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Referências bibliográficas
ALISSON, H. E. (1992) El idealismo transcendental de Kant: una
interpretación y defensa. Barcelona: Anthropos; México: Universidad
Autónoma Metropolitana, Iztapalapa.
AMBROSE, A. (1977) “The Yellow Book Notes in Relation to ‘The Blue
Book’”. In: Crítica: Revista Hispanoamericana de Filosofía , Vol. 9, No. 26,
pp. 3-23.
PUC-Rio - Certificação Digital Nº 0912803/CA
APPEL, K. (1976). “The proof of the four-color theorem”. In: New Scientist,
(21 de outubro).
_________. (1984) “The use of the Computer in the Proof of the Four
Color Theorem”. In: Proceedings of the American Philosophical Society.
Vol. 128, nº1. pp. 35-39.
APPEL & HAKEN, K. & W. (1976) “Every planar map is four colorable”
(Research announcements). In: Bulletin of the American Mathematical
Society. Volume 82, nº 5. Pp. 711-12.
_______________________. (1977) “The Solution of the Four-Color-Map
Problem”. In: Scientific American, v. 237, nº. 4, pp. 108-121.
_______________________. (1978) “The Four-Color Problem”. In:
STEEN, L. A. Mathematics Today. New York/ Heidelberg/ Berlin: Spring
Verlag, p. 153 –180.
_______________________. (1986) “The Four Color Proof Suffices”. In:
The Mathematical Intelligencer, v. 8, nº 1, pp. 10-20.
BARBOSA FILHO, B. (2008) “Notas sobre o conceito de jogo-delinguagem nas Investigações”. In: Wittgenstein no Brasil. São Paulo:
Escuta, pp. 163- 190.
BAKER, G. (2005) Wittgenstein’s Method: neglected aspects: essays on
Wittgenstein. Katherine J. Morris (ed.), Oxford: Wiley-Blackwell.
BAKER, G. & HACKER, P. M. S. (1980) Wittgenstein: Understanding and
Meaning – Volume 1 of an Analytical Commentary on the Philosophical
Investigations. Oxford: Blackwell.
____________________________. (1985) Wittgenstein: Rules, Grammar
and Necessity, Volume 2 of an Analytical Commentary on the
Philosophical Investigations. Oxford: Blackwell.
193
____________________________. (1985) Wittgenstein: Rules, Grammar
and Necessity, Volume 2 of an Analytical Commentary on the
Philosophical Investigations, Oxford: Blackwell (2nd extensively revised
edition 2009).
BASSLER, O. B. (2006) “The Surveyability of Mathematical Proof: A
Historical Perspective”. In: Synthese, 148, pp. 99-133.
BERNAYS, P. (1965) “Some empirical aspects of mathematics”. In: Dockx,
S. & Bernays, p. (eds.) Information and Prediction in Science. New
York/London: Academic Press, , pp. 123-128.
BIGGS, N.L., Lloyd, E.K., WILSON, R.J. (1997) Graph Theory 1736 –
1936. Oxford: Oxford University Press.
PUC-Rio - Certificação Digital Nº 0912803/CA
BOOLOS, G., “Don’t Eliminate Cut”. In: Logic, Logic and Logic, pp. 365 –
369. Cambridge, MA: Harvard University Press, 1998.
BOUVERESSE, J. (1971) La parole malheureuse – De l'alchimie
linguistique à la grammaire philosophique. Paris: Minuit.
_______________. (1987) La force de la règle – Wittgenstein et
l’invention de la necessité. Paris: Minuit.
BUNGE, M. (2000) Dicionário de filosofia. São Paulo: Perspectiva.
BURGE, T. (1998) “Computer proof, a priori knowledge and other minds”.
In: Philosophical Perspectives, vol. 12, pp. 1–37.
BURNYEAT, M. F. (1996) “Enthymeme: Aristotle on the Rationality of
Rhetoric” In: Essays on Aristotle's Rhetoric. Berkeley, Los Angeles,
London: University of California Press, pp. 88-115.
CASSIRER, E. (2011) A filosofia das formas simbólicas: terceira parte –
fenomenologia do conhecimento. São Paulo: Martins Fontes – Selo
Martins.
CAYGILL, H. (2000) Dicionário Kant. Tradução de Álvaro Cabral. Revisão
técnica de Valério Rohden. Rio de Janeiro: Jorge Zahar Ed.
