Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T07:12:20.943Z Has data issue: false hasContentIssue false
  • English
  • Français

19th Century Logic Between Philosophy and Mathematics

Published online by Cambridge University Press:  15 January 2014

Volker Peckhaus
Volker Peckhaus*
Affiliation:
Institut Für Philosophie Der Universität Erlangen-Nürnberg, BISMARCKSTR. 1, D-91054 ERLANGEN, E-mail:vrpeckha@phil.uni-erlangen.de
Get access Rights & Permissions [Opens in a new window]

Abstract

The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart).

In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided:

1. What were the reasons for the philosophers' lack of interest in formal logic?

2. What were the reasons for the mathematicians' interest in logic?

3. What did “logic reform” mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic?

4. Was mathematical logic regarded as art, as science or as both?

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 5 , Issue 4 , December 1999 , pp. 433 - 450
Copyright
Copyright © Association for Symbolic Logic 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Babbage, Charles, Passages from the life of a philosopher, Longman, Green, Longman, Roberts, & Green, London 1864; reprinted Greeg, Westmead, 1969.Google Scholar
[2] Bain, Alexander, Logic, 2 volumes, pt. 1: Deduction, pt. 2: Induction, Longmans, Green, & Co., London, 1870.Google Scholar
[3] Batóg, Tadeusz and Murawski, Roman, Stanisław Piątkiewicz and the beginnings of mathematical logic in Poland, Historia Mathematica, vol. 23 (1996), pp. 68–73.Google Scholar
[4] Beneke, Friedrich Eduard, Syllogismorum analyticorum origines et ordinem naturalem, Mittler, Berlin, 1839.Google Scholar
[5] Beneke, Friedrich Eduard, System der Logik als Kunstlehre des Denkens, 2 volumes, F. Dümmler, Berlin, 1842.Google Scholar
[6] Bentham, George, An outline of a new system of logic: With a critical examination of Dr. Whately's “Elements of logic”, Hunt and Clark, London, 1827; reprinted Thoemmes, Bristol, 1990.Google Scholar
[7] Bocheński, Joseph Maria, Formale Logik, Alber, Freiburg/München, 1956 (= Orbis Academicus, vol. III, no. 2), 41978.Google Scholar
[8] Boole, George, On a general method in analysis, Philosophical Transactions of the Royal Society of London for the Year MDCCCXLIV, pt. 1 (1844), pp. 225–282.Google Scholar
[9] Boole, George, The mathematical analysis of logic: Being an essay towards a calculus of deductive reasoning, Macmillan, Barclay, and Macmillan, Cambridge/George Bell, London, 1847; reprinted Basil Blackwell, Oxford, 1951.Google Scholar
[10] Boole, George, An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities, Walton & Maberly, London, 1854; reprinted Dover, New York, ca. 1951.Google Scholar
[11] Boyer, Carl B., A history of mathematics, John Wiley & Sons, New York/London/Sydney, 1968.Google Scholar
[12] Cannon, Susan Faye, Science in culture: The early Victorian period, Dawson Scientific History Publications, New York, 1978.Google Scholar
[13] Carroll, Lewis, The game of logic, MacMillan, London, 1887; reprinted in [15].Google Scholar
[14] Carroll, Lewis, Symbolic logic, MacMillan, London, 1896; reprinted in [15].Google Scholar
[15] Carroll, Lewis, Mathematical recreations of Lewis Carroll: Symbolic logic and The game of logic (both books bound as one), Dover Publications and Berkeley Enterprises, New York, 1958.Google Scholar
[16] Morgan, Augustus De, On the syllogism I: On the structure of the syllogism, and on the applications of the theory of probabilities to questions of arguments and authority, Transactions of the Cambridge Philosophical Society, vol. 8 (1846), pp. 379–408.Google Scholar
