Popper on definitions

Journal for General Philosophy of Science

Volumn 36, Issue 1, 2005, Pages 15-28

  Büttemeyer, Wilhelm ^a  

^a UNIVERSITY OF OLDENBURG   (Germany)

Author keywords

Aristotle; Essentialist definition; Nominalist definition; Pascal; Popper

Indexed keywords

EID: 23944441401     PISSN: 09254560     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10838-005-6037-2     Document Type: Article

References (59)

1. See K. R. Popper: 'Creative and Non-creative Definitions in the Calculus of Probability', Synthese 15, 1963, 167-186.
2. Popper discussed methodological essentialism mainly in his books The Open Society and Its Enemies, London, Routledge & Kegan Paul, 1945, Vol. I, Chap. Ill, Section vi,
3. and The Poverty of Historicism, London 1957, Chap. I, Section 10.
4. shall use the following abbreviations of Karl Popper's works: C&R - Conjectures and Refutations. The Growth of Scientific Knowledge, 5th rev. ed. London - New York, Routledge, 1989, repr. 2000;
5. GE - Die beiden Grundprobleme der Erkenntnistheorie, ed. by T. E. Hansen, Tübingen, Mohr, 1979;
6. LSD - The Logic of Scientific Discovery, London New York, Routledge, (1959) repr. 1992;
7. OK - Objective Knowledge. An Evolutionary Approach, rev. ed., Oxford, Clarendon, 1979, 7th impr. 1992;
8. OS - The Open Society and Its Enemies, 5th rev. ed., London, Routledge & Kegan Paul, 1966, repr. 1999;
9. PH - The Poverty of Historicism, 3rd rev. ed., London, Routledge & Kegan Paul, 1961, repr. 1994;
10. UQ - Unended Quest. An Intellectual Autobiography, new ed., London New York, Routledge, 2002.
11. See OS, Vol. II, Chap. XI, Section ii, especially note 38.
12. The traditional theory of definition is not limited to essential (and nominal) definitions, for Aristotle speaks also of causal definitions, which purport to explain why a thing exists: see An. post. II 10, 93b 38 ff.
13. C& R, p. 20;
14. OS II, p. 10;
15. see also OS I, p. 32.
16. OS, Vol. II, p. 11.
17. In point of fact, Aristotle admits of the possibility of intuition of essences via single experiences of relevant particulars; see An. post. II 19, 100a 15-100b 1.
18. OS, Vol. II, pp. 10 and 14.
19. Aristotle allows three kinds of basic premises of demonstrations: axioms (i.e., the general suppositions which are valid for all sciences), hypotheses (i.e., the special suppositions which are valid only for a single science) and definitions; and he underlines the methodological difference between propositions which describe a factual situation by saying that there is something (axioms, hypotheses), and definitions, which say what that something is; see An. post. I 2, 72a 14-24. Therefore, our knowledge depends on these three kinds of premises.
20. OS II, p. 16.
21. This is stressed by a thesis of his C& R, p. 28: "Intellectual intuition and imagination are most important, but they are not reliable: they may show us things very clearly [...]. They are indispensable as the main sources of our theories [...]. The most important function of observation and reasoning, and even of intuition and imagination, is to help us in the critical examination of those bold conjectures which are the means by which we probe into the unknown."
22. C&R, p. 279 and footnote 62;
23. OK, p. 195, note 6.
24. OS, Vol. II, pp. 14-15 and 18-20.
25. See Aristotle: An. post. II 7, 92 b 26 ff.
26. See OS II, pp. 14 and 291, note 44 (1);
27. PH, p. 29;
28. UQ, p. 28;
29. GE, p. 177.
30. OS II, p. 18: "But undoubtedly, the demand that we speak clearly and without ambiguity is very important, and must be satisfied. Can the nominalist view satisfy it? [...] It can."
31. Aristotle: An. post. I 3;
32. Aristotle: An. post. II 19;
33. Met. IX 6, 1048 a 36-37;
34. Met. VIII 3, 1043b 30.
35. J.-P. Schobinger: Biaise Pascals Reflexionen über die Geometrie im allgemeinen: "De l'esprit géométrique" und "De l'art de persuader", Basel - Stuttgart, Schwabe, 1974, p. 43: "On ne reconnaît en géométrie que les seules définitions que les logiciens appellent définitions de nom, c' est-à-dire que les seules impositions de nom aux choses qu'on a clairement désignées en termes parfaitement connus".
36. Ibid., pp. 49-51: "Ce n'est pas que tous les hommes aient la même idée de l'essence des choses, que je dis qu'il est impossible et inutile de définir. [...] Car les définitions ne sont faites que pour désigner les choses que l'on nomme, et non pas pour en montrer la nature."
