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  • Cited by 29
Publisher:
Cambridge University Press
Online publication date:
November 2015
Print publication year:
2015
Online ISBN:
9781316286425

Book description

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

Reviews

'For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963–4 in the British Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material … the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised.'

Michael Dummett Source: Nature

'The whole book, as well as being a delightful read, is of immense value to anyone concerned with mathematical education at any level.'

C. W. Kilmister Source: The Times Higher Education Supplement

'In this book the late Imre Lakatos explores 'the logic of discovery' and 'the logic of justification' as applied to mathematics … The arguments presented are deep … but the author's lucid literary style greatly facilitates their comprehension … The book is destined to become a classic. It should be read by all those who would understand more about the nature of mathematics, of how it is created and how it might best be taught.'

Source: Education

‘How is mathematics really done, and - once done - how should it be presented? Imre Lakatos had some very strong opinions about this. The current book, based on his PhD work under George Polya, is a classic book on the subject. It is often characterized as a work in the philosophy of mathematics, and it is that - and more. The argument, presented in several forms, is that mathematical philosophy should address the way that mathematics is done, not just the way it is often packaged for delivery.’

William J. Satzer Source: MAA Reviews

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Contents

Bibliography
Abel, N. H. [1825] ‘Letter to Holmboë’, in Lie, S. and Sylow, L. (eds.): Oeuvres Complètes, vol. 2. Christiana: Grøndahl, 1881, pp. 257–8.
Abel, N. H. [1826a] ‘Letter to Hansteen’, in Lie, S. and Sylow, L. (eds.): Oeuvres Complètes, vol. 2. Christiania: Grøndahl, 1881, pp. 263–5.
Abel, N. H. [1826b] ‘Untersuchungen über die Reihe 1+m1x+m.(m−1)2x2+m.(m−1)(m−2)2.3x3…’, Journal für die Reine und Angewandte Mathematik, 1, pp. 311–39.
Abel, N. H. [1881] ‘Sur les Séries’, in Lie, S. and Sylow, L. (eds.): Oeuvres Complètes, vol. 2. Christiania: Grøndahl, pp. 197–205.
Aetius [c. 150] Placita, in Diels, H. (ed.): Doxographi Graeci. Berolini: Reimeri, 1879.
Aleksandrov, A. D. [1956] ‘A General View of Mathematics’, in Aleksandrov, A. D., Kolmogorov, A. N. and Lavrent'ev, M. A. (eds.): Mathematics: its Content, Methods and Meaning. (English translation by S. H. Gould, K. A. Hirsch and T. Bartha. Cambridge, Massachusetts: M.I.T. Press, 1963).
Ambrose, A. [1959] ‘Proof and the Theorem Proved’, Mind, 68, pp. 435–45.
Arber, A. [1954] The Mind and the Eye. Cambridge: Cambridge University Press.
Arnauld, A. and Nicole, P. [1724] La Logique, ou L'Art de Penser. Lille: Publications de la Faculté des Lettres et Sciences Humaines de L'Université de Lille, 1964.
Bacon, F. [1620] Novum Organum. English translation in Ellis, R. L. and Spedding, J. (eds.): The Philosophical Works of Francis Bacon. London: Routledge, 1905, pp. 241–387.
Baltzer, R. [1862] Die Elemente der Mathematik, vol. 2. Leipzig: Hirzel.
Bartley, W. W. [1962] Retreat to Commitment. New York: Alfred A. Knopf
Becker, J. C. [1869a] ‘Über Polyeder’, Zeitschrift für Mathematik und Physik, 14, pp. 65–76.
Becker, J. C. [1869b] ‘Nachtrag zu dem Aufsätze über Polyeder’, Zeitschrift für Mathematik und Physik, 14, pp. 337–343.
Becker, J. C. [1874] ‘Neuer Beweis und Erweiterung eines Fundamentalsatzes über Polyederflächen’, Zeitschrift für Mathematik und Physik, 19, pp. 459-60.
Bell, E. T. [1945] The Development of Mathematics. Second edition. New York: McGraw-Hill.
Bérard, J. B. [1818–19] ‘Sur le Nombre des Racines Imaginaires des Équations; en Réponse aux Articles de MM. Tédenat et Servois’, Annales de Mathématiques, Pures et Appliquées, 9, pp. 345–72.
