Philosophia mathematicae

[thumb|200px|[David Hilbert, unus ex primis fautoribus formalismi.]]
[thumb|200px|*[Principia Mathematica,* unum ex operibus maximi monenti de philosophia mathematicae.]]
[thumb|200px|[Bertrandus Russell (1872-1970).]]
[thumb|200px|[Henricus Poincaré (1854–1912), unus ex primis fautoribus conventionalismi.]]
[thumb|200px|[Ioannes Stuart Mill 1806-1873), unus ex primis fautoribus psychologismi.]]
[thumb|200px|[Hilarius Whitehall Putnam (n. 1926), discipulus Quinianus et fautor argumenti indispensabilitatis realismi.]]
**Philosophia mathematicae** est provincia philosophiae qui philosophicas mathematicae assumptiones, fundamenta, et implicationes investigat. Cuius principale propositum est rationem naturae et methodologiae mathematicae habere, et locum mathematicae in vitis hominum intellegere. Logica et structuralis mathematicae natura hoc studium latum et unicam inter eius res gemellas faciunt.

Locutiones *philosophia mathematicae* et *philosophia mathematica* saepe adhibentur synonyma. Hic autem ad alia investigationis provincias attingendas adhiberi potest. Quarum una propositum philosophicae materiae formalizandae ut aesthetica, ethica, logica, metaphysica, vel theologia, in forma ut videtur subtiliori et severiori, ut, exempli gratia, labores theologorum scholasticorum vel ordinata Leibnitii et Spinozae proposita attingit. Alia ad usitatam exercitatoris singuli vel consensus mathematicorum exercitantium philosophiam attingit. Praetera, nonnulli intellegunt vocabulum *philosophia mathematica* esse allusionem ad accessum ad fundamenta mathematicae a Bertrando Russell in libris *Principia Mathematica* et *Introduction to Mathematical Philosophy* suasa.

## Argumenta recurrentia
Inter argumenta recurrentia sunt:
*Quae sunt partes hominum in mathematica evoluta?
*Qui sunt fontes rerum mathematicarum?
*Quid est ontologicus entitatum mathematicarum status?
*Quid significat res mathematica?
*Quid est proprietas propositionis mathematicae?
*Quid est cognatio logicae et mathematicae?
*Quid est partes hermeneuticae in mathematica?
*Qualia genera investigationis partes in mathematica agunt?
*Quae sunt proposita investigationis mathematicae?
*Quid facultatem experientiae tenendae mathematicae dat?
*Quae sunt proprietates humanae pro mathematica?
*Quid est pulchritudo mathematica?
*Quid est fons et natura veritatis mathematicae?
*Quid est coniunctio abstracti mathematicae mundi et universi materialis?

*Antirealismus
*Argumentum
*Ars inveniendi
*Constructivismus mathematicus
*Lingua formalis
*Fundamenta mathematicae
*Historia mathematicae
*Logica mathematica
*Metamathematica
*Metaphilosophia
*Philosophia linguae
**Philosophia mathematica* (periodicum)
*Philosophia probabilitatis
*Philosophia scientiae
*Pythagoras
*Ratio aurea
*Ratio scientifica
*Systema axiomaticum
*Systema formale
*Theorema fundamentale arithmeticae
*Theorema fundamentale calculi
*Theoremata Gödel de imperfectione
*Theoria categoriarum
*Theoria copiarum
*Theoria copiarum axiomaticarum
*Theoria probabilitatum
*Veritas