37. Ibid., p. 43: "Leur utilité et leur usage est d'éclaircir et d'abréger le discours, en exprimant, par le seul nom qu'on impose, ce qui ne se pourrait dire qu'en plusieurs termes".
38. Ibid., pp. 43-45: "D'où il paraît que les définitions sont très libres, et qu'elles ne sont jamais sujettes à être contredites; car il n'y a rien de plus permis que de donner à une chose qu'on a clairement désignée un nom tel qu'on voudra. Il faut seulement prendre garde qu'on n' abuse de la liberté qu'on a d'imposer des noms, en donnant le même à deux choses differentes".
39. Ibid., p. 87: "Substituer toujours mentalement les définitions à la place des définis, pour ne pas se tromper par l'équivoque des termes que les définitions ont restreints".
40. Ibid., p. 45-47: "... je reviens à l'explication du véritable ordre, qui consiste, comme je disais, à tout définir et à tout prouver. Certainement cette méthode serait belle, mais elle est absolument impossible: car il est évident que les premiers termes qu'on voudrait définir, en supposeraient de précédents pour servir à leur explication [...]; et ainsi il est clair qu'on n'arriverait jamais aux premières. Aussi, en poussant les recherches de plus en plus, on arrive nécessairement à des mots primitifs qu'on ne peut plus définir [...]. Mais il ne s'ensuit pas de là qu'on doive abandonner toute sorte d'ordre. Car il y en a un, et c'est celui de la géométrie [...]. Cet ordre, le plus parfait entre les hommes, consiste non pas à tout définir ou à tout démontrer, ni aussi à ne rien définir ou à ne rien démontrer, mais à se tenir dans ce milieu de ne point définir les choses claires et entendues de tous les hommes, et de définir toutes les autres".
41. La Logique ou l'art de penser..., Paris, Guignart-Saureux-Launay, 1662, part I, Chap. XIII, No. 1.
42. OS II, p. 296, note 50;
43. C& R, p. 62;
44. LSD, Appendix *X, pp. 440-441.
45. OS II, p. 290, note 39;
46. LSD, p. 74. See also 05 II, p. 19: "... our terms are a little vague (since we have learned to use them only in practical applications)"; C&R, p. 279: "I want only to say (again) that outside mathematics and logic problems of definability are mostly gratuitous. We need many undefined terms whose meaning is only precariously fixed by usage - by the manner in which they are used in the context of theories, and by the procedures and pratices of the laboratory."
47. LSD, p. 74.
48. See also H. Oetjens: Sprache, Logik, Wirklichkeit. Der Zusammenhang von Theorie und Erfahrung in K. R. Poppers "Logik der Forschung", Stuttgart-Bad Cannstatt, Frommann-Holzboog, 1975, pp. 126,169 ff.
49. C&R, p. 262. It was also remarked that abstract mathematical terms cannot be defined by examples;
50. see R. Robinson: Definition (1950), Oxford, Oxford University Press, 1972, Chap. V, § 5.
51. OS II, pp. 12 and 290, note 39.
52. Popper's use of explicit definitions in a logical context may be studied in his 'New Foundations for Logic', Mind 56, 1947, pp. 193-235.
53. See R. Carnap: Logical Foundations of Probability, Chicago 1950;
54. C. G. Hempel: Fundamentals of Concept Formation in Empirical Science, Chicago 1952.
55. For a similar objection see B. Messmer: Die Grundlagen von Poppers Sozialphilosophie, Bern, Lang, 1981, Chap. 3.1. Popper himself felt perhaps the usefulness of such a method, when discussing the notions of 'certainty' and 'verisimilitude'. Although emphasizing repeatedly to be "not interested in definitions," he commented on the first notion "for the sake of clarity". In the second case, he aimed at the "rehabilitation" of a concept which had been "suspected of being meaningless (or useless)," but which, being "much needed," should not be "logically misconceived, or 'meaningless'".
56. See OK, pp. 58, 78, 59;
57. K. Popper: 'Replies to my critics', in P. A. Schilpp (ed.): The Philosophy of Karl Popper, La Salle, Ill., Open Court, 1974, pp. 961-1197, especially 1100.
58. The road taken by him in order to find a definition of the notion of 'probabilistic independence', too, is very different from his method of nominalistic definition, and it bears more resemblance to the method of trial and error; see his letters to Georg Dorn in E. Morscher (ed.): Was wir Karl Popper und seiner Philosophie verdanken. Zu seinem 100. Geburtstag, Sankt Augustin, Academia Verlag, 2002, pp. 48-63 and 481-494.
59. C. v. Mettenheim: 'The Problem of Objectivity in Law and Ethics' in I. Jarvie/S. Pralong (eds.): Popper's Open Society after Fifty Years. The continuing relevance of Karl Popper, London - New York, Routledge, 2003, pp. 111-127, especially 112-113.