The relationship between the categories and logical forms of Quantity, Longue- nesse thinks, should be understood as follows: In quantitative synthesis, the understanding affects sensibility in its striving to bring the sensible given under concepts combined according to the logical forms of Quantity. In quantitative synthesis, we are striving to form judgments of the forms ‘All
A’s are B’, ‘Some A’s are B’ and ‘This Ais B’. In doing this, quantitative synthesis generates the schemata that enable us to apply the categories of Quantity to empirical objects.27 In this and the upcoming sections, I will make this idea more concrete. First, we will take a closer look at Kant’s quantitative logical forms.
Kant, Longuenesse points out, defines the quantitative logical forms in terms ofextensions of concepts:
In the universal judgment, the sphere of one concept is wholly enclosed within the sphere of another; in theparticular, a part of the former is enclosed under the sphere of the other; and in the singular judgment, finally, a concept that has no sphere at all is enclosed, merely as part then, under the sphere of another. (Logic,§21; Ak. 9: 102)28
When I form the judgment ‘AllA’s areB’, I state that conceptA’s extension is fully contained in the extension of conceptB. In the judgment ‘SomeA’s areB’, I claim that conceptA’s extension is partly contained in the extension of conceptB. In the judgment ‘This A is B’, finally, I state that “concept that has no sphere at all” is contained in the extension of conceptB.29
27
SeeKCJ, chapter 9, especially p. 250.
28KCJ: 247 29
What Kant means by this latter remark, Longuenesse does not really explain (she says something about it atKCJ: 247f., but it hardly makes Kant’s remark more compre-
We can understand Kant’s quantitative logical forms in two ways. Some judgments can be seen as mere combinations of concepts. If concept B is contained in conceptA’s intension, then conceptAand B can be combined to the judgment ‘AllA’s areB’ merely by analyzing conceptA (KCJ: 247). Onlyanalyticaljudgments can be formed in this way.30 To form thesynthetic
judgment ‘AllA’s areB’, however, considering conceptA’s intension is not sufficient. The justification of a synthetic judgment ‘AllA’s are B’ requires
sensibility. The synthetic judgment ‘AllA’s are B’ can only be justified by considering whether conceptB applies to all sensibly given objects that are thought underA (247-8).
This observation enables us to solve the problem concerning the log- ical forms of Quantity we encountered in the Introduction. In his Table of Judgments, Kant presents the quantitative logical forms of judgment in the following order: universal, particular, singular. This is puzzling, be- cause Kant presents the categories of Quantity in the orderunity,plurality,
totality. This suggests that Kant infers the category unity from the univer- sal,plurality from the particular, andtotality from the singular logical form.
1. Quantity of Judgments 1. Of Quantity
Universal Unity
Particular Plurality
Singular Totality
Longuenesse combines her ideas about the different kinds of judgments with an analysis of the categories and logical forms of Quantity Frede and Kr¨uger (1970) have provided. Frede and Kr¨uger have pointed out that Kant does not always present the logical forms of Quantity in the order in which he presents them in the Critique. In some of his lectures and notes on metaphysics, Kant arranges them in the order singular, particular, universal.31 In his published works and in his lectures on logic, he follows the orderuniversal,
hensible). In chapter 5 I will argue that Longuenesse’s interpretation of the logical forms of Quantity does not enable her to account for Kant’s remark.
30
This follows from Longuenesse’s explanation onKCJ: 247-8 and her remarks onibid: 127n.
31
See Reflection 4700, Ak. 17: 679;Metaphysic Volckmann, Ak. 28-1: 396;Metaphysic von Sch¨on, Ak. 28-1: 480;Metaphysic Dohna-Wundlacken, Ak. 28-2: 626 (KCJ: 248n.).
particular, singular (KCJ: 248; Frede and Kr¨uger, 1970: 31-2).32 In these published works Kant follows the Aristotelian tradition (32). Within this tradition, universal judgments are considered prior to particular judgments. The judgment ‘Some A’s are B’ should be seen as a ‘limitation’ of the judgment ‘AllA’s are B’ (33).
