Abstract
Of the various passages revised or completely rewritten for the Critique of Pure Reason’s second (1787) edition, scholars have focused primarily on the Deduction, the Refutation of Idealism, the Paralogisms, the Preface, and to a lesser extent on the Aesthetic. The Introduction too underwent a revision — it nearly doubled in length — but relatively little attention has been paid to the question of why Kant thought this revision advisable. This is perhaps understandable: the alteration consists almost entirely of an expansion of the treatment of synthetic a priori knowledge, for the most part simply taken over (frequently word-for-word) from the 1783 Prolegomena. And although a great deal of the Prolegomena is devoted to Kant’s indignant rejection of the Garve-Feder review of the 1781 Critique, the passages adopted for the B-Introduction seem independent of this reaction.1
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References
See the editor’s introduction to Immanuel Kant, Prolegomena zu einer jeden künftigen Metaphysik, die als Wissenschaft wird auftreten können, ed. Karl Vorländer (Hamburg: Felix Meiner Verlag, 1976), vii–xxii. For the latest (and most convincing) version of the page-misplacement hypothesis (“Blattversetzungshypothese”, xxxvii–xl) see P. Hoyningen-Huene, “Eine weitere Textverschiebungshypothese zu Kants Prolegomena (und zur 2. Auflage der KrV)” Kant-Studien 89 (1998), 84–9. (As customary, references to the Critique of Pure Reason [KdrV] cite the pagination of the first and second (A and B) original editions; all other references to Kant’s work are by volume, page (and where necessary, line) of the Prussian Academy edition [Ak] of Kant’s complete works, preceded by an abbreviation of the work in question: KdpV for Critique of Practical Reason, KdU for Critique of Judgment, Proleg. for Prolegomena, etc.)
Proleg., Ak.IV.261. See also Letter to Herz, 11 May 1781 (Ak X268–70), where Kant grants he will at first have “very few readers” and hopes to provide “popularity” later.
The Introduction in A notes the apriority of mathematics, but only implies that it is synthetic; the first place I find this actually stated is A39. A46–49 gives an explication of the synthetic a priori nature of mathematics, but this scarcely constitutes a defense of this claim. Kant’s failure to realize that the claim needed an explicit defense is perhaps explained by the fact that he had become so accustomed to viewing mathematics as synthetic for over 15 years (cf. “Deutlichkeit,” Ak 11.276 et passim; “Vorlesungen 1765–66,” Ak II.308f.) that by 1781 it seemed obvious to him.
Hume and Leibniz, e.g., both understood mathematics to be analytic, in the received sense of that term.
Lewis W. Beck, “Kant’s Theory of Definition,” in Robert Paul Wolff, ed, Kant. A Collection of Critical Essays (Notre Dame: Univ. of Notre Dame Press, 1968), 23–36 (see also “Analytic and Synthetic Judgments Before Kant”, in Beck, Essays on Kant and Hume (New Haven: Yale Univ. Press, 1978), 80–100.
Henry E. Allison, Kant’s Transcendental Idealism [KTI] (New Haven: Yale Univ. Press, 1983), 73 (and Chapter 4 generally).
Thomas Aquinas, Summa Theologia 1.2.2. See also Suarez, Metaphysicarum disputationum 29.3.1–2 for a reference to these two types of proof as a priori and a posteriori.
Antoine Arnauld, La Logique, ou l’ Art de Penser, 1662, Pt. IV, §1. English: The Art of Thinking. New York: Bobbs-Merrill, 1964, 301f.
Logik, Ak..IX. 22f.
Kant differentiates objective from subjective origins of cognitions; the first divide into rational or empirical, the second into rational or historical. The point apparently is to allow for the possibility of someone knowing, e.g., that the interior angles of a triangle are equivalent to two right angles, not because he followed the proof himself, but because he was told it and took it on authority. Then the cognition in question is objectively rational, but subjectively “historical.” See Logik, Ak. IX. 22. The use of “historical” here follows Meyer, §§17–18, Ak. XVI.93–94.
KdrV, A1. Cf B2f. Kant goes onto distinguish the relative from the absolute a priori, and restrict the discussion to the latter.
The sense of necessity and universality of Kant’s a priori concepts and intuitions is less straightforward than that of the cognitions, and can be questioned in individual cases; but I think it is fair to say that if these concepts and intuitions are considered, not individually, but as a system, this system is universal and necessary with respect to the system of empirical objects. Further pursuit of this theme is however beyond the scope of this treatment
E.g. KdrV, A56/B80f: a priori employment, cognition, determination, relatioa
Logik, Ak. IX.22f.
