3.7 A puzzle
4.1.3 What does Kant mean by “formal”?
Kant invokes formality both in distinguishing general logic from special logics (A54/B78) and in distinguishing general logic from transcendental logic (A556/B80). Pure general logic, Kant holds, “. . . abstracts from all content of knowledge, that is, from all relation of knowledge to the object, and considers only the logical form in the relation of any knowl- edge to other knowledge; that is, it treats of the form of thought in general” (A55/B79). This claim is repeated in many places throughout Kant’s works, with minor variations (no doubt all intended as equivalent). General logic abstracts entirely from the objects them- selves (KrV:B ix; JL:51, 16)—or more properly, from relation of thought to the objects (KrV:A55/B79), that is, from the content of thought (KrV:A54/B78, A55/B79, A70/B95; JL:94).13 Thus it is the science of “the mere form of thought” (JL:13) and deals “. . . with nothing but the mere form of thought” (KrV:A54/B78; cf. A55/B79, A56/B80, A70/B95, A131/B170). Its laws are “without content and merely formal” (A152/B191, emphasis added).
I suggest that the sense of formality at issue here is 3-formality: abstraction from
12Here I concur with Smit 1999:214. Putnam 1994 claims to find in Kant the idea that “illogical
thought is not, properly speaking, thought at all” (246; cf. Conant 1991). I see little basis for this reading of Kant, but there are a few passages that might support it. At KrV:A150/B189, Kant says that self-contradictory judgments are “nothing” (nichts: Kemp-Smith softens this to “null and void”). (I owe this observation to Steve Engstrom.) And in the Vienna Logic, Kant is reported to have said: “Logic has the peculiarity that the subjective laws are also objective rules, because the universal rules are the sole condition of our thought” (VL:791).
all semantic content of the representations used in thought.14 What this means can be clarified by the consequences Kant draws from it. Because logic is formal, he says, it affords no knowledge of objects:15
. . . if I separate understanding from sensibility to obtain a pure understanding, then nothing remains but the mere form of thinking without intuition, by which form alone I can know nothing definite and consequently no object. (Pr:§57) For logic teaches us nothing whatsoever regarding the content of knowledge, but lays down only the formal conditions of agreement with the understanding; and since these conditions can tell us nothing at all as to the objects concerned, any attempt to use this logic as an instrument (organon) that professes to extend and enlarge our knowledge can end in nothing but mere talk. . . (KrV:A61/B86, cf. A60/B85)
That is, logic (properly understood) does not claim to tell us how things are with objects in the world. It delivers no knowledge of fact—not even of the most abstract and general facts (facts about identity or existence, for example). In this it contrasts with thea priori mathematical sciences, which purport to give us real knowledge about empirical objects (though only as to their sensibleforms). Whereas a transcendental deduction is needed to ensure the applicability of mathematics to empirical objects, no comparable assurance is needed for logic, because logic (unlike mathematics) makes no claims about objects. The point is not just that it does not tell us aboutactualobjects: it does not tell us aboutpossible objects, either.16 The “logical possibility”—that is, freedom from self-contradiction—of a concept does not suffice for its objective validity or “real possibility”—that is, its relation to some definite object “in the sum of all possibilities” (KrV:B xxvi n.). For example, the concept two-sided figure is free from logical contradiction, yet no possible object is a two-sided figure.
So much for the negative aspect of Kantian “formality.” What about the positive aspect?
14It is certainly not 2-formality, since algebra and arithmetic are 2-formal but not “merely formal”
in Kant’s sense. Nor is it 1-formality, or “generality.” As we will see in section 4.1.4, below, Kant regards “generality” and “formality” as distinct, though intimately related properties.
15The qualification “of objects” is essential, because Kant allows that logical laws afford knowledge
of the truth ofanalytic propositions (A151/B190), which make explicit the contents ofconcepts.
16In his reply to Eberhard, Kant says that logical principles “. . . completely abstract from every-
What does it mean to say that logic “treats of the form of thought in general”?
One should not picture “the form of thought in general” as a kind of mental glue by means of which representations are stuck together, and logic as a quasi-psychological investigation of its adhesive properties. The form of thought is not any kind of thing (not even a mental thing). It is, rather, a set of norms: in fact, the laws of logic themselves. If this is right, then Kant’s “positive” characterization of formality adds nothing substantive to the “negative” characterization. To say that logic treats of the form of thought in general is to say that it treats of the laws of logic. Let me explain why.