Bernays, P. [1947] Review of Pólya [1945], Dialectica 1, pp. 178–88.
Bolzano, B. [1837] Wissenschaftslehre. Leipzig: Meiner, 1914–31.
Bourbaki, N. [1949] Topologie Général. Paris: Hermann.
Bourbaki, N. [1960] Éléments d'Histoire des Mathématiques. Paris: Hermann.
Boyer, C. [1939] The Concepts of the Calculus. New York: Dover, 1949.
Braithwaite, R. B. [1953] Scientific Explanation. Cambridge: Cambridge University Press.
Brouwer, L. E. J. [1952] ‘Historical background, Principles and Methods of Intuitionism’, South African Journal of Science, 49, pp. 139–46.
Carnap, R. [1937] The Logical Syntax of Language. New York and London: Kegan Paul. (Revised translation of Logische Syntax der Sprache, Vienna: Springer, 1934.)
Carslaw, H. S. [1930] Introduction to the Theory of Fourier's Series and Integrals. Third edition. New York: Dover, 1950.
Cauchy, A. L. [1813a] ‘Recherches sur les Polyèdres’, Journal de L'École Polytechnique, 9, pp. 68–86. (Read in February 1811.)
Cauchy, A. L. [1813b] ‘Sur les Polygones et les Polyèdres’, Journal de L'École Polytechnique, 9, pp. 87–98. (Read in January 1812.)
Cauchy, A. L. [1821] Cours d'Analyse de L'École Royale Polytechnique. Paris: de Bure.
Cauchy, A. L. [1826] ‘Mémoire sur les Développements des Functions en Séries Périodiques’, Mémoires de L'Académie des Sciences 6, pp. 603–12.
Cauchy, A. L. [1853] ‘Note sur les Séries Convergentes dont les Divers Terms sont des Fonctions Continues d'une Variable Réelle ou Imaginaire entre des Limites Données’, Comptes Rendus Hebdomadaires des Séances de L'Académie des Sciences, 37, pp. 454–9.
Cayley, A. [1859] ‘On Poinsot's Four New Regular Solids’, The Landon, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4th Series, 17, pp. 123–8.
Cayley, A. [1861] ‘On the Partitions of a Close’, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4th Series, 21, pp. 424–8.
Church, A. [1956] Introduction to Mathematical Logic, vol. 1. Princeton: Princeton University Press.
Clairaut, A. C. [1741] Elements de Géométrie. Paris: Gauthier-Villars.
Copi, I. M. [1949] ‘Modern Logic and the Synthetic A Priori’, The Journal of Philosophy, 46, pp. 243–5.
Copi, I. M. [1950] ‘Gödel and the Synthetic A Priori: a Rejoinder’, The Journal of Philosophy, 47, pp. 633–6.
Crelle, A. L. [1826–7] Lehrbuch der Elemente der Geometrie, vols. 1 and 2, Berlin: Reimer.
Curry, H. B. [1951] Outlines of a Formalist Philosophy of Mathematics. Amsterdam: North Holland.
Darboux, G. [1874a] ‘Lettre à Houel, 12 Janvier’. (Quoted in Rostand, F.: Souci d'exactitude et Scrupules des Mathématiciens. Paris: Librairie Philosophique J. Vrin, 1960, p. 11.)
Darboux, G. [1874b] ‘Lettre à Houel, 19 Fèvrier’. (Quoted in Rostand, F.: Souci d'exactitude et Scrupules des Mathématiciens. Paris: Librairie Philosophique J. Vrin, 1960, p. 194.)
Darboux, G. [1875] ‘Mémoire sur les Fonctions Discontinues’, Annales Scientifiques de L'École Normale Supérieure, second series 4, pp. 57–112.
Darboux, G. [1883] ‘Lettre à Houel, 2 Septembre’. (Quoted in Rostand, F.: Souci d'exactitude et Scrupules des Mathématiciens. Paris: Librairie Philosophique J. Vrin, 1960, p. 261.)
Denjoy, A. [1919] ‘L'Orientation Actuelle des Mathématiques’, Revue du Mois, 20, pp. 18–28.
Descartes, R. [1628] Rules for the Direction of the Mind. English translation in Haldane, E. S. and Ross, G. R. T. (eds.): Descartes’ Philosophical Works, vol. 1, Cambridge: Cambridge University Press, 1911.
