Abstract
As Kant explains his concept of intuition, it seems clear that a representation must satisfy two conditions in order to be an intuition: it must be singular and it must relate immediately to its object. Charles Parsons has referred to these as “the singularity condition” and “the immediacy condition,” and has doubts that within Kant’s philosophy they boil down to the same thing.1 Jaakko Hintikka, on the contrary, maintains that in Kant the immediacy condition is only the singularity condition stated in another way, so that “Kant’s notion of intuition is not very far from what we would call a singular term.”2 Both Parsons and Hintikka focus their attention primarily on Kant’s philosophy of mathematics, and Parsons holds that “Hintikka’s theory really stands or falls on the interpretation of the role of intuition in mathematics” (p. 46). In this paper I want to emphasize Kant’s treatment of empirical judgments and the role that intuition plays in them, as I believe (and will try to show in the course of my discussion) that this context was the primary one for Kant.
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Notes
“Kant’s Philosophy of Arithmetic,” Philosophy, Science, and Method,eds. S. Morgenbesser, P. Suppes, M. White. New York: St. Martin’s Press, 1969; reprinted in this volume pp. 43–79. All page references to Parsons are to this volume.
“On Kant’s Notion of Intuition (Anschauung),” The First Critique: Reflections on Kant’s Critique of Pure Reason, eds. T. Penelhum, J. Macintosh. Belmont, Calif.: Wadsworth Publishing Co., 1969, pp. 38–53. All page references to Hintikka are to this work. But see below, end of footnote 23.
I follow the usual practice in giving references to the Critique of Pure Reason: A for the 1st ed. and B for the 2nd. The numbers are always page numbers in the respective editions. When only one reference is given, the passage does not appear in the other edition. All quotations from the Critique are from the translation by Norman Kemp Smith, London, 1929.
That is, when one expresses the singular judgment in language one uses a sentence with a proper name as subject. The name then represents the singular concept in that it does the job in the sentence, viz., the job of representing exactly one object, that the concept does in the judgment. While the name thus represents both a concept and an object, this point should occasion no confusion if one remembers that the name represents the concept only in the sense that it represents in the sentence what the concept represents in the judgment. Whether or not one can make judgments without sentences to express them is beside the point, since I am concerned only with judgments that are so expressed.
References to Kant’s Logic are to Jäsche’s edition of Immanuel Kant’s Logik: Ein Handbuch zu Vorlesungen, 1800. The translations are mine.
The mistake (Fehler) Kant is referring to must be that of failing to see that it is a mere tautology. I make considerable use of this passage in my interpretation of Kant. Parsons (n. 5) quotes only the first half of the sentence and does not mention the mistake or the distinction between a division of concepts themselves and a division of their use.
The difference between singular and universal judgments can be ignored only with syllogisms in the four direct moods of the first figure. The difference must be recognized in the conversions required for the reduction of indirect moods and figures. ‘Some mortal is Caius’ converts to `Caius is mortal’, but an I does not convert to an A proposition. Of course, Kant regarded the doctrine of indirect moods and figures as false sophistry or a needless subtlety to be removed from traditional logic. Cf. his Die falsche Spitzfindigkeit der vier syllogistischen Figuren eris’iesen, 1762; also, B viii, B 141 n.
Intuitions are also referred to as species of knowledge or cognition (Erkenntnisse) in the passage from the Logic (§ 15, Note) mentioned above. I will turn to this passage in Section III.
Kant: Prolegomena, tr. by P. G. Lucas, Manchester: Manchester University Press, 1953, p. 146, n.
In a footnote in the B version of the transcendental deduction (B 160), Kant seems to acknowledge this point. The note begins:
Space, represented as object (as we are required to do in geometry), contains more than mere form of intuition; it also contains combination of the manifold, given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only a manifold, the formal intuition gives unity of representation [italics in Smith’s tr.].
By “space represented as object” Kant must mean space as determined by geometrical figures and not space as a form of sensibility. Through the accompanying formal (pure) intuition the manifold of empirical intuition is unified as a spatial something identified by a particular geometrical figure. That this formal intuition is a cognitive representation prior to conceptual synthesis is brought out by the rest of the note, which continues:
In the Aesthetic I have treated this unity as belonging merely to sensibility, simply in order to emphasize that it precedes any concept, although, as a matter of fact, it presupposes a synthesis which does not belong to the senses but through which all concepts of space and time are possible. For since by its means (in that the understanding determines the sensibility) space and time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding (cf. § 24) [first italics mine].