CAYLEY, A. (1879) “On the Colouring of Maps”. In: Proceedings of the
Geographical Society and Monthly Record of Geography. New Monthly
Series. Vol. 1, nº 4 (Abril), pp. 259 – 261.
CHATEAUBRIAND, O. (2005) Logical Forms Part II – Logic, Language,
and Knowledge. Campinas: Centro de Lógica, Epistemologia e História da
Ciência.
____________________. (2007) “Lógica e conhecimento”. In: Analytica
(UFRJ), v. 11, p. 13-52.
194
____________________. (2008a) “Dialectical rhetoric: response to Abel
Lassalle Casanave”. In: Manuscrito – Logic Language and Knowledge –
Essays on Chateaubriand’s Logical Forms. Vol. 31– nº1 (Jan. – Jun), pp.
25 – 43.
___________________. (2008b) “Proof in mathematics: response to Jairo
José da Silva”. In: Manuscrito – Logic Language and Knowledge – Essays
on Chateaubriand’s Logical Forms. Vol. 31– nº1 (Jan. – Jun), pp. 197 –
202.
COFFA, A. (1991) The semantic tradition from Kant to Carnap: to the
Vienna Station. Cambridge: Cambridge University Press.
PUC-Rio - Certificação Digital Nº 0912803/CA
COHEN, D. (1991) “The superfluous paradigm”. In: The mathematical
revolution inspired by computing. New York: Clarendon Press, pp. 323329.
CURRY, H. B. (1941) “Some aspects of the problem of mathematical
rigour”. In: Bulletin of the American Mathematical Society, n. 47, pp. 221241.
____________. (1951) Outlines of a Formalist Philosophy of Mathematics.
Amsterdam: North-Holland Publishing Company.
D’AMORE, B. (2007) Elementos de Didática da Matemática. Tradução
Maria Cristina Bonomi. São Paulo: Editora Livraria da Física.
DETLEFSEN, M. & LUKER, M. (1980) “The four-color theorem and
mathematical proof”. In: The Journal of Philosophy, vol. 77, pp. 803-820.
DEVLIN, K. (1999) Mathematics: the new golden age. New Yor: Columbia
University Press.
DIEUDONNÉE, J. (1980) “Les grandes lignes de l’évolution
mathématique”. In: Cahiers Fundamenta Scientiae. Séminaire sur les
Fondements des Sciences Strasbourg, n. 94, pp. 1-13.
DOWEK, G. (2007) Les métamorphoses du calcul. Paris: Pommier.
DUMMETT, M. A. E. (1978). Truth and other enigmas. London:
Duckworth.
__________________.
(1986)
“Wittgenstein’s
Philosophy
of
Mathematics”. In: Wittgenstein: Critical Assessements – Volume Three:
from the Tractatus to Remarks on the feoundations of mathematics, pp.
121 – 137.
ENGELMANN, M. (2009a) “The Multiple Complete Systems Conception
as Fil Conducteur of Wittgenstein’s Philosophy of Mathematics”. In:
Proceedings of the 32nd Wittgenstein International Symposium. v. 32.
195
________________. (2009b) “O que é o Big Typescript?” In: DoisPontos,
vol. 6, n. 1, pp. 35-61.
ESQUISABEL, O. M. (2012) “Representing and abstracting: An Analysis
of Leibniz’s Concept of Symbolic Knowledge”. In: Symbolic Knowledge
from Leibniz to Husserl. Studies in Logic, London: College Publications,
vol. 41, pp. 1- 49.
FEFERMAN, S. “The logic of Mathematical Discovery versus The logical
Structure of Mathematics”. In: In the light of logic. New York: Oxford
University Press, 1998, pp. 77-93.
FERRATER MORA, J. (2009) Diccionario de filosofía. Nueva edición
revisada, aumentada y actualizada por Josep-Maria Terricabas.
Barcelona: Editorial Ariel.
PUC-Rio - Certificação Digital Nº 0912803/CA
FLORIDI, L. (2004) The Blackwell Guide to the Philosophy of Computing
and Information. Oxford: Blackwell Publishing.
FRASCOLLA, P. (1994) Wittgenstein’s Philosophy of Mathematics.
London and New York: Routledge.