Descartes, R. [1639] De Solidorum Elementis. (First published in Foucher de Careil: Oeuvres Inédites de Descartes, vol. 2, Paris: August Durand, 1860, pp. 214–34. For a considerably improved text see C. Adam and P. Tannery (eds.): Oeuvres de Descartes, vol. 10, pp. 257–78, Paris: Cerf, 1908.)
Dieudonné, J. [1939] ‘Les Méthodes Axiomatiques Modernes et les Fondements des Mathématiques’, Revue Scientifique, 77, pp. 224–32.
Diogenes Laertius [c. 200] Vitae Philosophorus. With an English translation by Hicks, R. D.. Vol. 2, London: Heinemann, 1925.
Dirichlet, P. L. [1829] ‘Sur la Convergence des Séries Trigonométriques que servent à représenter une Fonction Arbitraire entre des Limites Données’, Journal für die Reine und Angewandte Mathematik, 4, pp. 157–69.
Dirichlet, P. L. [1837] ‘Über die Darstellung Ganz Willkürlicher Functionen durch Sinus- und Cosinusreihen’, in Dove, H. W. and Moser, L. (eds.): Repertorium der Physik, 1, pp. 152–74.
Dirichlet, P. L. [1853] ‘Letter to Gauss, 20 February, 1853’, in Kronecker, L. (ed.): Werke, vol. 2. Berlin: Reiner, 1897, pp. 385–7.
du Bois-Reymond, P. D. G. [1875] ‘Beweis, das die Coefficienten der Trigono-metrischen Reihe f(x)=∑p=0p=∞(apcospx+bpsinpx) die werte a0=12π displaystyle=“true” ∫−π+πdαf(α),ap=1π displaystyle=“true” ∫−π+πdαf(α)cospα,bp=1π displaystyle=“true” ∫−π+πdαf(α)sinpα haben, jedesmal wenn diese Integrale Endlich und Bestimmt sind’, Abhandlungen der Königlich-Bayerischen Akademie der Wissenschaften, Mathematisch-Physikalischen Classe, 12, 1, pp. 117–66.
du Bois-Reymond, P. D. G. [1876] ‘Untersuchungen über die Convergenz und Divergenz der Fourier'schen Darstellungsformeln’, Abhandlungen der Königlich–Bayerischen Akademie der Wissenschaften, Mathematisch-Physikalischen Classe, 12, 2, pp. i–xxiv and 1–102.
du Bois-Reymond, P. D. G. [1879] ‘Erläuterungen zu den Anfangsgründen der Variationrechnung’, Mathematische Annalen, 15, pp. 282–315, 564–76.
du Bois-Reymond, P. D. G. [1885] Über den Begriff der Länge einer Curve’, Acta Mathematica, 6, pp. 167–8.
Dyck, W. [1888] ‘Beiträge zur Analysis Situs’, Mathematische Annalen, 32, pp. 457–512.
Einstein, A. [1953] ‘Letter to P. A. Schilpp’. Published in P. A. Schilpp: ‘The Abdication of Philosophy’, Kant Studien, 51, pp. 490–1, 1959–60.
Euler, L. [1756–7] ‘Specimen de usu Observationum in Mathesi Pura’, Novi Commentarii Academiae Scientiarum Petropolitanae, 6, pp. 185–230. Editorial summary, pp. 19–21.
Euler, L. [1758a] ‘Elementa Doctrinae Solidorum’, Novi Commentarii Academiae Scientiarum Petropolitanae, 4. pp. 109–40. (Read in November 1750.)
Euler, L. [1758b] ‘Demonstratio Nonnullarum lnsignium Proprietatus Quibus Solida Hedris Planis Inclusa sunt Praedita’, Novi Commentarii Academiae Scientiarum Petropolitanae, 4, pp. 140–60. (Read in September 1751.)
Eves, H. and Newsom, C. V. [1958] An Introduction to the Foundations and Fundamental Concepts of Mathematics. New York: Rinehart.
Félix, L. [1957] L'Aspect Moderne des Mathématiques. (English translation by J. H. Hlavaty and F. H. Hlavaty: The Modern Aspect of Mathematics, New York: Basic Books, 1960.)
Forder, H. G. [1927] The Foundations of Euclidean Geometry. New York: Dover, 1958.