The two kinds of judgments Longuenesse distinguishes, she states, help us understand why Kant presents the logical forms of Quantity in two dif- ferent orders. The traditional orderuniversal,particular,singularapplies to judgments that combine concepts without appealing to sensibility. In such judgments, general judgments are prior to particular judgments. We regard the extensions of the concepts combined as given, and the subject concept’s extension can either fully or partly be contained in the extension of the predicate concept. For such judgments, therefore, the particular judgment ‘Some A’s are B’ should be seen as a limitation of the universal judgment ‘AllA’s are B’ (KCJ: 248).
For judgments that do rely on sensibility, this is different. Consider the synthetic judgments ‘Some swans are white’, ‘All birds have a beak’ or ‘All apples on this table are red’. We should not see the judgment ‘Some swans are white’ as a limitation of the universal judgment ‘All swans are white’. Rather, we should understand this judgment as a conjunction of
singular judgments. We form this judgment by determining for various sensibly given objects we think under the concept ‘swan’ that the concept ‘white’ applies to them. We thus move from singular judgments (‘This swan is white’, ‘That swan is white’) to a particular judgment (ibid). In forming a universal judgment like ‘All birds have a beak’, we do the same. In this case, we progress from singular judgments to a particular judgment, and, eventually, to the universal judgment ‘All birds have a beak’ (ibid).33 To the logical forms of Quantity we can apply the distinction between judgments of perception and judgments of experience we encountered in chapter 134 (ibid). The judgment “All birds have a beak” might be a mere judgment of perception. In this case, the judgment results from the accidental circum- stance I have never seen a bird without a beak. The judgment, however, may also be the result of an extensive investigation. In that case, it is a judgment of experience.
Taking into account the sensible conditions under which most judgments are formed gives rise to an order of the quantitative logical forms that dif-
32
See Logic,§21, Ak. 9: 102; Prolegomena, §21, Ak. 4: 302; Metaphysic P¨olitz, Ak. 28-2: 747 and all Kant’s lectures on logic (KCJ: 248n.).
33
Frede and Kr¨uger see this similarly, see Frede and Kr¨uger (1970): p. 44.
34
fers from the traditional one. If we adopt this perspective on judgments, we should regard singular judgments as prior to particular judgments, and regard particular judgments as prior to universal judgments. This gives rise to the ordersingular,universal,particular (ibid).
Now the question is: which order of logical forms does Kant use to derive the categories of Quantity? This becomes clear from a footnote in theProlegomena Frede and Kr¨uger point to:
I would prefer this designnation [judica plurativa] for judgments that are called in logic particularia. For the latter expression already contains the thought that the judgments are not univer- sal. But when I start from unity (in singular judgments) and so proceed to totality, I cannot yet include any reference to total- ity; I only think plurality without totality, not the exclusion of totality. This is necessary if logical moments are to underlie the pure concepts of the understanding; in logical usage, things can stay they are. (Prolegomena,§20n., Ak. 4, 302; 45, n. 13)35
In this footnote Kant explains why he prefers to call particular judgments ‘plurative’ judgments. The reason he prefers this name is that the name ‘particular judgment’ implies the judgment is not universal. Kant seems to say that calling particular judgments ‘plurative’ would do justice to the fact we form these judgments on the basis of singular ones, and that we infer universal judgments from particular ones. This “is necessary, if logical moments are to underlie the pure concepts of the understanding”. The passage suggests, therefore, that Kant infers the categories of Quantity from the logical forms in the order singular, particular, universal. This would mean that he relates the category unity to singular, the category plurality
to particular, and the category totality to universal judgments. This, it seems, is indeed what Kant has in mind: we “start from unity (in singular judgments)”, and “proceed to totality”. Why, then, does Kant present his logical forms of Quantity in the order universal, particular,singular? This is answered by the last remark: “In logical usage, things can stay as they are”. In logic, where sensibility does not play a role, the logical forms of judgment can be understood in their traditional way. This explains why
35
SeeKCJ: 249. This translation is derived from Thompson (1989): 171. Thomp- son follows the translation provided by Peter G. Lucas (1953) Manchester: Manchester University Press. This translation differs slightly from the translation Longuenesse is us- ing and the Carus-Ellington translation I use. I think this translation is more accurate. Because this passage returns in the later chapters, I have chosen to use this translation.
Kant presents them in their traditional order, and keeps calling particular judgments ‘particular’ in stead of ‘plurative’.36