[17] Enros, Philip C., The analytical society (1812–1813): Precursor of the renewal of Cambridge Mathematics, Historia Mathematica, vol. 10 (1983), pp. 24–47.CrossRefGoogle Scholar
[18] Gregory, Duncan Farquharson, On the real nature of symbolical algebra, Transations of the Royal Society of Edinburgh, vol. 14 (1840), pp. 208–216.Google Scholar
[19] Gregory, Duncan Farquharson, On a difficulty in the theory of algebra, The Cambridge Mathematical Journal, vol. 3 (1842), pp. 153–159.Google Scholar
[20] Hamilton, William, Logic. In reference of the recent English treatises on that science, Edinburgh Review, vol. 66 (04 1833), pp. 194–238; again in [21], pp. 16–174.Google Scholar
[21] Hamilton, William, Discussions on philosophy and literature, education and university reform. Chiefly from the Edinburgh Review; corrected, vindicated, enlarged, in notes and appendices, Longman, Brown, Green and Longmans, London/Maclachlan and Stewart, Edinburgh, 1851.Google Scholar
[22] Hamilton, William, Lectures on metaphysics and logic, 4 volumes (Mansel, H. L. and Veitch, J., editors), William Blackwood and Sons, Edinburgh/London, 1859–1866.Google Scholar
[23] Heath, Peter, Introduction, in Morgan, Augustus De, On the syllogism and other logical writings (Heath, Peter, editor), Routledge & Kegan Paul, London, 1966 (= Rare masterpieces of philosophy and science), pp. vii–xxxi.Google Scholar
[24] Friedrich Hegel, Georg Wilhelm, Wissenschaft der Logik, vol. 1: Die objective Logik, Johann Leonhard Schrag, Nürnberg, 1812/1813; critical edition: HEGEL, , Wissenschaft der Logik. Erster Band. Die objektive Logik (Hegemann, Friedrich and Jaeschke, Walter, editors), Felix Meiner, Hamburg, 1978 (= Hegel, Gesammelte Werke , vol. 11).Google Scholar
[25] Wilhelm, Georg, Encyclopädie der philosophischen Wissenschaften im Grundrisse. Zum Gebrauch seiner Vorlesungen. Dritte Ausgabe, Oßwald'scher Verlag, Heidelberg, 1830. Critical edition HEGEL, , Enzyklopädie der philosophischen Wissenschaften im Grundrisse (1830) (Bonsiepen, Wolfgang and Lucas, Hans-Christian, editors), Felix Meiner, Hamburg, 1992 (= Hegel, Gesammelte Werke , vol. 20).Google Scholar
[26] Hilbert, David, Axiomatisches Denken, Mathematische Annalen, vol. 78 (1918), pp. 405–415.CrossRefGoogle Scholar
[27] Jevons, William Stanley, Pure logic or the logic of quality apart from quantity with remarks on Boole's system and the relation of logic and mathematics, E. Stanford, Londone, 1864; reprinted in [30], pp. 3–77.Google Scholar
[28] Jevons, William Stanley, The principles of science. A treatise on logic and scientific method, 2 volumes, Macmillan and Co., London, 1874 [New York, 1875].Google Scholar
[29] Jevons, William Stanley, John Stuart Mill's philosophy tested, The Contemporary Review, vol. 31 (1877/78), pp. 167–182 and 256–275; vol. 32 (1878), pp. 88–99; again in [30], pp. 137–172.Google Scholar
[30] Jevons, William Stanley, Pure logic and other minor works (Adamson, Robert and Jevons, Harriet A., editors), Macmilland and Co., London/New York, 1890; reprinted Thoemmes Press, Bristol, 1991.Google Scholar
[31] Kant, Immanuel, Critik der reinen Vernunft, 2nd ed., Johann Friedrich Hartknoch, Riga, 1787; again in Kant's gesammelte Schriften , vol. 3 (Königlich Preußische Akademie der Wissenschaften, editor), Reimer, Berlin, 1911.Google Scholar
[32] Kneale, William and Kneale, Martha, The development of logic, Clarendon Press, Oxford, 1968; reprinted 1986.Google Scholar