FREGE, G. (1971)“Que la science justifie un recours à une idéographie”.
In: Écrits logiques et philosphiques. Tradução francesa de Claude Imbert.
Paris: Points Seuil, pp. 63-69.
_________. (1980) Os fundamentos da aritmética. Tradução Luiz
Henrique Lopes Santos. São Paulo: Abril Cultural.
FRIEDMAN, M. (1999) Reconsidering Logical Positivism. Cambridge:
Cambridge University Press.
FRITSCH & FRITSCH, R. & G. (1998) The Four-Color Theorem. Trad.
Julie Peschke. New York/ Heidelberg/ Berlin: Spring Verlag.
GLOCK. J. (1997) Dicionário Wittgenstein. Tradução Helena Martins,
revisão técnica Luiz Carlos Pereira. Rio de Janeiro: Jorge Zahar.
GRANGER, G-G. (1974) Filosofia do Estilo. Trad. Scarlett Marton. São
Paulo: Perspectiva.
_______________. (1994) Formes, opérations, objets. Paris: VRIN.
GINSBURG, C. (2002) Relações de força: história, retórica, prova.
Tradução Eduardo Brandão. São Paulo: Companhia das Letras.
GLAS. E. (2001a) “The ‘Popperian Programme’ and Mathematics. Part I:
the Fallibilist Logic of Mathemarical Discovery”. In: Studies in History and
Philosophy of Science, Vol. 32, n. 1, pp. 119-137.
196
________. (2001b) “The ‘Popperian Programme’ and Mathematics. Part II:
from Quasi-Empiricism to Mathematical Research Programmes”. In:
Studies in History and Philosophy of Science, vol. 32, n. 2, pp. 355-376.
GÖDEL, K. (1931) “Über formal unentscheidbare Sätze der Principia
Mathematica und verwandter Systeme I”. In: Monatshefte für Math. und
Physik 38, pp. 173-198.
_________. (1936) “Über die langue von Beweisen”. Ergebnisse eines
mathematischen Koloquiuns, 2: 23-24.
GONTHIER, G. “Formal Proof: The Four Color Theorem”. In: Notices of
the American Mathematical Society, vol. 55, n. 11, 2008, pp. 1382- 1393.
PUC-Rio - Certificação Digital Nº 0912803/CA
HACKER, P. M. S. (2009) “Proof in Mathematics”. Disponível em
www.math.ru.nl/~landsman/Hacker.pdf
HADAMARD, J. (2009) A psicologia da invenção na matemática. Rio de
Janeiro: Contraponto.
HAKEN, W. (1977) “An Attempt to Understand the Four Color Problem”.
In: Journal of Graph Theory, vol. 1, pp. 193 – 206.
HANNA, G. (1990) “Some pedagogical aspects of proofs”. In: Interchange,
Volume 21, Issue 1, pp 6-13.
HARDY, G. H. (1929) “Mathematical proof”. In : Mind, vol. 38, n. 149, pp.
1-25.
HILBERT, D. (1923a) “The logical foundations of mathematics”. In: van
Heijenoort. From Kant to Hilbert – Vol II. Oxford: Oxford University Press,
1996, pp. 1134-1148.
HOUAISS, A. & VILLAR, M. e S. (2009) Dicionário Houaiss da Língua
Portuguesa. Rio de Janeiro: Objetiva.
JOURDAN, C. A. (2009). Impredicatividade, Generalidade e o
Desenvolvimento do Pensamento de Wittgenstein. Tese (Doutorado em
Filosofia) – Pontifícia Universidade Católica do Rio de Janeiro. Orientador:
Luiz Carlos Pereira. Rio de Janeiro.
JOURDAN, C. A. & PEREIRA, L. C. P. D. “Provas como Figuras e Figuras
como Provas em Wittgenstein”. In: Visualização das Ciências Formais.
London: College Publications, 2012, p. 105 – 124.
KALMÁR, L. (1967) “Foundations of Mathematics: Whither Now?”. In:
Lakatos, I. (Ed.) Problems in the Philosophy of Mathematics –
Proceedings of the International Colloquium in the Philosophy of Science,
London, 1965. Amterdam: Noth-Holland, pp. 187-207.
