and Proof Theory: Proceedings of the 5th Annual Kurt Gödel Colloquium, August 25–29, 1997. Lecture Notes in Computer Science, Vol. 1289. Heidelberg & New York: Springer, pp. 54–64.
Robinson J. A. (2000). Proof = guarantee + explanation. In Hölldobler S., editor. Intellectics and Computational Logic. Applied Logic Series, Vol. 19. Dordrecht: Kluwer Academic Publishers, pp. 277–294.
Robinson J. A. (2004). Logic is not the whole story. In Hendricks V., Neuhaus F., Scheffler U., Pedersen S. A., and Wansing H., editors. First-Order Logic Revisited. Berlin: Logos Verlag, pp. 287–302.
Russell B. (1913). The philosophical importance of mathematical logic. The Monist, 22(4), 481–493.
Ryle G. (1954). Dilemmas. Cambridge: Cambridge University Press.
Sher G. (1991). The Bounds of Logic: A Generalized Viewpoint. Cambridge, MA: MIT Press.
Sieg W. (2009). On computability. In Irvine A., editor. Handbook of the Philosophy of Mathematics. North-Holland: Elsevier, pp. 535–630.
Sjögren J. (2010). A note on the relation between formal and informal proof. Acta Analytica, 25(4), 447–458.
Stenning K. & Van Lambalgen M. (2008). Human Reasoning and Cognitive Science. Cambridge, MA: MIT Press.
Sundholm G. (2012). “Inference versus consequence” revisited: Inference, consequence, conditional, implication. Synthese, 187(3), 943–956.
Suppes P. (2005). Psychological nature of verification of informal mathematical proofs. In Artemov S., Barringer H., d’Avila Garcez A., Lamb L. C., and Woods J., editors. We Will Show Them: Essays in Honour of Dov Gabbay, Vol. 2. London: College Publications, pp. 693–712.
Tanswell F. (2015). A problem with the dependence of informal proofs on formal proofs. Philosophia Mathematica, 23(3), 295–310.
Tarski A. (1936/2002). On the concept of following logically. History and Philosophy of Logic, 23, 155–196.
Tarski A. (1986). What are logical notions?
History and Philosophy of Logic, 7(2), 143–154.
Thurston W. P. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30(2), 161–177.
Van Benthem J. (1989). Logical constants across varying types. Notre Dame Journal of Formal Logic, 30(3), 315–342.
Weir A. (2016). Informal proof, formal proof, formalism. The Review of Symbolic Logic, 9(1), 23–43.
Yablo S. (2014). Aboutness. Princeton: Princeton University Press.