[33] Kusch, Martin: Psychologism. A case study in the sociology of philosophical knowledge, Routledge, London/New York, 1995 (= Psychological issues in science).Google Scholar
[34] Liard, Louis Un nouveau système de logique formelle. M. Stanley Jevons, Revue philosophique de la France et de l'Étranger, vol. 3 (1877), pp. 277–293.Google Scholar
[35] Liard, Louis, La logique algébrique de Boole, Revue philosophique de la France et de l'Étranger, vol. 4 (1877), pp. 285–317.Google Scholar
[36] Liard, Louis, Les logiciens anglais contemporains, Germer Baillière, Paris, 1878, 5 1907.Google Scholar
[37] Liard, Louis, Die neuere englische Logik (Imelmann, J[ohannes], editor), Denicke's Verlag, Berlin, 1880, 2 1883.Google Scholar
[38] Lindsay, Thomas M., On recent logical speculation in England, in [64], pp. 557–590.Google Scholar
[39] MacColl, Hugh, The calculus of equivalent statements (second paper), Proceedings of the London Mathematical Society, vol. 9 (1877–1878), pp. 177–186.Google Scholar
[40] Mill, John Stuart, A system of logic, ratiocinative and inductive: Being a connective view of the principles of evidence and the methods of scientific investigation, 2 volumes, J. W. Parker, London, 1843.Google Scholar
[41] Neil, Samuel, John Stuart Mill, The British Controversialist and Literary Magazine n.s. (1864), pp. 161–173 and 241–256.Google Scholar
[42] Peacock, George, A treatise on algebra, J. & J. J. Deighton, Cambridge/G. F. & J. Rivington, London, 1830.Google Scholar
[43] Peacock, George, Report on the recent progress and present state of certain branches of analysis, in Report of the third meeting of the British Association for the Advancement of Science held at Cambridge in 1833, John Murrary, London, 1834, pp. 185–352.Google Scholar
[44] Peckhaus, Volker Ernst Schröder und die ‘pasigraphischen Systeme’ von Peano und Peirce, Modern Logic, vol. 1 (Winter 1990/1991), no. 2/3, pp. 174–205.Google Scholar
[45] Peckhaus, Volker, Leibniz als Identifikationsfigur der britischen Logiker des 19. Jahrhunderts, in VI. Internationaler Leibniz-Kongreβ. Vorträge I. Teil, Hannover, 18.–22.7.1994, Gottfried- Wilhelm-Leibniz-Gesellschaft, Hannover, 1994, pp. 589–596.Google Scholar
[46] Peckhaus, Volker, Wozu Algebra der Logik? Ernst Schröders Suche nach einer universalen Theorie der Verknüpfungen, Modern Logic, vol. 4 (1994), pp. 357–381.Google Scholar
[47] Peckhaus, Volker, Hermann Ulrici (1806–1884): Der Hallesche Philosoph und die englische Algebra der Logik. Mit einer Auswahl von Texten Ulricis und einer Bibliographie seiner Schriften, Hallescher Verlag, Halle a. S., 1995 (= Schriftenreihe zur Geistes- und Kulturgeschichte. Texte und Dokumente).Google Scholar
[48] Peckhaus, Volker, Logik, Mathesis universalis und allgemeine Wissenschaft. Leibniz und die Wiederentdeckung der formalen Logik im 19. Jahrhundert, Akademie Verlag, Berlin, 1997 (= Logica Nova).Google Scholar
[49] Rabus, Georg Leonhard, De neuesten Bestrebungen auf dem Gebiete der Logik bei den Deutschen und Die logische Frage, Deichert, Erlangen, 1880.Google Scholar
[50] Rath, Matthias, Der Psychologismus in der deutschen Philosophie, Karl Alber Verlag, Freiburg/München, 1994.Google Scholar
[51] Richards, Joan L., Mathematical visions: The pursuit of geometry in Victorian England, Academic Press, Boston, etc., 1988.Google Scholar
[52] Riehl, Alois, Die englische Logik der Gegenwart, Vierteljahrsschrift für wissenschaftliche Philosophie, vol. 1 (1877), pp. 51–80.Google Scholar