Fourier, J. [1808] ‘Mémoire sur la Propagation de la Chaleur dans les Corpe Solides (Extrait)’, Nouveau Bulletin des Sciences, par la Société Philomathique de Paris, I, pp. 112–16.
Fréchet, M. [1928] Les Éspaces Abstraits. Paris: Gauthier-Villars.
Fréchet, M. [1938] ‘L'Analyse Générale et la Question des Fondements’, in Gonseth, F. (ed.): Les Entretiens de Zurich, sur les Fondements et la Méthode des Sciences Mathématiques, Zürich: Leemans Frères et Cie, 1941, pp. 53–73.
Frege, G. [1893] Grundgesetze der Arithmetik, vol. 1, Hildesheim: George Olms, 1962.
Gamow, G. [1953] One, Two, Three … Infinity. New York: The Viking Press.
Gauss, C. F. [1813] ‘Disquisitiones Generales Circa Seriem Infinitam 1+αβ1.γ.x+α(α+1)β(β+1)1.2.γ(γ+1)x.x+α(α+1)(α+2)β(β+1)(β+2)1.2.3.γ(γ+1)(γ+2).x3+etc.’, in Werke, vol. 3, pp. 123–62. Leipzig: Teubner.
Gergonne, J. D. [1818] ‘Essai sur la Théorie des Definitions’, Annales de Mathématiques, Pures et Appliquées, 9, pp. 1–35.
Goldschmidt, R. [1933] ‘Some Aspects of Evolution’, Science, 78, pp. 539–47.
Grunert, J. A. [1827] ‘Einfacher Beweis der von Cauchy und Euler Gefundenen Sätze von Figurennetzen und Polyedern’, Journal für die Reine und Angewandte Mathematik, 2, p. 367.
Halmos, P. [1950] Measure Theory. New York and London: Van Nostrand Reinhold.
Hankel, H. [1882] ‘Untersuchungen über die Unendlich oft Oscillierenden und Unstetigen Functionen’, Mathematische Annalen, 20, pp. 63–112.
Hardy, G. H. [1918] ‘Sir George Stokes and the Concept of Uniform Convergence’, Proceedings of the Cambridge Philosophical Society, 19, pp. 148–56.
Hardy, G. H. [1928] ‘Mathematical Proof’, Mind, 38, pp. 1–25.
Haussner, R. (ed.) [1906] Abhandlungen über die Regelmassigen Sternkörper. Ostwald's Klassiker der Exacten Wissenschaften, No. 151, Leipzig: Engelmann.
Heath, T. L. [1925] The Thirteen Books of Euclid's Elements. Second edition. Cambridge: Cambridge University Press.
Hempel, C. G. [1945] ‘Studies in the Logic of Confirmation, 1 and 2’, Mind, 54, pp. 1–26 and 97–121.
Hermite, C. [1893] ‘Lettre à Stieltjes, 20 Mai 1893’, in Baillaud, B. and Bourget, H. (eds.): Correspondence d'Hermite et de Stieltjes, vol. 2. Paris: Gautheirs-Villars, 1905, pp. 317–19.
Hessel, J. F. [1832] ‘Nachtrag zu dem Euler'schen Lehrsatze von Polyedern’, Journal für die Reine und Angewandte Mathematik, 8, pp. 13–20.
Heyting, A. [1939] ‘Les Fondements des Mathématiques du Point de Vue lntuitionniste’, in Gonseth, F.: Philosophie Mathématique, Paris: Hermann, pp. 73–5.
Heyting, A. [1956] Intuitionism: An Introduction. Amsterdam: North Holland.
Hilbert, D. and Cohn-Vossen, S. [1932] Anschauliche Geometrie. Berlin: Springer. English translation by P. Nemenyi: Geometry and the Imagination. New York: Chelsea, 1956.
Hobbes, T. [1651] Leviathan, in Molesworth, W. (ed.): The English Works of Thomas Hobbes, vol. 3, London: John Bohn, 1839.
Hobbes, T. [1656] The Questions Concerning Liberty, Necessity and Chance, in Molesworth, W. (ed.): The English Works of Thomas Hobbes, vol. 5, London: John Bohn, 1841.
Hölder, O. [1924] Die Mathematische Methode. Berlin: Springer.
Hoppe, R. [1879] ‘Ergänzung des Eulerschen Satzes von den Polyedern’, Archiv der Mathematik und Physik, 63, pp. 100–3.
