Bernard Bolzano, analyticity and the Aristotelian model of science

Kant-Studien

Volumn 92, Issue 3, 2001, Pages 328-349

  De Jong, Willem R ^a  

^a NONE

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EID: 70449886639     PISSN: 00228877     EISSN: None     Source Type: Journal    
DOI: 10.1515/kant.92.3.328     Document Type: Review

References (56)

1. W. v. O. Quine, "Two Dogmas of Empiricism." From a Logical Point of View. 9 Logico-Philosophical Essays. (2 d rev. ed.). New York 1963, pp. 20-46; cf. pp. 20-21
2. Cf. J. Proust, Questions de Forme. Logique et Propositions analytique de Kant á Carnap. Paris 1986
3. J. A. Coffa, The Semantic Tradition from Kant to Carnap: The Vienna Station (ed. by L. Wessels). Cambridge 1993
4. H. Scholz, "Die Wissenschaftslehre Bolzanos. Eine Jahrhundert-Betrachtung." Abhandlungen der Fries'schen Schule (N. F.) 6 (1937), 399-472; cf. pp. 452-53
5. J. Berg, Bolzano's Logic. Stockholm 1962, pp. 161-62
6. G. Buhl, "Ableitbarkeit und Abfolge in der Wissenschaftstheorie Bolzanos." Kantstudien, Ergänzungshefte 83 (1961), cf. pp. 57-64
7. W. R. de Jong, "How Is Metaphysics as a Science Possible? Kant on the Distinction between Philosophical and Mathematical Method." The Review of Metaphysics 48 (1995), pp. 235-74
8. Idem, "Gottlob Frege and the Analytic-Synthetic Distinction within the Framework of the Aristotelian Model of Science." Kant-Studien 87 (1996), 290-324
9. Cf. Y. Bar-Hillel, "Bolzano's Definition of Analytic Propositions." Theoria 16 (1950), pp. 91-117; p. 100
10. W. and M. Kneale, The Development of Logic, Oxford 1962, p. 367
11. J. Berg, "Introduction." In: B. Bolzano, Theory of Science (ed. by J. Berg; transl. by B. Terrell). Dordrecht 1973, pp. 1-44; p. 18
12. Coffa, The Semantic Tradition, p. 34
13. B. Bolzano, Wissenschaftslehre (intr. by J. Berg)
14. Bernard Bolzano-Gesamtausgabe (ed. by E. Winter et all.). Stuttgart-Bad Canstatt, 1969- ); Reihe 1, vol. 11-14. The Wissenschaftslehre is indicated by WL, followed by the section number. For citations I used Bolzano's Theory of Science. To Berg's introduction I will refer as "Einleitung."
15. Cf. WL §§ 123, 291, 19, 34
16. see also: Berg, Bolzano's Logic, pp. 45-48, 63-65
17. Scholz and Beth have endeavored to characterize this concept of science without however distinguishing adequately between the ordo essendi and the ordo cognoscendi
18. H. Scholz, "Die Axiomatik der Alten." Mathesis Universalis. Abhandlungen zur Philosophie als strenger Wissenschaft (ed. by H. Hermes et al.). Basel and Stuttgart 1961, pp. 27-44; cf. pp. 29-30
19. E. W. Beth, The Foundations of Mathematics. A Study in the Philosophy of Science. Amsterdam 1965, pp. 31-32
20. WL §§ 216, 220
21. Cf. Berg, "Introduction," p. 24
22. Cf. Aristotle, Posterior Analytics (trans. by J. Barnes). Oxford 1994, 71 b30
23. Notice that Bolzano clearly differs from Kant on this point. According to Bolzano a (pure) concept as such does not need to be universal (cf. WL § 73)
24. WL § 1; cf. § 536; see however §§ 39-23, 414, 426-7
25. Cf. Aristotle, Posterior Analytics 86 a38-87 b4
26. cf. R. D. McKirahan, Principles and Proofs: Aristotle's Theory of Demonstrative Science. Princeton 1992, pp. 29-35
27. References to Kant's works are to the well-known Akademie Text-Ausgabe of Kant's Gesammelte Schriften (henceforth AK). However, the Kritik der reinen Vernunft is cited in the customary way with references to the pagination of the first (A) and/or second (B) printing