From the reference to § 24, we must conclude that the “presupposed” synthesis here is the figurative synthesis explained in that section and distinguished from the “intellectual synthesis” which “is thought in the mere category in respect of the manifold of an intuition in general” (B 151). See, note 20.
In this remark I pass over the complications introduced by Kant’s view of modalities. “In a judgment [Urtheil] the relation of different representations in the unity of consciousness is thought merely as problematic; in a proposition [Satz], on the contrary, it is thought as assertoric. A problematic proposition is a contradictio in adjecto” (Logic, § 30, Note 3). It might seem that a closed sentence corresponds more to a Kantian proposition, while a judgment is formed from a proposition by the addition of a modal operator. But Kant continues in the next sentence, “Before
I have a proposition I must first make a judgment; and I judge concerning many things about which I have not reached a decision, which I must do as soon as I have determined a judgment as a proposition.“ This suggests that a proposition is formed from a judgment, which in itself is always problematic.
Kant admitted that the second of these conditions is satisfied in the case of one, but only one, concept — that of an ens realissimum. “For only in this one case is a concept of a thing — a concept which is in itself universal — completely determined in and through itself, and known as the representation of an individual” (A 576 = B 604). But this concept is an idea of reason and Kant argues at length that it cannot represent an existing object.
In the sentence from A 320 = B 376–77 quoted by Hintikka, Smith’s translation of einzeln as “single” seems plausible, although in the Logic, § I the word is paired with the Latin singularis and must mean “singular.” An intuition thus differs from a concept both in being single (a single occurrence) and in being a singular representation (a representation of but one object).
P. F. Strawson chooses to ignore this point when he claims that for Kant “the preservation of the unity of space from judgment to judgment requires the persistence and re-identifiability of occupants of space.” The Bounds of Sense, London: Methuen, 1966, p. 83. By taking reidentifiable particulars as basic, Strawson is forced to maintain an identificatory as distinct from a referential function for singular terms that is foreign to Kant. See Note 15.
Kant is thus in agreement with Quine and opposed to Strawson on the issue of whether singular terms have an identificatory function that cannot be dispensed with in favor of general terms and variables of quantification. “In Word and Object a conspicuous effect of regimentation is that a predication of the form ‘Fa’, with identificatory singular term in the ’a’ place, goes over into the symmetrical form ’(3x) (Fx • Ax)’. A uniqueness clause regarding ’A’ may still be added, but the identificatory work of singular terms has lapsed.” (W. V. Quine, “Replies: To Strawson,” Synthese 19 (1968–69), p. 293; reprinted in Words and Objections, Donald Davidson and Jaakko Hintikka, eds. Dordrecht: D. Reidel Publishing Co., 1969, p. 321. Strawson needs the separateness of the identificatory function because he assumes that reidentifiable particulars are required to preserve the unity of space and time. (See, note 14.) But then does Quine’s position require a Kantian-like assumption that the unity of space and time (or space-time) is independent of the ontological unity of particular spatiotemporal objects?
There is of course no existence claim to be satisfied since space and time are not existing objects but the forms of intuition under which all existing objects are experienced.
This point, implied in the Aesthetic, is stated explicitly in the Analytic. We “cannot obtain for ourselves a representation of time, which is not an object of outer intuition, except under the image of a line, which we draw” (B 156).
I come later to my reason for saying “schematic letters” here rather than “variables.” For this use of ‘schematic letter’, cf. W. V. Quine, From a Logical Point of View, Cambridge, Mass.: Harvard University Press, 1953 and 1961; Set Theory and Its Logic, Cambridge, Mass.: Harvard University Press, 1963, revised ed., 1969.
Kant: Philosophical Correspondence, ed. & trans. by A. Zweig, Chicago: University of Chicago Press, 1967, p. 130. The letter appears in Kant’s Gesammelte Schriften, ed. by the Prussian Academy of Sciences, vol. X.