Husserl, E. [1900] Logische Untersuchungen, vol. 1. Tubingen: Niemeyer, 1968.
Jonquières, E. de [1890a] ‘Note sur un Point Fondamental de la Théorie des Polyèdres’, Comptes Rendus des Séances de L'Académie des Sciences, 110, pp. 110-15,
Jonquières, E. de [1890b] ‘Note sur le Théorème d'Euler dans la Théorie des Polyèdres’, Comptes Rendus des Séances de L'Académie des Sciences, 110, pp. 169–73.
Jordan, C. [1866a] ‘Recherches sur les Polyèdres’, Journal für die Reine und Angewandte Mathematik, 66, pp. 22–85.
Jordan, C. [1866b] ‘Résumé de Recherches sur la Symétrie des Polyèdres non Euleriens’, Jounal für die Reine und Angewandte Mathematik, 66, pp. 86–91.
Jordan, C. [1881] ‘Sur Ia Série de Fourier’, Comptes Rendus des Séances de L'Académie des Sciences, 92, pp. 228–33.
Jordan, C. [1887] Cours d'Analyse de L'École Polytechnique, vol 3, first edition. Paris: Gauthier-Villars.
Jordan, C. [1893] Cours d'Analyse de L'École Polytechnique, vol. 1, second edition. Paris: Gauthier-Villars.
Jourdain, P. E. B. [1912] ‘Note on Fourier's Influence on the Conceptions of Mathematics’, Proceedings of the Fifth International Congress of Mathematics, 2, pp. 526–7.
Kant, I. [1781] Critik der Reinen Verunft. First edition.
Kepler, I. [1619] Harmonice Mundi, in Caspar, M. and Dyck, W. von (eds.): Gesammelte Werke, vol. 6. Munich: C. H. Beck, 1940.
Knopp, K. [1928] Theory and Application of Infinite Series. (Translated by Young, R. C., London and Glasgow: Blackie, 1928.)
Lakatos, I. [1961] Essays in the Logic of Mathematical Discovery, unpublished Ph.D. Dissertation, Cambridge.
Lakatos, I. [1962] ‘Infinite Regress and the Foundations of Mathematics’, Aristotelian Society Supplementary Volumes, 36, pp. 155–84.
Lakatos, I. [1970] ‘Falsification and the Methodology of Scientific Research Programmes’, in Lakatos, I. and Musgrave, A. E. (eds.): Criticism and the Growth of Knowledge, Cambridge: Cambridge University Press, pp. 91–196.
Landau, E. [1930] Grundlagen der Analysis. Leipzig: Akademische Verlagsgesellschaft.
Lebesgue, H. [1923] ‘Notice sur la Vie et les Travaux de Camille Jordan’, Mémoires de L'Académie de L'Institute de France, 58, pp. 34–66. Reprinted in H. Lebesgue, Notices d'Histoire des Mathématiques, Genève. pp. 40–65.
Lebesgue, H. [1928] Leçons sur L'Intégration et la Recherche des Fonctions Primitives. Paris: Gauthier-Villars. (Second, enlarged edition of the original 1905 version.)
Legendre, A.-M. [1809] Éléments de Géométrie. Eighth edition. Paris: Didot. The first edition appeared in 1794.
Leibniz, G. W. F. [1687] ‘Letter to Bayle’, in Gerhardt, C. I. (ed.): Philosophische Schriften, vol. 3, Hildesheim: George Olms (1965), p. 52.
Lhuilier, S. A. J. [1786] Exposition Élémentaire des Principes des Calculs Supérieurs. Berlin: G. J. Decker.
Lhuilier, S. A. J. [1812–13a] ‘Mémoire sur la Polyèdrométrie’, Annales de Mathématiques, Pures et Appliquées, 3, pp. 168–91.
Lhulier, S. A. J. [1812–13b] ‘Mémoire sur les Solides Réguliers’, Annales de Mathématiques, Pures et Appliquées, 3, pp. 233–7.
Listing, J. B. [1861] ‘Der Census Räumlicher Complexe’, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 10, pp. 97–182.
Loève, M. [1955] Probability Theory. New York: Van Nostrand.
Matthiessen, L. [1863] ‘Über die Scheinbaren Einschränkungen des Euler'schen Satzes von den Polyedern’, Zeitschrift für Mathematik und Physik, 8, pp. 449–50.
