Proof phenomenon as a function of the phenomenology of proving

Progress in Biophysics and Molecular Biology

Volumn 119, Issue 3, 2015, Pages 360-367

  Hipólito, Inês ^a  

^a UNIVERSIDADE NOVA DE LISBOA   (Portugal)

Author keywords

Intention; Intuition; Mathematical proof; Natural science; Neutral language; Phenomenological conscious experience; Proving; Shareable meanings

Indexed keywords

ANIMAL; ARTIFICIAL INTELLIGENCE; CONSCIOUSNESS; HUMAN; MATHEMATICS; PROCEDURES;

ANIMALS; ARTIFICIAL INTELLIGENCE; CONSCIOUSNESS; HUMANS; MATHEMATICS;

EID: 84949219203     PISSN: 00796107     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pbiomolbio.2015.06.014     Document Type: Review

References (59)

1. Bermudez J., Marcel A.J., Eilan N. The Body and the Self 1995, MIT Press, Cambridge, MA.
2. Bruni R. Gödel, Turing, the Undecidability Results and the Nature of Human Mind 2006, 37.
3. Chalmers D.J. Facing up to the problem of consciousness. J. Conscious. Stud. 1995, 2(3):200-219.
4. Chalmers David J. Facing up to the problem of consciousness. Toward a Science of Consciousness: the First Tucson Discussions and Debates 1996, vol. 1:5.
5. Cellucci C. Filosofia e matematica. Monograph Collection (Matt - Pseudo) 2002.
6. Clark A. Being There: Putting Brain, Body, and World Together Again 1997, MIT Press, Cambridge, MA.
7. De Preester H. Naturalizing Husserlian phenomenology: an introduction. Psychoanal. Perspect. 2002, 4:633-647.
8. Eco U. The Name of the Rose 2006, Everyman's Library, London.
9. Føllesdal D. Gödel and Husserl. Naturalizing Phenomenology 1999, Stanford University Press.
10. Gallagher S. On the possibility of naturalizing phenomenology. The Oxford Handbook of Contemporary Phenomenology 2012, Oxford University Press.
11. Gallagher S., Varela F. Redrawing the map and resetting the time: phenomenology and the cognitive sciences. Can. J. Philos. 2003, 29(Suppl.):93-132.
12. Geuvers J.H. Proof assistants: history, ideas and future. Sadhana Acad. Proc. Eng. Sc. - Indian Acad. Sci. 2009, 34(1):3-25.
13. Gödel K. Russell's mathematical logic. The Philosophy of Bertrand Russell 1944, 119-141. Northwestern University Press. Feferman, Dawson, Kleene (Eds.).
14. Gödel K. Some basic theorems on the foundations of mathematics and their implications. Collected Works 1951, vol. III. Oxford University Press.
15. Gödel K. What is Cantor's continuum problem?. Benacerraf and Putnam 1964, 258-273.
16. Gödel K. Collected Works III, 1961 1981, Oxford University Press.
17. Gödel K. Collected Works II. Publications 1938-1974 1990, Oxford University Press.
18. Hales T.C. Formal proof. Not. AMS 2008, 55(11):1370-1380.
19. Harrison J. Formal proof - theory and practice. Notices AMS 2008, 55:11.
20. Hass L. Merleau-Ponty's Philosophy 2008, Indiana University Press, Bloomington.
21. Hintikka J. The notion of intuition in Husserl. Rev. Int. Philos. 2003, 2:57-79.
22. Husserl E. Philosophy as a rigorous science. Phenomenology and the Crisis of Philosophy 1965, 71-147. Harper and Row, New York, (Original work published 1910-1911). Q. Lauer (Ed.).
23. Husserl E. Cartesian Meditations 1970, (trans: Cairns D.), Martinus Nijhoff, The Hague.
24. Husserl E. Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie I 1976, Husserliana III/1-2, Martinus Nijhoff, The Hague.
25. Husserl E. Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy. First Book. General Introduction to a Pure Phenomenology 1982, Martinus Nijhoff, The Hague, Trans. F. Kersten.
26. Husserl E. Logical Investigations 2001, 3 vols. Routledge, London, trans. J.N. Findlay.
27. Husserl Edmund Phantasy, Image Consciousness, and Memory (1898-1925). Collected Works 2005, vol. XI. Springer, Dordrecht, Trans. J. B. Brough.
28. James W. The Principles of Psychology 1890, Holt, New York.
29. Lawlor L. 'Becoming and Auto-affection (Part II): Who Are We?' Invited Lecture, ICNAP, 2009 2009, Published at:, (accessed 15.01.15.). http://www.icnap.org/meetings.htm.