The transcendental synthesis framed from concepts alone referred to in this passage is undoubtedly the “intellectual synthesis” referred to in § 24 of the B version of the transcendental deduction (B 151; See, note 10). This intellectual synthesis relates to “objects of intuition in general, whether that intuition be our own or any other, provided only it be sensible” (B 150). The forms of our intuition, space and time, are required for a preconceptual representation of an existing object unified merely as a spatiotemporal something, and this representation is achieved by the figurative synthesis of § 24. The intellectual synthesis provides a necessary but not a sufficient condition for a priori knowledge of existing objects, i.e., the knowledge that the object is singular; the figurative synthesis, which is simply the former carried out in productive imagination rather than concepts, provides a necessary and sufficient condition, i.e., the knowledge that the object as singular is a spatiotemporal something. The philosopher alone is competent to deal with the intellectual synthesis, since qua philosopher he is concerned with a priori knowledge of existence and is thus led to see the necessity of the figurative synthesis. Qua mathematician, one is concerned only with a priori knowledge of the constructibility of concepts and not with a priori knowledge of the application of concepts to existence. If as mathematician one begins with the intellectual synthesis, one can succeed only in thinking about numbers as objects, and this is not according to Kant, the way one does arithmetic or the way one relates arithmetic to reality.
Hilary Putnam in “Mathematics Without Foundations” (Journal of Philosophy, LXIV (1967), pp. 5–22) distinguishes two views of mathematics, an “object” view, according to which “mathematics is wholly extensional, but presupposes a vast totality of eternal objects”; and a “modal” view, according to which “mathematics has no special objects of its own, but simply tells us what follows from what” (p. I l). The second view seems Kantian in spirit in that it affords a way of interpreting quantifiers in mathematical formulations that does not require the existence of mathematical objects. But the extent to which this view can actually be accommodated in Kant’s philosophy of mathematics depends on what we make of Kant’s distinction between demonstrations and discursive proofs and his claim that logical necessity (what follows from what) is grasped intuitively in the one case and conceptually in the other. I do not see how the side of Kant’s philosophy of mathematics can be squared with Putnam’s modal view, and I am inclined to think that there is no way in which one can subscribe to much of Kant’s position without restricting arithmetic to what can be expressed in free-variable formulas.
R.L. Goodstein, Essays in the Philosophy of Mathematics, Leicester: Leicester Univ. Press, 1965, p. 72.
Since general logic so conceived contains symbolic constructions and demonstrations, it would seem at least in this sense to be something Kant would have to regard as a branch of mathematics. One may be tempted to take Kant’s reconstructed position to be that general (formal) logic uses symbolic constructions and demonstrations to determine valid forms of discursive proof, and is thus a special case of mathematics. This is essentially the position of C.S. Peirce. But this position conflicts with Kant’s view that logical possibility is purely conceptual and constructibility intuitive. Parsons holds that the priority of constructibility “is a consequence to be accepted and is even in general accord with Kant’s statements that synthesis underlies even the possibility of analytic judgments” (p. 67). But as I read Kant the underlying synthesis in this case is purely conceptual and not intuitive. The shift from ’S is P’ to `F,’ as the form of predication achieves conceptual clarity, not intuitive certainty; and the role of quantifiers is no less discursive than the role Kant assigned to the copula. The use of symbolic constructions and demonstrations in quantificational logic, though far more extensive, is not essentially different from the constructions Kant recognized in general logic — the square of opposition, the use of circles and squares to diagram the relation of S and P in categorical judgments (cf. Logic §§ 21, 29), and the four figures of the syllogism (though he regarded the latter as needless subtleties).
These remarks on the relation between mathematics and logic, and indeed much of what I have said in section IV, are contrary to the reconstruction of Kant’s position proposed by Hintikka in papers I have not mentioned, since I did not have space here to comment on them. I have thus not done full justice to his position. Cf. in particular his “Kant on the Mathematical Method,” The Monist, 51 (1967), pp. 352–375; reprinted in this volume, pp. 21–42.
I am indebted to Charles Parsons for helpful criticisms of an earlier version of this paper.
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Thompson, M. (1992). Singular Terms and Intuitions in Kant’s Epistemology. In: Posy, C.J. (eds) Kant’s Philosophy of Mathematics. Synthese Library, vol 219. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8046-5_4
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