This claim might seem to run afoul of the a priori nature of mathematics: the properties of a triangle are a priori, but not all empirical objects are triangular. If we take the propositions of mathematics as hypothetical, however, i. e. “for all empirical objects: if they are triangular, then they have these properties…”, the problem disappears. Cf. KdrV, A56/B80f.
KdrV, A6f./B10.
Logik, §36, Ak. IX 111. Cf. R3928, Ak. XVII.350.2.
The term predicate has two senses here. In a judgment such as “All A is B,” the concept B serves as the predicate for this particular judgment, the concept A as the subject; but A is also a predicate of the objects falling under it, but in a wider sense, i. e. considered without reference to any particular judgment Where the possibility of confusion obtains, I will refer to the former sense as the logical predicate.
Allison (AT/, 73–5) grants that “containment” and ‘thought through identity” are equivalent, but considers “explicative/ampliative” to constitute a second version of the distinction I think, on the contrary, the latter is formally equivalent to the first two, but whereas the first two make no reference to concepts with respect to their origin and development, there is a hint of this in the latter.
Beck, “Can Kant’s Synthetic Judgments be Made Analytic?” in Wolff, op.cit, 3–22 (see esp. 6–9).
KTI, 74.
KdrV, A55f/B79f Cf also A54/B78, A76/B102, etc.
Ibid.
The three main sources for Kant’s views on general logic all derive from the courses he gave on the subject from 1755 to around 1796 (see Ak. XXIV.955). These are: Logik, i. e. Immanuel Kant’s Logik (Ak. DC1–.150), compiled by G. B. Jäsche in 1800 from Kant’s lecture notes; these notes (Reflexionen) themselves, as contained in Ak. XVI; and student notes from the lectures, contained in Ak. XXIV/1 and XXIV/2.
See Logik, Ak. IX.34, and the student notes on Kant’s logic lectures, Ak. XXIV., 40, 340, 510, 565, 701, 752, 805; cf Meyer, Auszug aus der Vernunftlehre (the text Kant used in his logic lectures), §123, Ak. XVI.316 (also §10,.76).
E.g., KdrV, A19f/B33f; A320/B376f; Logik §1, Ak.IX.92.
Letter to J. S. Beck of Dec. 4, 1792, Ak.. XI.395.29. This passage agrees with KdrV, A34/B50 and A50/B74, where a representation is seen as a determination of the mind Cf also KdrV, A98f, and R1676, Ak. XVT.76ff. In Meyer, a representation “behaves like a picture,” a view which Kant criticizes (in R1676) as requiring a mental entity to be itself spatial in order to stand for (refer to, represent) something spatial. I ignore here the interesting questions of unconscious representations (Ak. VIII.217, XXIX 17.24) and representations in animals (see Ak. V.464n., VII.395f, XI.52, XI.345, XV. 166, XXVIII.275f).
There is a well-known ambiguity in the terms “representation,” “intuition”, and related terms. An intuition can be 1. a mental entity referring to some other singular thing, 2. the process of constituting this reference, or 3. the something else referred to; and the type-token distinction can be applied to at least some of these. “Representation” has the same ambiguities (though #3 is rare). In this context, representations and intuitions are mental entities, types rather than tokens (i. e., I have the same representation or concept of heaviness on two occasions). Where another sense is intended I will try to indicate it
Logik, Ak. IX.91; cf KdrV, A320/B376f; Logik, IX.64f This first characterization illustrates the difference between general and transcendental logic, and the difficulty involved in keeping them separate. The claim that “concept” is a species of “representation” stands in prima facie conflict with passages where Kant holds that a representation is something given which must undergo a kind of transformation in order to become a concept (e.g., KdrV, A76/B102; Logik, Ak IX.33f.,.94; R2854, R2876, Ak. XVI.547,.555f; LogWienXXIV.907.17). In the Logic (Ak. K.94), general logic is not allowed to address the question of how representations arise, but is supposed to deal only with the production of concepts out of representations, however these latter may have arisen It would seem that the conflict between species and transformation cannot be removed by distinguishing general and transcendental logic.
KdrV, A189/B234f.
Logik, IX. 91.17; cf. VorlLogXXIV/1.257.4; /2.567.29; /2.655.37; /2.908.30.
KdrV, A19/B33, A68f./B93f, etc.
The treatment of determination below gives a good example of the accrual of background conceptual content to an intuition
Logik, Ak. IX.97; cf LogDoh, Ak. XXIV.754f; LogWien, Ak. XXIV.911. Since any allegedly lowest species is for Kant still a concept and therefore still a universal, it is in principle applicable to an indefinite number of different objects, the differences among which can always be used to establish a further sub-concept.