28. For citations I have made use to the extent possible of The Cambridge Edition of the Works of Immanuel Kant (ed. by P. Guyer and A. W. Wood), which is presently appearing. I also used: I. Kant, Prolegomena to Any Future Metaphysics that Will Be Able to Present Itself as a Science (transl. by P. G. Lucas). Manchester 1971
29. Cf. W. R. de Jong, "Kant's Analytic Judgments and the Traditional Theory of Concepts." Journal of the History of Philosophy 33 (1995), 613-41; esp. p. 628
30. WL §§ 64, 120
31. See also: U. Neeman, "Analytic and Synthetic Propositions in Kant and Bolzano." Ratio 12 (1970), 1-25; cf. p. 7
32. Cf. Quine, "Two Dogmas", p. 21
33. Cf. Coffa, The Semantic Tradition, pp. 20, 34-35
34. see also: Kneale, The Development of Logic, p. 367
35. Cf. P. B. Thompson, "Bolzano's Deductibility and Tarski's Logical Consequence." History and Philosophy of Logic 2 (1981), pp. 11-20
36. Cf. WL § 65. Bolzano believes that the general structure of a proposition can be presented as: A has b. But by taking has and not is as the copula he departs strongly from the usual approach in traditional logic: "Propositions of the form, A is B, would always be more clearly and correctly expressed as follows: A-has-(the property of a B or) b," in which b is the abstractum corresponding to the concretum B (WL § 127; cf. § 126)
37. WL § 147. Lacking a technically precise language Bolzano characterises the notion of universal (contra)validity in a rather loose way. In recent reconstructions this notion of Bolzano is usually defined with respect to sequences or classes of ideas; see for instance: Berg, "Introduction, " pp. 17-18. My speaking of 'simultaneous variation' intends to do the same. The condition that a proposition should be denotative - die Gegenständlichkeit des Satzes - corresponds to the requirement usually found in traditional logic that the (logical) subject of a proposition should have existential import
38. Cf. Bar-Hillel, "Bolzano's Definition of Analytic Propositions," p. 92
39. Neeman, "Analytic and Synthetic Propositions in Kant and Bolzano," p. 1
40. Haller, "Der Streit um die 'analytisch-synthetisch' Dichotomy." Deskription, Analyticität und Existenz (ed. P. Weingartner). Salzburg and Munich 1966, pp. 159-74, p. 161
41. Berg, "Introduction," p. 19: the class of logically analytic propositions "is much more interesting from a modern point of view."
42. Berg, "Einleitung", 12.1, p. 18
43. Cf. Berg, Bolzano's Logic, p. 101
44. Cf. Proust, Questions de Forme, pp. 128-36
45. Cf. WL § 155. See also: Berg, "Introduction", pp. 20-22
46. B truth represents a rather simple type of derivability. It is what is traditionally called an immediate inference; that is, an argument in which a conclusion is inferred from one premiss
47. Proust, Questions de Forme, p. 149; cf. pp. 145-53, p. 171
48. Aristotle, Posterior Analytics 78 a30-b3
49. See also McKirahan, Principles and Proofs, pp. 22-23
50. WL § 198, cf. § 162. See also Scholz, "Die Wissenschaftslehre Bolzanos," pp. 452-60
51. WL § 221 n.; cf. WL §§ 603, 604
52. B truth F(x) ∧ (G(x) ∨ ∼G(x)) and not the other way around (cf. the simplicity condition)
53. Various aspects of the matter ought really to be worked out against the background of the development of Bolzano's thought, but to do that here would convey us beyond the scope of this article
54. See also WL § 532 and the manuscript "Einleitung zur 'Grossenlehre.'" Bernard Bolzano Gesamtausgabe, series IIA, vol. 7, p. 31
55. Cf. Aristotle, Posterior Analytics 76a37-b15
56. See also Th. L. Heath (ed.), The Thirteen Books of Euclid's Elements. New York 1966. Vol. 1, pp. 117-24