197
KANT. I. (2001) Crítica da razão pura. Trad. Manuela Pinto dos Santos e
Alexandre Fradique Mourujão. 5ª ed. Lisboa: Fundação Calouste
Goulbenkian. (CRP)
KREISEL, G. (1972) “Informal Rigour and Completeness Proofs”. In:
Problems in the Philosophy of Mathematics. North-Holland, pp. 138 – 186.
___________. (1977) “From foundations to science: Justifying and
unwinding proofs”. In: Recueil des travaux de 1'1nstitut Mathématique –
Nouvelle serie (Symposium: Set theory. Foundations of Mathematics,
Beograd, 29.08 - 2.09.1977). Tome 2 (10), pp. 63-72.
KRIPKE, S. (1980) Naming and Necessity. Oxford: Blackwell.
PUC-Rio - Certificação Digital Nº 0912803/CA
_________. (1978) “Some facts from the theory of proofs and some
fictions from general proof theory”. In: Essays on Mathematical and
Philosophical Logic Synthese Library, Vol. 122, pp. 3-23.
LAKATOS, I. (1967) (Ed.) Problems in the Philosophy of Mathematics –
Proceedings of the International Colloquium in the Philosophy of Science,
London, 1965. Amsterdam: Noth-Holland.
____________. (1976) Proofs and Refutations: The Logic of Mathematical
Discovery. London: Cambridge University Press.
____________. (1998) “A Renaiscence of Empiricism in the Philosophy of
Mathematics”. In: New Directions in the Philosophy of Mathematics. New
Jersey: Princeton University Press, pp. 29-47.
LASSALLE CASANAVE, A. (1999) “La concepción de demonstración de
Oswaldo Chateaubriand”. In: Manuscrito – Logic Language and
Knowledge – Essays in Honour of Oswaldo Chateaubriand Filho. Vol.
XXII, nº2, Outubro, pp. 95-107.
________________________. (2006) “Matemática elemental, cálculo y
normatividad”. O Que nos Faz Pensar, v. 20, p. 67-72.
________________________. (2008) “Entre la retórica y la dialectica”. In:
Manuscrito – Logic Language and Knowledge – Essays on
Chateaubriand’s Logical Forms. Vol. 31– nº1 (Jan-Jun), pp. 11 – 18.
________________________. (2012a) (Ed.) Symbolic Knowledge from
Leibniz to Husserl. Studies in Logic, vol. 41. London: College Publications.
________________________. (2012b) “Demonstraciones catholicas y
echteticas”. In: Visualização das Ciências Formais. London: College
Publications, 2012, p. 47 – 58.
198
________________________. (2012c) “Por construção de conceitos”. In:
Comentários às obras de Kant: Crítica da Razão Pura, Joel Thiago Klein
(org.). Florianópolis: NEFIPO.
________________________. (2012d) “Kant’s avatar of symbolic
knowledge”. In: Symbolic Knowledge from Leibniz to Husserl. Studies in
Logic, vol. 41. London: College Publications, pp. 51-77.
LAUSBERG, H. (1975) Elementos de retórica literária. Madrid: Biblioteca
Románica Hispánica/ Editorial Gredos.
LEGRIS, J. (2012) “Between Calculus and semantic Analysys: Symbolic
Knowlwdge in the origins of Mathematical Logic”. In: Symbolic Knowledge
from Leibniz to Husserl. Studies in Logic, vol. 41. London: College
Publications, pp. 79-113.
PUC-Rio - Certificação Digital Nº 0912803/CA
LOLLI, G. (2008) Deduction, Computation, Experiment: Exploring the
Effectiveness of Proof. Berlin/Helderberg/New York: Springer, pp. 65-79.
MacKENZIE, D. (2001) Mechanizing Proof: Computer, Risk and Trust.
Cambridge/London: The MIT Press.
–––––––––––––. (2005) “Computing and the cultures of proving”. In:
Philosophical Transactions: Mathematical, Physical and Engineering
Sciences, vol. 363, nº 1835 – The Nature of Mathematical Proof, pp. 2335
– 2350.
McLUHAN, M. (1964) Understanding media: the extensions of man.
London: Abacus.
MANCOSU, P. (2001) “Explanation in Mathematics”. In: The Stanford
Encyclopedia
of
Philosophy.
URL:
http://plato.stanford.edu/archives/sum2011/entries/mathematicsexplanation/
____________. (2010) “Mathematical Style”. In: The Stanford
Encyclopedia
of
Philosophy.