Meister, A. L. F. [1771] ‘Generalia de Genesi Figurarum Planarum et inde Pendentibus Earum Affectionibus’, Novi Commentarii Societatis Reglae Scientiarum Gottingensis, 1, pp. 144–80.
Menger, K. [1928] Dimensionstheorie. Berlin: Teubner.
Möbius, A. F. [1827] Der Barycentrische Calcul. Hildesheim: George Olms, 1968.
Möbius, A. F. [1865] ‘Über die Bestimmung des Inhaltes eines Polyeders’, Berichte Königlich-Sächsischen Gesellschaft der Wissenschaften, Mathematisch–Physikalische Classe, 17, pp. 31–68.
Moigno, F. N. M. [1840–1] Leçons de Calcul Differentiel et de Calcul Intégral, 2 vols. Paris: Bachelier.
Moore, E. H. [1902] ‘On the Foundations of Mathematics’, Science, 17, pp. 401–16.
Morgan, A. de [1842] The Differential and Integral Calculus. London: Baldwin and Gadock.
Munroe, M. E. [1953] Introduction to Measure and Integration. Cambridge, Massachusetts: Addison-Wesley.
Neumann, J. von [1947] ‘The Mathematician’, in Heywood, R. B. (ed.): The Works of the Mind. Chicago: Chicago University Press.
Newton, I. [1717] Opticks. Second edition. London: Dover, 1952.
Olivier, L. [1826] ‘Bemerkungen über Figuren, die aus Behebigen, von Geraden Linien Umschlossenen Figuren Zusammengesetzt sind’, Journal für die Reine und Angewandt Mathematik, 1, pp. 227–31.
Pascal, B. [1659] Les Réflexions sur la Géométrie en Général (De L'Ésprit Géométrique et de L'Art de Persuader). In Chevalier, J. (ed.): Oeuvres Complètes, Paris: La Librairie Gallimard, 1954, pp. 575–604.
Peano, G. [1894] Notations de Logique Mathématique. Turin: Guadagnini.
Pierpont, J. [1905] The Theory of Functions of Real Variables, vol. 1. New York: Dover, 1959.
Poincaré, H. [1893] ‘Sur la Généralisation d'un Théorème d'Euler relatif aux Polyèdres’, Comptes Rendus Je Séances de L'Académie des Sciences, 117, p. 144.
Poincaré, H. [1899] ‘Complément à L'Analysis Situs’, Rendiconti del Circolo Matematico di Palermo, 13, pp. 285–343.
Poincaré, H. [1902] La Science et L'Hypothèse. Paris: Flammarion. Authorised English translation by G. B. Halsted: The Foundations of Science, Lancaster, Pennsylvania: The Science Press, 1913, pp. 27–197.
Poincaré, H. [1905] La Valeur de la Science. Paris: Flammarion. Authorised English translation by G. B. Halsted: The Foundations of Science, Lancaster, Pennsylvania: The Science Press, 1913, pp. 359–546.
Poincaré, H. [1908] Science et Méthode. Paris: Flammarion. Authorised English translation by G. B. Halsted: The Foundations of Science, Lancaster, Pennsylvania: The Science Press, pp. 546–854.
Poinsot, L. [1810] ‘Mémoire sur les Polygones et les Polyèdres’, Journal de L'École Polytéchnique, 4, pp. 16–48. (Read in July 1809.)
Poinsot, L. [1858] ‘Note sur la Théorie des Polyèdres’, Comptes Rendus de L'Académie des Sciences, 46, pp. 65–79.
Pólya, G. [1945] How to Solve It. Princeton: Princeton University Press.
Pólya, G. [1954] Mathematics and Plausible Reasoning, vols. 1 and 2. London: Oxford University Press.
Pólya, G. [1962a] Mathematical Discovery, vol. 1. New York: Wiley.
Pólya, G. [1962b] ‘The Teaching of Mathematics and the Biogenetic Law’, in Good, I. J. (ed.): The Scientist Speculates. London: Heinemann, pp. 352–6.
Pólya, G. and Szegö, G. [1927] Aufgaben und Lehrsätze aus der Analysis, vol. 1. Berlin: Springer.
Popper, K. R. [1934] Logik der Forschung. Vienna: Springer.
Popper, K. R. [1935] ‘Letter to the Editor’, Erkenntnis, 3, pp. 426–9. Republished in Appendix *i to Popper [1959], pp. 311–14.