### Res coniunctae
*Historia et philosophia scientiae
*Historia mathematicae
*Historia philosophiae

## Notae

## Bibliographia
*Aristoteles. 1938. Prior Analytics, conv. Hugh Tredennick. In *Aristotle,* vol. 1:181–531. Loeb Classical Library. Londinii: William Heinemann.
*Benacerraf, Paul, et Hilary Putnam, eds. 1964. *Philosophy of Mathematics, Selected Readings.* Englewood Cliffs Novae Caesareae: Prentice-Hall.
*Benacerraf, Paul, et Hilary Putnam, eds. 1983. *Philosophy of Mathematics, Selected Readings.* Ed. 2a. Englewood Cliffs Novae Caesareae: Prentice-Hall. Cantabrigiae: Cambridge University Press.
*Berkeley, George. 1734. *The Analyst; or, a Discourse Addressed to an Infidel Mathematician: Wherein It is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith,* ed. David R. Wilkins. Londinii et Dublin. Eprint.
*Bourbaki, N. 1994. *Elements of the History of Mathematics,* conv. John Meldrum. Berolini: Springer-Verlag.
*Chandrasekhar, Subrahmanyan. 1987. *Truth and Beauty: Aesthetics and Motivations in Science,* Sicagi: University of Chicago Press.
*Colyvan, Mark. 2004. Indispensability Arguments in the Philosophy of Mathematics. *Stanford Encyclopedia of Philosophy,* Edward N. Zalta. Eprint.
*Davis, Philip J., et Reuben Hersh. 1981. *The Mathematical Experience.* Novi Eboraci: Mariner Books.
*Devlin, Keith. 2005. ''The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs).'' Novi Eboraci: Thunder's Mouth Press.
*Dummett, Michael. 1991a. *Frege, Philosophy of Mathematics.* Cantabrigiae Massachusettae: Harvard University Press.
*Dummett, Michael. 1991b. *Frege and Other Philosophers.* Oxoniae: Oxford University Press.
*Dummett, Michael. 1993. *Origins of Analytical Philosophy.* Cantabrigiae Massachusettae: Harvard University Press.
*Ernest, Paul. 1998. *Social Constructivism as a Philosophy of Mathematics.* Albaniae Novi Eboraci: State University of New York Press.
*George, Alexandre, ed. 1994/ *Mathematics and Mind.* Oxoniae: Oxford University Press.
*Hadamard, Jacques. 1949. *The Psychology of Invention in the Mathematical Field.* Princetoniae: Princeton University Press.
*Hardy, G. H. 1940. ''A Mathematician's Apology.*
*Hart, Wilbur Dye., ed. 1996. *The Philosophy of Mathematics.* Oxoniae: Oxford University Press.
*Hendricks, Vincent F., et Hannes Leitgeb, eds. 2006. *Philosophy of Mathematics: 5 Questions.* Novi Eboraci: Automatic Press / VIP. Situs interretialis.
*Huntley, H. E. 1970. *The Divine Proportion: A Study in Mathematical Beauty.* Novi Eboraci: Dover Publications.
*Irvine, A., ed. 2009. *The Philosophy of Mathematics.* Handbook of the Philosophy of Science. Amsterlodami: North-Holland Elsevier.
*Klein, Jacob. 1968. *Greek Mathematical Thought and the Origin of Algebra,* conv. Eva Brann. Cantabrigiae Massachusettae: MIT Press.
*Kline, Morris. 1959. *Mathematics and the Physical World.* Novi Eboraci: Thomas Y. Crowell Company.
*Kline, Morris. 1972. *Mathematical Thought from Ancient to Modern Times.* Novi Eboraci: Oxford University Press.
*König, Julius. 1905. Über die Grundlagen der Mengenlehre und das Kontinuumproblem. *Mathematische Annalen* 61:156-160.
*Körner, Stephan. 1960. *The Philosophy of Mathematics, An Introduction.* Harper Books.
*Lakoff, George, et Rafael E. Núñez. 2000 *Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being.* Novi Eboraci: Basic Books.
*Lakatos, Imre. 1976. *Proofs and Refutations: The Logic of Mathematical Discovery,* ed. J. Worrall et E. Zahar. Cantabrigiae: Cambridge University Press.
*Lakatos, Imre. 1978. *Mathematics, Science and Epistemology: Philosophical Papers.* Vol. 2, ed. J. Worrall et G. Currie. Cantabrigiae: Cambridge University Press.
*Lakatos, Imre. 1968. *Problems in the Philosophy of Mathematics.* North Holland.