Kant characterizes the understanding as “the faculty of rules” (A13/B171) or “the source of rules” (JL:12). The reason is that the work of the understanding—the “spontaneous” production of concepts, judgments, and inferences—consists in the institution of norms. A concept, for Kant, is not an image or a collection of habitually associated images. Instead, it is constituted by a rule which determines how it can be correctly applied in particular cases. To say that the conceptanimalis one of the marks of the conceptcat, for example, is not to say that when we think of a cat, we think of an animal; it is to say that applying the conceptcat to a particular object of intuitioncommits one to applying the conceptanimal. Thus
. . . a concept is always, as regards its form, something universal which serves as a rule. . . . The concept of body, in the perception of something outside us, necessitates the representation of extension, and therewith representations of impenetrability, shape, etc. (KrV:A106)17
In a similar way, a judgment is a rule for the relation of representations. If I judge that all cats are cunning, I institute arule by the lights of which I amrequired to apply the concept cunning to anything to which I apply the concept cat:
Judgments, when considered merely as the condition of the union of given rep- resentations in a consciousness, are rules. (Pr:§23).18
17As Longuenesse explains, a concept “. . . is a rule in that thinking an object under a concept
provides a reason to predicate of this object the marks that define the concept” (1998:50). A concept is also a rule for the unification of the manifold of intuition. See Longuenesse 1998:48-52 for a much more nuanced discussion of the rulishness of concepts.
The essential rulishness of judgments (and derivatively of the concepts whose contents they explicate) manifests itself most clearly when they are used as major premises of syllogisms: “the syllogism is itself nothing but a judgment made by means of the subsumption of its condition under a universal rule (the major premiss)” (KrV:A307/B364).
Broadly speaking, Kant thinks of this normative aspect of concepts and judgments— their rulishness—as theirform. Thus, the form of concepts isuniversality(JL:§2, 91), while the form of judgments is the determination of the relation between representations: that is, “. . . the determination of the way that the various representations [i.e., the matter of the judgment] belong, as such, to one consciousness” (JL:§18, 101). In a categorical judgment, for example, the subject and predicate are the matter, while the normative relation between them (e.g., “one ought to apply B to everything to which one applies A”) is the form (JL:105). The logical functions of judgment (as displayed in the table of judgment) are the different possible normative relations: “the various modes of uniting representations in consciousness” (Pr:§22).
Every concept and judgment has a form, then—its “rulishness.” But what is “the form of thought in general”? The form of thought in general is that which makes thought possible: the “. . . formal conditions of all judgments in general (and hence of all rules in general)” (Pr:§23). But what are the conditions of all rules in general? What must be in place before the understanding can institute a norm—say, a the norm that one ought not apply A and B to the same thing? One needs a way of indicating incompatibility—say, the symbol “⊥”—but that is not fundamental. For we must then ask in virtue of what the symbol “⊥” indicates incompatibility. And the answer is clear: a symbol “⊥” can only indicate incompatibility if there is a particular kind of norm for its use: a norm like
(⊥-rule)If A⊥B, then one ought not apply A and B to the same thing.
Hence the condition for the understanding’s activity is a set of norms that make it possible to institute norms of incompatibility, universality, and so on. These norms—which we can judgments are can be either “objective” and necessary for every consciousness or “subjective” and necessary for a particular consciousness at a particular time (Pr:§22-3). General logic abstracts from this distinction.
now recognize as the laws of logic—are the rules according to which the source of rules itself proceeds (JL:12-13). Thus the form of thought in general, of which logic treats, is nothing other than the necessary rules for the employment of the understanding (JL:13), or norms for thought as such. It is in this light that we should understand Kant’s claim at JL:13 that the “science of the necessary laws of the understanding and of reason in general” and the science of “the mere form of thought as such” are “one and the same.”
The positive part of Kant’s claim that general logic “. . . abstracts from all content of knowledge . . . and . . . treats of the form of thought in general,” then, adds nothing to his characterization of it as “general” (that is, as 1-formal). It is the negative part of the claim that adds something new: namely, that the norms for thoughtas such are in no sense about the world, abstract entirely from the content of thought, and can give us no knowledge of objects.