Popper, K. R. [1945] The Open Society and its Enemies. 2 volumes, London: Routledge and Kegan Paul.
Popper, K. R. [1947] ‘Logic Without Assumptions’, Aristotelian Society Proceedings, 47, pp. 251–92.
Popper, K. R. [1952] ‘The Nature of Philosophical Problems and their Roots in Science’, The British Journal for the Philosophy of Science, 3, pp. 124–56. Reprinted in Popper [1963a].
Popper, K. R. [1957] The Poverty of Historicism. London: Routledge and Kegan Paul.
Popper, K. R. [1959] The Logic of Scientific Discovery. English translation of [1934].London: Hutchinson.
Popper, K. R. [1963a] Conjectures and Refutations. London: Routledge and Kegan Paul.
Popper, K. R. [1963b] ‘Science: Problems, Aims, Responsibilities’, Federation of American Societies for Experimental Biology: Federation Proceedings, 22, pp. 961–72.
Popper, K. R. [1972] Objective Knowledge. Oxford: Oxford University Press.
Pringsheim, A. [1916] ‘Grundlagen der Allgemeinen Functionenlehre’, in Burkhardt, M., Wutinger, W. and Fricke, R. (eds.): Encyklopädie der Mathematischen Wissenschaften, vol. 2. Erste Teil, Erste Halbband, pp. 1–53. Leipzig: Teubner.
Quine, W. V. O. [1951] Mathematical Logic. Revised edition. Cambridge, Massachusetts: Harvard University Press.
Ramsey, F. P. [1931] The Foundations of Mathematics and Other Essays. Edited by Braithwaite, R. B.. London: Kegan Paul.
Raschig, L. [1891] ‘Zum Eulerschen Theorem der Polyedrometrie’, Festschrift des Gymnasium Schneeberg.
Reichardt, H. [1941] ‘Losung der Aufgabe 274’, Jarhresberichte der Deutschen Mathematiker-Vereinigung, 51, p. 23.
Reichenbach, H. [1947] Elements of Symbolic Logic. New York: Macmillan.
Reiff, R. [1889] Geschichte der Unendlichen Reihen. Tubingen: H. Laupp'schen.
Reinhardt, C. [1885] ‘Zu Möbius Polyedertheorie. Vorgelegt von F. Klein’, Berichte über die Verhandlungen der Königlich-Sachsischen Gesellschaft der Wissenschaften zu Leipzig, 37, pp. 106–25.
Riemann, B. [1851] Grundlagen der eine Allgemeine Theorie der Functionen einer Veranderlichen Complexen Grösse (inaugural dissertation). In Weber, M. and Dedekind, R. (eds.): Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass. Second edition. Leipzig: Teubner, 1892, pp. 3–48.
Riemann, B. [1868] ‘Über die Darstellbarkeit einer Function durch eine Trigonometrische Reihe’, Abhandlungen der Königlichen Gesellschafi der Wissenschaften zu Göttingen, 13, pp. 87–132.
Robinson, R. [1936] ‘Analysis in Greek Geometry’, Mind, 45, pp. 464–73.
Robinson, R. [1953] Plato's Earlier Dialectic. Oxford: Oxford University Press.
Rudin, W. [1953] Principles of Mathematical Analysis. First edition. New York: McGraw-Hill.
Russell, B. [1901] ‘Recent Work in the Philosophy of Mathematics’, The International Monthly, 3. Reprinted as ‘Mathematics and the Metaphysicians’, in his [1918], pp. 59–74.
Russell, B. [1903] Principles of Mathematics. London: Allen and Unwin.
Russell, B. [1918] Mysticism and Logic. London: Allen and Unwin.
Russell, B. [1959] My Philosophical Development. London: Allen and Unwin.
Russell, B. and Whitehead, A. N. [1910–13] Principia Mathematica. Vol. I, 1910; Vol. 2, 1912; Vol. 3, 1913. Cambridge: Cambridge University Press.
Saks, S. [1933] Théori de L'Intégrale. English translation by L. C. Young: Theory of the Integral. Second edition. New York: Hamer, 1937.
Schläfli, L. [1852] ‘Theorie der Vielfachen Kontinuität’. Published posthumously in Neue Denkschriften der Allgemeinen Schweizerischen Gesellschaft für die Gesamten Naturwissenschaften, 38, pp. 1–237. Zürich, 1901.