Beck, “Kant’s Theory of Definition”, in Wolff; op. cit, 23–36.
KdrV, A727ff./B755ff.; cf R3000, Ak. XVI.609; LogPhil, Ak. XXIV.457ff, LogBlom, Ak. XXIV.268f; LogPöl, Ak. XXIV.571f; LogBus, Ak. XXIV.657; LogDoh, Ak. XXIV.757; LogWien, Ak. XXIV.915,.918.
See the passages on definition in the Logic, §§99–107 (Ak. DC 140–145), and the corresponding sections in Ak. XXIV cited above.
Logik, §99, Ak. IX. 140.23; R2927, Ak XVI.578; LogBlom, Ak. XXIV.264.35. Cf. Ak XX.409.5.
Leibniz, G. W., Philosophical Papers and Letters (ed and tr. by Leroy E. Loemker), Chicago: Chicago University Press, 1956, rpt Dordrecht: D Reidel, 1969, 320, also 183, 291–5, 625f, 646. Cf. Allison, “The Originality of Kant’s Distinction between Analytic and Synthetic Judgments,” in Richard Kennington, ed, The Philosophy of Immanuel Kant (Washington, D.C.: Catholic University of America Press, 1985), 15–38; Beck, “Analytic and Synthetic Judgments before Kant,” op. cit.
Logik, Ak. IX.63. Cf. KdrV, A764f/B792f; Logik, Ak. IX.63, 141f; LogWien, Ak. XXIV.915.14; R2959, Ak. XVI.587. (For the equation of marks with partial concepts, see Logik, Ak. IX.58.) These passage characterize empirical concepts as made; there are, however, others in which Kant says they are given.
KdrV, B130; A77/B103.
The term “determination” suffers from the same sort of ambiguity as intuition and representation: it can refer to 1. a kind of mental entity representing a feature of an object; 2. the process of endowing the object with that feature; or 3. the feature represented In sense 1, a determination is roughly equivalent to a concept In sense 3, it is similar to a mark or property of an object What is peculiar about both these senses is the implication that the mental entity arose or the feature was specified as a result of the process intended in sense 2; this is the sense at issue here.
Ak.XI.338f, 347.
KdrV A764/B792, emphasis mine. Cf “Deutlichkeit”, Ak. II.276f
“Discourse on Metaphysics’ §8, Loemker 307f; cf. Monadohgy §36, 646. See also Beck, “Analytic and Synthetic Judgments before Kant,” op. cit, 85f
See Loemker, 363.
For references indicating that this is in fact Kant’s view, see “Entdeckung”, Ak. VIII.239.19; Logik, Ak. IX.111.12. Cf. H. J. De Vleeschauwer, La Déduction transcendental dans l’ oeuvre de Kant (Antwerp: De Sikkel, 1937), vol.III, 410f: (“In an analytic judgment, the concept of the subject is already formed… But if we take [the subject] in its originary constitution, [the judgment] is synthetic…”). Cf Logik, Ak. IX.63f; “Deutlichkeit”, Ak. II.276. Cf also KdrV, B141f
The important problem of the individuation of objects, and the role of conceptual and spatio-temporal determination in it, is beyond the scope of this paper.
KdrV B147, B165f., etc etc. and A50ff./B74ff. etc.etc.
“Made”: Log IX.141.25; R2959, XVI.587; R2910, XVI.572. “Given”: Log IX.93.23; VorlLog XXIV.571.20,.654,.656; LogBlomXXIV.270.4. (The example of an empirically given concept is “body,” which seems to fit in with the notion of “thing” as the only given empirical concept — R2935, cf R2936.) See the discussion of transcendental judgments and the associated notions, below.
KdrV, A133f/B172f, and the footnote to that passage.
KdrV, A78/B103.
KdrV, A141/B180.
E.g., in “Anschauung und Mannigfaltiges in der transzendentalen Deduktion,” Kant-Studien 72 (1981), 140–48.
If marks are basically properties of objects, they could serve as the universals Aristotle called “present in” an object, i. e. accidents, but not as sortal or kind-universals “predicable of an object, i. e. the species and genera of objects: “snubness” could be a mark, and hence a representation and a concept of Socrates, but “man” and “animal” could not — Aristotle, Categories Chs. 2–5.
Logik, §6, Ak. IX.94; LogWien, Ak. XXIV.907ff.; R2881, Ak. XVI.557 (cf however LogBlom, Ak. XXIV.252.25).
KdrV, A52f./B77.
KdrV, A262f./B318f.
Kant’s discussions give no sense that the empirical determination he intends could be wild or idiosyncratic: cf. KdrV, A721/B749, A727ff/B755ff; R2936, Ak. XVL581.