30. Levine J. Materialism and qualia: the explanatory gap. Pac. Philos. Q. 1983, 64(4):354-361.
31. Lohmar D. Intuition in mathematics: on the function of eidetic variation in mathematical proofs. Phenmonenology and Mathematics 2010, Springer.
32. Lucas J.R. Minds, machines and gödel. Philosophy 1961, XXXVI:112-127.
33. Mac Lane S. Categories for the Workinh Mathematician 1971, Springer-Verlag, New York.
34. Marbach E. Mental Representation and Consciousness: towards a Phenomenological Theory of Representation and Reference 1993, Kluwer Academic Publishers, Dordrecht.
35. Marbach E. Towards a formalism for expressing structures of consciousness. Handbook of Phenomenology and Cognitive Science 2010, Springer, Dordrecht. S. Gallagher, D. Schmicking (Eds.).
36. Marchal B. The universal numbers. From biology to physics. J. Prog. Biophys. Mol. Biol 2015, 119(3):368-381. Special issue biomathics: life sciences.
37. Merleau-Ponty M. La structure du comportement 1942, PUF, Paris.
38. Merleau-Ponty M. Signs 1964, (trans: McCleary RC), Northwestern University Press, Evanston, IL.
39. Merleau-Ponty M. Phénoménologie de la perception 1971[1945], Gallimard, Paris, first published 1962 by Routledge & Kegan Paul. English ed.
40. Merleau-Ponty M. The Prose of the World 1973, Northwestern University Press, Evanston, John O'Neill (trans.).
41. Palombi F. The Star and the Whole: Gian-Carlo on Mathematics and Phenomenology 2011, CRC Press, Boca Raton.
42. Penrose R. Shadows of the Mind 1994, Oxford University Press, Oxford.
43. Post E. Absolutely Unsolvable Problems and Relatively Undecidable Propositions: Account of an Anticipation 1922, 338-433. In [Davis, 1965].
44. Powell A. Philosophy and mathematics. Theorema 1997, XVI(2):97-108.
45. Rota G. The phenomenology of mathematical proof. Synthese 1997, 111:183-196.
46. Rota G. Indiscrete Thought 1997, Birkäuser, Boston, MA. F. Palombi (Ed.).
47. Rota G. The Primacy of Identity 1997, 195-203. In: 1997b.
48. Roy J.-M., Petitot J., Pachoud B., Varela F.J. Beyond the gap: an introduction to naturalizing phenomenology. Varela, Pachoud & Petitot, Naturalizing Phenomenology 1999, Stanford University Press.
49. Shepard R. On the status of "direct" psychophysical measurement. Perception and Cognition Issues in the Foundations of Psychology 1978, University of Minnesota, USA. Savage (Ed.).
50. Shepard R. Lecture 1: Perception, Imagination, and Science 1999, April 12 at 2:15, Engineering Pavillion II.
51. Shepard R. Perceptual-cognitive universals as reflections of the World. Behav. Brain Sci. 2001, 24:581-601.
52. Simeonov P., Brezina E., Cottam R., Ehresmann A., Gare A., Goranson T., Gomez-Ramirez J., Josephson B., Marcha B., Matsuno K., Root-Bernstein R., Rössler, Salthe S., Schroeder M., Seaman B., Siregar P., Smith L. Stepping beyond the Newtonian paradigm in biology towards an integrable model of life: accelarating discovery in the biological foundations of science. Integral Biomathics 2012, Springer, Heidelberg.
53. Thiel C. Philosophie und Mathematik. Eine Einführung in ihre Wechselwirkungen und in die Philosophie der Mathematik 1995, Wissenschaftliche Buchgesellschaft, Darmstadt.
54. Thompson E. Mind in Life: Biology, Phenomenology, and the Sciences of Mind 2007, Harvard University Press, Cambrige, MA.
55. Tieszen R. Phenomenology, Logic, and the Philosophy of Mathematics 2009, Cambridge University Press.
56. Turing A. 'Intelligent machinery', report for National Physical Laboratory. Machine Intelligence 7 1948, B. Meltzer, D. Michie (Eds.).
57. Varela F., Thompson E., Rosch E. The Embodied Mind: Cognitive Science and Human Experience 1991, MIT Press, Cambridge, MA.
58. Weyl H. The Continuum. A Critical Examination of the Foundation of Analysis 1994, Dover, New York.
59. Zahavi D. Phenomenology and the project of naturalization. Phenomenol. Cognit. Sci. 2004, 3:331-347. Kluger Academic Publishers.