URL:
http://plato.stanford.edu/archives/spr2010/entries/mathematical-style/
MAYER, J. (1980) “Paul Valéry et le Problème de Quatre Couleurs”. In:
Regards sur la théorie des graphes. Presses Polytechniques Romandes
de Lausanne.
MÁTÉ, A. (2006) “Árpád Szabó and Imre Lakatos – Or the relation
between history and philosophy of mathematics”. In: Perspectives on
Science, pp. 282 – 301.
MaCKENZIE. D. (2001) Mechanizing proof – computing, risk and trust.
Cambridge/London: The MIT Press.
199
McEVOY , M. “Experimental mathematics, computers and the a priori”. In:
Synthese. 2011. Disponível em:
http://rd.springer.com/article/10.1007/s11229- 011-0035-1#
MARION, M. (1998) Wittgenstein, Finitism, and the Foundations of
Mathematics. Oxford: Oxford University Press.
___________. (1994) Ludwig Wittgenstein – Introduction au Tractatus.
Paris: PUF.
___________. (2004) “Pertinence et actualité de la philosophie des
mathématiques de Wittgenstein”. In: Wittgenstein et les mathématiques,
E. Rigal (Ed.). Mauvezin : T.E.R., pp. 87-115.
PUC-Rio - Certificação Digital Nº 0912803/CA
____________. (2009) “Radical anti-realism, Wittgenstein, and the length
of proofs”. In: Synthese, Volume 171, Number 3 / December, pp. 419 –
432.
____________. (2011) “Wittgenstein on the Surveyability of Proofs”. In:
The Oxford Handbook on Wittgenstein, M. McGinn & O. Kuusela (Eds.).
Oxford: Oxford University Press, pp. 138-158.
MARTINS, H. (2011). “A escrita poética de Wittgenstein, sua tradução”. In:
Revista Brasileira de Literatura Comparada, v. 19, pp. 109-125.
MÜHLHÖLZER, F. (2005) “‘A mathematical proof must be surveyable’ –
what Wittgenstein mean by this and what it implies”. In: Grazer
Philosophische Studien vol. 71, pp. 57–86.
ÖBERG, A. (2011) Hilary Putnam on Meaning and Necessity. Dissertation
presented at Uppsala University for the degree of Doctor of Philosophy.
Advisor: Sören Stenlund, 166p.
PAGIN, P. (1994) “Knowledge of Proofs”. In: Topoi 13: 93 – 100.
PAP, A. (1944) “The different kinds of a priori”. The Philosophical Review.
Vol. 53, n. 5, pp. 465-484.
_______. (1946) The A Priori in Physical Theory. New York: King's Crown
Press; London: G. Cumberlege.
_______. (1970) Semántica y verdad necessária – Una investigación
sobre los fundamentos de la Filosofía Analítica. Trad. César N. Molina
Flores. México: Fondo de Cultura Económica.
PERELMAN, C & OLBRECHTS-TYTECA, O. (2005). Tratado da
argumentação: a nova retórica. 6ª ed. São Paulo: Martins Fontes, 2005.
PIAGET, J. (1960) “Les sctructures mathématiques et les structures
opératoires de l’intelligence”. In: L’Enseignement des mathématiques.
200
Publication collective de la Comission pour l’étude et l’amélioration de
l’enseignement des mathématiques. Paris: Delachaux & Niestlé, pp. 1133.
POINCARÉ, J. H. (1908) “L’invention mathématique”. In: Bulletin of the
Institute of General Psychology, Vol. 8, pp. 175-187.
____________. J. H. (1995) O valor da ciência. Tradução de Maria
Helena Franco Martins. Rio de Janeiro: Contraponto.
PÓLYA, G. (1981) Mathematical Discovery: On Understanding, Learning,
and Teaching Problem Solving (Combined edition). New York : John
Wiley.
PUC-Rio - Certificação Digital Nº 0912803/CA
PORCHAT PEREIRA, O. (2001) Ciência e Dialética em Aristóteles. São
Paulo: Editora UNESP.
PRAWITZ, D. (2008) “Proofs verifying programs and programs producing
proofs”. In: Deduction, Computation, Experiment: Exploring the
Effectiveness of Proof. Berlin/Helderberg/New York: Springer, pp. 81-94.