*Leibniz, G. W.. 1966. *Logical Papers (1666–1690),* ed. et conv. G. H. R. Parkinson. Londinii: Oxford University Press.
*Maddy, Penelope. 1997. *Naturalism in Mathematics.* Oxoniae: Oxford University Press. 
*Maziars, Edward A. 1969. Problems in the Philosophy of Mathematics. *Philosophy of Science* 36(3):325. doi:10.1086/288262.
*Maziarz, Edward A., et Thomas Greenwood. 1995. *Greek Mathematical Philosophy.* Barnes and Noble Books.
*Mount, Matthew. *Classical Greek Mathematical Philosophy.*
*Parsons, Charles. 2014. *Philosophy of Mathematics in the Twentieth Century: Selected Essays.* Cantabrigiae Massachusettae: Harvard University Press. ISBN 9780674728066.
*Peirce, Benjamin. 1870. Linear Associative Algebra, § 1. *American Journal of Mathematics* 4 (1881).
*Peirce, C. S.. 1931–1935, 1958. *Collected Papers of Charles Sanders Peirce.* vols. 1-6, ed. Charles Hartshorne et Paul Weiss; vols. 7-8, ed. Arthur W. Burks. Cantabrigiae Massachusettae: Harvard University Press.
*Plato. 1930. The Republic, Volume 1, conv. Paul Shorey. In *Plato, Volume 5.* Loeb Classical Library. Londinii: William Heinemann.
*Plato. 1935. The Republic, Volume 2, conv. Paul Shorey. In *Plato, Volume 6.* Loeb Classical Library. Londinii: William Heinemann.
*Resnik, Michael D. 1980. *Frege and the Philosophy of Mathematics.* Cornell University.
*Resnik, Michael. 1997. *Mathematics as a Science of Patterns.* Oxoniae: Clarendon Press. ISBN 9780198250142.
*Robinson, Gilbert de B. 1940, 1959. *The Foundations of Geometry.* Ed. 4a. Toronti: University of Toronto Press.
*Raymond, Eric S. 1993. *The Utility of Mathematics.* Eprint.
*Smullyan, Raymond M. 1993. *Recursion Theory for Metamathematics.* Oxoniae: Oxford University Press.
*Russell, Bertrand. 1919. *Introduction to Mathematical Philosophy.* Londinii: George Allen and Unwin.
*Shapiro, Stewart. 2000/*Thinking About Mathematics: The Philosophy of Mathematics.* Oxoniae: Oxford University Press.
*Strohmeier, John, et Peter Westbrook. 1999. *Divine Harmony, The Life and Teachings of Pythagoras.* Berkeleiae: Berkeley Hills Books.
*Styazhkin, N. I. 1969. *History of Mathematical Logic from Leibniz to Peano.* Cantabrigiae Massachusettae: MIT Press.
*Tait, William W. 1986. Truth and Proof: The Platonism of Mathematics. *Synthese* 69:341-370.
*Tarski, A. 1956, 1983. *Logic, Semantics, Metamathematics: Papers from 1923 to 1938,* conv. J. H. Woodger. Oxoniae: Oxford University Press. 1983 Ed 2a., ed. John Corcoran. Indianapoli: Hackett Publishing.
*Ulam, S. M. 1990. *Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and His Los Alamos Collaborators,* ed. A. R. Bednarek et Françoise Ulam. Berkeleiae: University of California Press.
*van Heijenoort, Jean, ed. 1967. *From Frege To Gödel: A Source Book in Mathematical Logic, 1879-1931.* Cantabrigiae Massachusettae: Harvard University Press.
*Wigner, Eugene. 1960. The Unreasonable Effectiveness of Mathematics in the Natural Sciences. *Communications on Pure and Applied Mathematics* 13(1):1-14.  Eprint.
*Wilder, Raymond L. 1980. *Mathematics as a Cultural System.* Pergamon.
*Witzany, Guenther. 2011. Can mathematics explain the evolution of human language? *Communicative and Integrative Biology* 4(5):516-520.

## Nexus externi
*Jones, R. B. Situs de philosophia mathematicae, www.rbjones.com
*Peirce, C. S.*Kaina Stoicheia,* www.cspeirce.com
**London Philosophy Study Guide,* www.ucl.ac.uk
**Philosophy of Mathematics, www.ucl.ac.uk
**Mathematical Logic, www.ucl.ac.uk
**Set Theory & Further Logic, www.ucl.ac.uk
*"The Philosophy of Real Mathematics," golem.ph.utexas.edu (bloh)
*

### Periodica
**Philosophia Mathematica,* philmat.oxfordjournals.org
**The Philosophy of Mathematics Education Journal,'' www.ex.ac.uk