Kant, as is well known, argures in the Transcendental Aesthetic (KdrV, A23/B38, B40, A30/B46, and elsewhere) that space and time are not concepts (at least not empirical ones), but “a priori intuitions”; and this would then appear to hold of the mathematics based on them. But elsewhere he feels free to refer to mathematical concepts, and I follow this latter usage.
“Deutlichkeit”, Ak. II.276f. See also the references in the discussion of mathematical judgments below.
Logik, Ak. IX.93.
See Beck, Essays, 97: “[Kant] feels justified in classifying judgments according to their grounds (Wahrheitsgründe) and not merely as they are classified in formal logic…”
“Deutlichkeit”, Ak 11.276. Cf. Ak. XXIV.35;.654,.656; R2942, XVI.583; R2957,.586.
A712ff/7B740ff, esp. A723/B751: “With respect to the [form of intuition] we can determine our concepts a priori in intuition, in that by homogeneous synthesis we create for ourselves the objects in space and time, in that we regard them merely as quanta.”
It seems clear from this that Kant could not support the “logicist” view of the foundations of mathematics expressed by Russell in Principia Mathematics according to which the definitions and axioms can be derived from logic alone. This pre-Critical view seems close to the ‘Tormalist” position, though one might expect the Critical view to be closer to Brouwer’s “intuitionist” position, which appeals explicitly to Kant
KdrV, B147; A165/B206; A733/B761; Proleg., Ak. IV.285.9. 67 KdrV, Bxii, A713/B741; Proleg, Ak. IV.281; Logik, Ak. IX.23; etc.
KdrV, A23ff./B38ff., A30ff./B46ff.
KdrV, A713/B741. Cf. “Entdeckung”., Ak. VIII.191f., note; KdrV A223/B271; Ak. XX.325.22.
This explication follows that of Paul Lorenzen; see Lorenzen and Wilhelm Kamlah, Logische Propädeutik (Mannheim: Bibliographisches Institut, 1967), 219–23.
Letter to Herz, Ak. X.131; Diss. §1 n.2, Ak. 11.389.33.
KdrV, B15f See also Proleg. Ak. IV.269;KdrV, A164f./B205f.
KdrV, B16f. (also Proleg. Ak. IX.269); KdrV, A164/B204f.
KdrV, B15f (also Proleg. Ak. IV.269); KdrV A164/B205.
Logik, §99, Ak. IX.140. See also KdrV, A727n./B755n.; R2979, Ak. XVI.598.5; R2927, Ak. XVI.578.
For examples see my “Kant’s Synthetic A Priori: A Contextual Interpretation,” Akten des VIIth Internationalen Kant-Kongresses (Bonn: Bouvier, 1991), vol. II, 159–70.
KdrV, A165/B206.
Logik, Ak. 1X93,.141f. cf. R2836, 2852–55, Ak. XVI.538f.,.546f. (cf. also R2849, Ak. XVI.549).
There are passages, however, with a distinct innatist flavor. “There are definitions for concepts which we have already and are not yet properly designated by the name, e.g. metaphysics. And here it is not so much the meaning of a word that is analysed as a concept which is inherent in us [uns beiwohnt]… (R3003, Ak. XVI.610). But in the Eberhard polemic, Kant explains that though the Critique takes all representations to be acquired, there is a kind of original acquisition (of space, time and the categories), and the ground of this acquisition can count as innate (“Entdeckung”, Ak. VIII.221ff,.249; cf Proleg Ak. IV.330).
KdrV, A727ff./B755ff; Logik, §105, Ak. IX.142f.
See LogWien, Ak. XXIV.917.4; LogPhil, Ak. XXIV/1.457.11; R2936, Ak. XVI.581.14. Cf Logik, §100–104, Ak.IX.141f.
Logik §100, IX.141.
LogPhil, Ak. XXIV.452.24. Cf. LogBlom, Ak. XXIV.252.36.
KdrV, B135.
KdrV, A184/B227.
KdrV, B149, B289; cf. R5650, Ak.XVIII.301f.
Ak.XX.408f.
Beck, “Can Kant’s Synthetic Judgments be Made Analytic?” in Wolff, op.cit., 14. I take the interpretation proposed here to be largely in accord with Beck’s conclusions in this essay.
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Robinson, H. (2000). Kant on Apriority, Syntheticity, and Judgments. In: Wiegand, O.K., Dostal, R.J., Embree, L., Kockelmans, J., Mohanty, J.N. (eds) Phenomenology on Kant, German Idealism, Hermeneutics and Logic. Contributions to Phenomenology, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9446-2_15
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