[53] Risse, Wilhelm, Bibliographica Logica. Verzeichnis der Druckschriften zur Logik mit Angabe ihrer Fundorte, vol. 2: 1801–1969, Olms, Hildesheim/New York, 1973 (= Studien und Materialien zur Geschichte der Philosophie; 1).Google Scholar
[54] Schröder, Ernst, Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende, vol. 1 [no further volumes published]: Die sieben algebraischen Operationen, B. G. Teubner, Leibzig, 1873.Google Scholar
[55] Schröder, Ernst, Der Operationskreis des Logikkalkuls, Teubner, Leipzig, 1877; reprinted as “special edition”, Wissenschaftliche Buchgesellschaft, Darmstadt, 1966.Google Scholar
[56] Schröder, Ernst, Vorlesungen über die Algebra der Logik (exakte Logik), vol. 1, B.G. Teubner, Leipzig, 1890; reprinted in [61].Google Scholar
[57] Schröder, Ernst, Vorlesungen über die Algebra der Logik (exakte Logik), vol. 2, B.G. Teubner, Leipzig, 1891; reprinted in [61].Google Scholar
[58] Schröder, Ernst, Vorlesungen über die Algebra der Logik (exakte Logik), vol. 3, pt. 1: Algebra und Logik der Relative, B. G. Teubner, Leipzig, 1895; reprinted in [61].Google Scholar
[59] Schröder, Ernst, Vorlesungen über die Algebra der Logik )exakte Logik), vol. 2, pt. 2 (Müller, Karl Eugen, editor), B. G. Teubner, Leipzig, 1905; reprinted in [61].Google Scholar
[60] Schröder, Ernst, Grossberzoglich Badischer Hofrat Dr. phil. Ernst Schröder[,] ord. Professor für Mathematik an der Technischen Hochschule in Karlsruhe i. Baden, in Geistiges Deutschland. Deutsche Zeitgenossen auf dem Gebiete der Literatur, Wissenschaften und Musik, Adolf Eckstein, Berlin-Charlottenburg, 1901.Google Scholar
[61] Schröder, Ernst, Vorlesungen über die Algebra der Logik (exakte Logik), [“second edition”], 3 volumes, Chelsea, Bronx, New York, 1966.Google Scholar
[62] Trendelenburg, Friedrich Adolf, Zur Geschichte von Hegel's Logik und dialektischer Methode. Die logische Frage in Hegel's Systeme. Eine Auffoderung [sic!] zu ihrer wissenschaftlichen Erledigung, Neue Jenaische Allgemeine Literatur-Zeitung, vol. 1 (23 April 1842), no. 97, pp. 405–408; (25 April 1842) no. 98, pp. 409–412; (26 04 1842) no. 99, pp. 413–414; separately published in Trendelenburg, Die logische Frage in Hegel's System. Zwei Streitschriften , Brockhaus, Leipzig, 1843.Google Scholar
[63] Ueberweg, Friedrich, System der Logik und Geschichte der logischen Lehren, Adolph Marcus, Bonn, 1857.Google Scholar
[64] Ueberweg, Friedrich, System of logic and history of logical doctrines, translated from the German with notes and appendices by Thomas M. Lindsay, Longmans, Green, and Co., London, 1871; reprinted Thoemmes Press, Bristol, 1993.CrossRefGoogle Scholar
[65] Ulrici, Hermann, Review of [10], Zeitschrift für Philosophie und philosophische Kritik, vol. 27 (1855), pp. 273–291.Google Scholar
[66] Evra, James Van, Richard Whately and the rise of modern logic, History and Philosophy of Logic, vol. 5 (1894), pp. 1–18.Google Scholar
[67] Venn, John, Symbolic logic, 2nd ed., “revised and rewritten,” Macmillan & Co., London, 1894; reprinted Chelsea Publishing, Bronx, New York, 1971.Google Scholar
[68] Wernicke, Alexander, Review of [57], Deutsche Litteraturzeitung, vol. 12 (1891), col. 196–197.Google Scholar
[69] Whately, Richard, Elements of logic: Comprising the substance of the article in the Encyclopaedia Metropolitana: with additions &c., J. Mawman, London, 1826.Google Scholar
[70] Windelband, Wilhelm, Logik, in Windelband, (ed.), Die Philosophie im Beginn des zwanzigsten Jahrhunderts. Festschrift für Kuno Fischer, vol. 1, Carl Winter, Heidelberg, 1904, pp. 163–186.Google Scholar