PUDLÁK, P. “The lenght of proofs” In: Studies in logic and the foundations
of mathematics: Handbook of Proof Theory. pp. 547 – 637, 1997.
PUTNAM, H. (1975) “What is mathematical truth?”. In: Philosophical
Papers, vol. 1. Cambridge: Cambridge University Press, pp. 60-78.
ROBERTSTON, N., SANDERS, D., SEYMOUR, P. & THOMAS,R. (1997)
The Four-Color Theorem. In: Journal of Combinatorial Theory, Series B, v.
70, pp. 2-44.
ROSSI, P. (2004) A chave universal: artes da memorização e lógica
combinatória desde Lúlio até Leibniz. Trad. Antonio Angonese. Bauru:
EDUSC.
SAATY, T. & KAINEN, C. (1986) The Four-Color Problem: Assaults and
conquest. New York: Dover Publications.
SHANKER, S. (1986) “The Appel-Haken solution of the Four-Colour
Problem”. In: Wittgenstein: Critical Assessements – Volume Three: from
the Tractatus to Remarks on the foundations of mathematics. London:
Routledge, pp. 395-412.
___________ . (1987) Wittgenstein and the Turning Point in the
Philosophy of Mathematics. London: Croom Helm.
___________ . (1998) Wittgenstein’s Remarks on the foundation of AI.
London, New York: Routledge.
201
SHAPIRO, S. (2000). Thinking about mathematics. Oxford: Oxford
University Press.
SIEG, W. (1999) “Hilbert’s Programs: 1917-1922”. In: The Bulletin of
Symbolic Logic, v. 5 n. 1, pp. 1-44.
SILVA, J.J. da. (2008) “On Proofs in Mathematics”. In: Manuscrito – Logic
Language and Knowledge – Essays on Chateaubriand’s Logical Forms.
Vol. 31– nº1 (Jan-Jun), pp. 185 – 196.
SINGH, S. (2008) O último teorema de Fermat: a história do enigma que
confundiu as maiores mentes do mundo durante 358 anos. Rio de
Janeiro: Editora Record.
PUC-Rio - Certificação Digital Nº 0912803/CA
SMITH, D. E. (1929) A source book in Mathematics. New York: McGrawHill Book Company.
STEINER, M. (1996) “"Wittgenstein: Mathematics, Regularities, Rules”. In:
Benacerraf and His Critics, edited by Adam Morton and Stephen P. Stich.
Oxford: Blackwell Publishing, pp. 190-212.
_____________.
(2009) “Empirical Regularities in Wittgenstein’s
Philosophy of Mathematics”. In: Philosophia Mathematica (III) 17, pp. 1–
34.
STENLUND, S. (1990) Language and philosophical problems. London:
Routledge.
____________.
(2012a) “The ‘Middle Wittgenstein’ and Modern
Mathematics”. In: Epistemology versus Ontology. Logic, Epistemology,
and the Unity of Science Volume 27, pp. 139-159.
____________. (2012b) “Wittgenstein and Symbolic Mathematics”. In: O
que nos faz pensar, vol 33 – no prelo.
SUNDHOLM, G. (1993) “Questions of proof”. In: Manuscrito. XVI (2), out.,
pp. 47-70.
STEWART, I.
Publications.
(1995)
Concepts
of
Modern
Mathematics.
Dover
SWART, E.R. (1980) “The Philosophical Implications of the Four-Color
Problem”. The American Mathematical Monthly, v. 87, n. 9, pp. 697-707.
STILLWELL, S. (1992) “Empirical Inquiry and Proof”. In: Proof and
Knowledge in Mathematics. New York: Routledge, pp. 110-134.
TELLER, P. (1980) “Computer Proof”. In: The Journal of Philosophy, vol.
77, pp. 797 - 803.
202
TOULMIN, S. (2001) Os usos do argumento. Tradução Reinaldo Guarany.
São Paulo: Martins Fontes.
TURNER, R. & EDEN, A. (2009) “The Philosophy of Computer Science”.
Entry of the Stanford Encyclopedia of Philosophy. URL =
<http://plato.stanford.edu/archives/win2011/entries/computer-science/>
TYMOCZKO, T. (1979) “The Four-Color Problem and its Philosophical
Significance”. In: The Journal of Philosophy, Vol 27, nº 2, pp 57-83.
