In this chapter, I have explained Longuenesse’s general theory. Contrary to most authors, Longuenesse thinks that, to understand why Kant’s cat- egories are “conditions of the possibility of experiences”, we must consider the relationship of these categories to the logical forms Kant derives them from.
Experience arises when we think objects under concepts combined in judgments with an objective logical form. The logical forms Kant lists in his Table of Judgments are the elementary logical forms such an objective judgment can contain. Judgments are generated by the logical functions of the understanding. Each elementary function of the understanding generates one of the elementary logical forms. Therefore, the Table of Judgments contains two tables in one: a table of logical forms, and a table offunctions. To make experience possible, objects must be given to us in a way that enables us to bring them under concepts. This is warranted by figurative synthesis. In figurative synthesis the functions of the understanding affect sensibility. The understanding generates combinations ofsensible represen- tations, which provides us with proto-phenomena: empirical objects that can be brought under concepts. This also explains why the categories as ‘full-fledged’ concepts – the categories as Kant lists them in the category ta- ble – can be applied to empirical objects. In figurative synthesis, the func- tions of the understanding generate the transcendental schemata. These schemata form a special kind of marks of empirical objects. The categories as full-fledged concepts express those marks.
Longuenesse’s interpretation of Kant, we saw, can be described as ‘cogni- tive’. According to Longuenesse, Kant is mainly concerned with experience in a rather weak sense. Kant considers how our day to day experience of empirical objects is possible. Longuenesse’s interpretation differs from Fried- man’s epistemological reading. According to Friedman, Kant only considers
how scientific knowledge is possible.
In chapter 2, we will have a closer look at Longuenesse’s theory. There, we will see how she applies her theory to the categories and logical forms of Quantity.
Chapter 2
Quantity
In the previous chapter I discussed Longuenesse’s theory that we can only understand how the categories make experience possible by looking at the logical forms of judgment. InKant and the Capacity to Judge, Longuenesse applies this general theory to three groups of categories: the categories of Quantity, the categories of Quality and the categories of Relation. In this chapter, we will see how she applies her theory to the categories of Quantity. I will begin this chapter by explaining what Longuenesse means by ‘quan- titative synthesis’. Longuenesse distinguishes between ‘quantitative’, ’quali- tative’ and ‘relational’ synthesis. In section 2.1, I discuss the relationship of these different acts of synthesis to the act of figurative synthesis discussed in chapter 1. In 2.2, we will have a closer look at the different kinds of syntheses and see what ‘quantitative’ synthesis consists in. We will see that quantitative synthesis enables us to represent “manifolds” of representa- tions. In 2.3 we will consider the logical forms of Quantity. As we will see, these forms are possible because quantitative synthesis enables us to repre- sent collections of representations we think under the one concept. In 2.4, I discuss how the schema of Quantity is related to the act of quantitative synthesis and the logical forms of Quantity. I will show why we can regard this schema as being generated by the activity of quantitative synthesis that aims at making possible the logical forms of Quantity. In 2.5 we will con- sider how the categories of Quantity apply to different kinds of quantities, and consider the exact relationship between these categories and the logical forms of Quantity.
2.1
Elementary Syntheses
In chapter 1 we saw that, according to Wolff, the activity ofjudgment can be said to contain different ‘aspects’. Within the act of judgment, we exercise a complex action which Kant calls a function of the understanding. This function of the understanding is a complex function. Within the complex act of judgment we exercise various elementary actions. These elementary actions are “functions” as well: elementary functions. There are, we saw, four kinds of elementary functions that can be exercised in judgment: quan- titative,qualitative,relational andmodal functions. Each of these functions can be exercised in three different ways.1
Longuenesse, we saw, thinks empirical objects (proto-phenomena and phenomena) are generated byfigurative synthesis. Figurative synthesis, we saw, is an “effect of the understanding on sensibility”. The complex logical function the understanding exercises begins ‘earlier’ than we might think. We do not start judging the moment we begin to form discursive judgments about empirical objects. The act of figurative synthesis that generates em- pirical objects should be seen as a part of the activity of judgment. The activity of figurative syntheses makes sure empirical objects are given to us in such a way that these objects can be brought under concepts combined in judgments.
In figurative synthesis the complex function of the understanding, with its four elementary functions, affects sensibility. Now within figurative syn- thesis, these elementary functions can be distinguished as well. Just like the activity of judgment, figurative synthesis is a complex act that ‘contains’ cer- tain elementary actions. Both the complex act of figurative synthesis and the elementary actions it contains, Kant calls ‘syntheses’. Following Wolff, we can call these acts ‘elementary’ syntheses. Just like there are four kinds of elementary logical functions, there are four kinds of elementary syntheses: quantitative, qualitative, relational and modal synthesis.2
The complex act of figurative synthesis warrants empirical objects are given to us in such a way that forming judgments about these objects be- comes possible. The four kinds of figurative synthesis Longuenesse distin- guishes: quantitative, qualitative, relational and (probably3) modal synthe-
1
See section 1.3.
2As I said in chapter 1, footnote 35, Longuenesse does not explicitly explain these
points in this way. From her analysis of the different acts of synthesis, however, we can derive that this is how she sees this. SeeKCJ, chapter 9-11. As Longuenesse only discusses the categories of Quanity, Quality and Relation, she does not discuss ‘modal’ synthesis.
3
sis, all aim to make possible those forms of judgment that belong to them. Each of the syntheses warrants that empirical objects are given in such a way that these forms of judgment become possible. By doing this, these synthe- ses generate in these empirical objects the varioustranscendental schemata. The categories express these transcendental schemata (KCJ: 245-6). Rela- tional synthesis, for instance, warrants that objects are given to us in such a way that the categorical, hypothetical and disjunctive forms of judgment become possible. Relational synthesis thus generates in these objects the transcendental schemata of Relation. These schemata justify the applica- tion of categories like ‘cause’ and ‘substance’ to these empirical objects. In the upcoming sections, we will see how Longuenesse applies this theory to the categories ofQuantity.