Schröder, E. [1862] ‘Über die Vielecke von Gebrochener Seitenzahl oder die Bedeutung der Stern-Polygone in der Geometrie’, Zeitschrift für Mathematik und Physik, 7, pp. 55–64.
Seidel, P. L. [1847] ‘Note über eine Eigenschaft der Reihen, welche Discontinuirliche Functionen Darstellen’, Abhandlungen der Mathematisch-Physikalischen Klasse der Königlich Bayerischen Akademie der Wissenschaften, 5, pp. 381–93.
Sextus Empiricus [c. 190] Against the Logicians. Greek text with an English translation by Bury, R. G.. London: Heinemann, 1933.
Sommerville, D. M. Y. [1929] An Introduction to the Geometry of N Dimensions. London: Dover, 1958.
Steiner, J. [1826] ‘Leichter Beweis eines Stereometrischen Satzes von Euler’, Journal für die Reine und Angewandte Mathematik, 1, pp. 364–7.
Steinhaus, H. [1960] Mathematical Snapshots. Revised and enlarged edition. New York: Oxford University Press.
Steinitz, E. [1914–31] ‘Polyeder und Raumeinteilungen’, in Meyer, W. F. and Mohrmann, H. (eds.): Encyklopädie der Mathematischen Wissenschaften, vol. 3, AB. 12. Leipzig: Teubner.
Stokes, G. [1848] ‘On the Critical Values of the Sums of Periodic Series’, Transactions of the Cambridge Philosophical Society, 8, pp. 533–83.
Szabó, Á. [1958] ‘“Deiknymi” als Mathematischer Terminus fur “Beweisen”’, Maia, N.S. 10, pp. 1–26.
Szabó, Á. [1960] ‘Anfänge des Euklidischen Axiomensystems’, Archive for the History of Exact Sciences, 1, pp. 37–106.
Szökefalvi-Nagy, B. [1954] Valós Függvények és Függvénysorok. Budapest: Tankönyvkiadó.
Tarski, A. [1930a] ‘Über einige Fundamentale Begriffe der Metamathematik’, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, 23, Cl. III, pp. 22–9. Published in English in J. H. Woodger (ed.) [1956], pp. 30–7.
Tarski, A. [1930b] ‘Fundamentale Begriffe der Methodologie der Deduktiven Wissenschaften, 1’, Monatshefte für Mathematik und Physik, 37, pp. 361–404. Published in English in J. H. Woodger (ed.) [1956], pp. 60–109.
Tarski, A. [1935] ‘On the Concept of Logical Consequence’. Published in J. H. Woodger (ed.) [1956], pp. 409–20. This paper was read in Paris in 1935.
Tarski, A. [1941] Introduction to Logic and to the Methodology of Deductive Sciences. Second edition. New York: Oxford University Press, 1946. (This is a partially modified and extended version of On Mathematical Logic and Deductive Method, published in Polish in 1936 and in German translation in 1937.)
Turquette, A. [1950] ‘Gödel and the Synthetic A Priori’, The Journal of Philosophy, 47, pp. 125–9.
Waerden, B. L. van der [1941] ‘Topologie und Uniformisierung der Riemannschen Flächen’, Berichte über die Verhandlungen der Königlich-Sachsischen Gesellschaft der Wissenschaften zu Leipzig, 93, pp. 147–60.
Whewell, W. [1858] History of Scientific Ideas. Vol. 1. (Part one of the third edition of The Philosophy of the Inductive Sciences.)
Wilder, R. L. [1944] ‘The Nature of Mathematical Proof’, The American Mathematical Monthly, 52, pp. 309–23.
Woodger, J. H. (ed.) [1956] Logic, Semantics, Metamathematics. Oxford: Clarendon Press.
Young, W. H. [1903–4] ‘On Non-Uniform Convergence and Term-by-Term Integration of Series’, Proceedings of the London Mathematical Society, 1, second series, pp. 89–102.
Zacharias, M. [1914–31] ‘Elementargeometrie’, in Meyer, W. F. and Mohrmann, H. (eds.): Encyklopädie der Mathematischen Wissenschaften, 3, Erste Teil, Zweiter Halbband, pp. 862–1176. Leipzig: Teubner.
Zygmund, A. [1935] Trigonometrical Series. New York: Chelsea, 1952.

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