–––––––––––––––– (1998) (Ed.) New Directions in the Philosophy of
Mathematics. (Revised and expanded edition). Princeton: Princeton
University Press.
PUC-Rio - Certificação Digital Nº 0912803/CA
von PLATO, J. (2008) "The Development of Proof Theory". Entry of The
Stanford
Encyclopedia
of
Philosophy
(Fall
Edition).
URL=<http://plato.stanford.edu/archives/fall2008/entries/prooftheorydevelopment/>.
VAZ, B.R.L. O papel dos diagramas na geometria euclidiana. Tese
(Doutorado em Filosofia) – Pontifícia Universidade Católica do Rio de
Janeiro. Orientador: Luiz Carlos Pereira. Rio de Janeiro.
WANG, H. (1955) “On formalization”. In: Mind, New Series, vol. 64, nº. 254
(Abril), pp. 226-238.
________. (1960) “Toward Mechanical Mathematics”. In: IBM Journal of
Research and Development vol. 4, pp. 2–22.
________. (1963) “The Axiomatic Method”. In: A Survey of Mathematical
Logic. Pecking: Science Press, Amsterdam: North-Holland Publishing
Company, pp. 1-28.
_________. “The Formalization of Mathematics”. In: The Journal of
Symbolic Logic, vol. 19, n. 4, 1954, pp. 241-266.
_________. (1981) Popular Lectures on Mathematical Logic. New York:
Dover Publications.
_________. (1991) “To and from philosophy – discussions with Gödel and
Wittgenstein”. In: Synthese 88, 229–277.
WONG, K-Y. “Computers, Mathematical Proof, and A Priori Knowledge”.
Aguardando orientação do autor sobre como citar.
WEBER, K. (2002) “Beyond Proving and Explaining: Proofs That Justify
the Use of Definitions and Axiomatic Structures and Proofs That Illustrate
Technique”. In: For the learning of mathematics, vol 22, n.3, pp. 14-17.
203
WILSON, R. J. Four Colours Suffice: How the Map Problem Was Solved.
London: Penguin Books, 2002.
WRIGLEY, M. (1986) “Wittgenstein’s Philosophy of Mathematics”. In:
Wittgenstein: Critical Assessements – Volume Three: from the Tractatus to
Remarks on the foundations of mathematics, pp. 183 – 192.
___________. (1993) “The continuity of Wittgenstein’s Philosophy of
Mathematics”. In: Wittgenstein's Philosophy of Mathematics, K. Puhl, (ed.),
Vienna: Verlag Hölder-Pichler-Tempsky: 73-84.
WRIGHT, C. (1980). Wittgenstein on the Foundations of Mathematics.
London: Duckworth.
PUC-Rio - Certificação Digital Nº 0912803/CA
WITTGENSTEIN, L. (1969) On certainty. Ed. By G. E. M. Anscombe and
G. H. Von Wright. Translated by Denis Paul and G. E. M. Anscombe. New
York: Harper Torchbooks.
_________________. (1976) Wittgenstein's Lectures on the Foundations
of Mathematics. Diamond, C. (ed.), Ithaca, N.Y: Cornell University Press.
(LFM)
_________________. (1978) Remarks on the foundations of Mathematics.
Edited by G.H. Von Wright, R. Rhees, G.E.M. Anscombe. Translated by
G.E.M. Anscombe. Third Edition. Basil Blackwell, Oxford. (RFM)
_________________. (1980) Culture and Value. G.H. von Wright (ed.), P.
Winch (trans.), Oxford: Blackwell.
_________________. (1983) Remarques sur les fondements des
mathématiques. Traduit de l’allemand par Marie-Anne Lescourret. Paris:
Gallimard.
_________________. (2000) Da certeza. Edição bilíngue. Lisboa: Edições
70.
_________________. (2001) Philosophical Investigations. Third edition
(The german text with a revised english translation). Oxford: Blackwell
Publishing.
_________________. (2008) Tratado lógico-filosófico & Investigações
filosóficas. Lisboa: Fundação Calouste Goulbenkian.
_________________. (2008) Tractatus Logico-Philosophicus. Trad. Luís
Henrique Lopes dos Santos. São Paulo: Editora da Universidade de São
Paulo. (TLP)