Definitions of Kant's categories

Abstract

The consensus view in the literature is that, according to Kant, definitions in philosophy are impossible. While this is true prior to the advent of transcendental philosophy, I argue that with Kant's Copernican Turn definitions of some philosophical concepts, the categories become possible. Along the way I discuss issues like why Kant introduces the ‘Analytic of Concepts’ as an analysis of the understanding, how this faculty, as the faculty for judging, provides the principle for the complete exhibition of the categories, how the pure categories relate to the schematized categories, and how the latter can be used on empirical objects.

Keywords::

• Kant
• categories
• definitions

Acknowledgements

In preparing the final version of this essay I received helpful comments from Lisa Shabel and Emily Carson. I have presented earlier versions of this material to audiences at a workshop on the table of categories at Merton College, Oxford, and the 2011 Princeton-Penn-Columbia Conference in the History of Philosophy. In addition, this essay has also benefited from the feedback of Ralf Bader, John McDowell, and Karl Schafer. I also owe special thanks to Steve Engstrom and Anja Jauernig, both for comments on the paper and insights gained through their seminars on Kant.

Notes

^1. There are, to my knowledge, nine substantive treatments of the subject of Kant's view of definitions. In all of them, the question concerning the possibility of philosophical definitions is answered negatively. (Beck 1956) is the essay which most directly addresses the subject of definition and most of the subsequent treatments follow his to a greater or lesser degree. The others are: Stuhlmann-Laeisz (1976, §6), Capozzi (1981, 424), von Wolff-Metternich (1995, §4: 1.1), Carson (1999, §4), Maddy (1999, §2), Dunlop (2005, ch. 5), Dunlop (2011, §2), and Rosenkoetter (2009, 200–201). Of these, Rosenkoetter's comes closest to admitting the possibility of defining the categories, since, although he maintains Kant rejects this, he nonetheless holds that the categories together give a real definition of ‘the object as such [Gegenstand überhaupt]’. For an illuminating treatment of Kant's views on definition in the pre-critical period in relation to those of Leibniz and Wolff, see Sutherland (2010).

^2. I do not think that this exhausts the philosophical definitions that become possible according to Kant. In particular, he also thinks that many concepts in morals and in the metaphysics of extended matter can be defined, and this is so in a more robust way than the categories, because these definitions also make possible the construction of their objects (albeit in quite different senses). At one point it even sounds as if Kant thinks he can define the concept of time as ‘the order of things, in so far as they follow one after the other’ (Busolt Logic, 24:659), but it is not clear to me how he would secure this definition. I will not discuss these further kinds of philosophical definitions here.

^3. All of my references to Kant's works will be to the Akademie Ausgabe (vol:page number), except in the case of references to the Critique of Pure Reason, which will be cited using the pagination of the first (A) and second (B) editions. I will also usually abbreviate the work in question as follows: KrV (Critique of Pure Reason), Prol. (The Prolegomena to Any Future Metaphysics), MAN (Metaphysical Foundations of Natural Science), JL (Jäsche Logic), Refl. (Reflexionen). Translations are my own, but were done in consultation with the Cambridge editions. When interpreting Kant's logical views, we are faced with the problem that Kant did not himself author a treatise on logic. Rather, what we have are fragmentary notes contained in the Reexionen zurLogik and various transcripts of his lectures on logic taken by students. Of these, the Logic prepared by Jäsche, which was authorized by Kant, and prepared consulting his handwritten notes, stands out as the privileged one. Here I am agreeing with Young, among others (Kant and Young 2004, xix). For more on the respectability of Kant's various logical remarks see Kant and Young (2004, xvii–xix) and Boswell (1988).

^4. In Kant's German, ‘Exposition, Explication, Declaration und Definition’, compared with ‘Erklärung’.

^5. Another example is the exposition he gives of the faculty of desire. This is the faculty of a being to be the cause of the object of one of its representations, through that representation (KpV, 5:9n). In the end, we might discover that the concept of this faculty includes that it is always determined through pleasure, but this is left open in Kant's exposition.

^6. We need not dwell on the differences between the other various kinds of explanations, but briefly: descriptions are expositions that are not precise (JL, §105); declarations are arbitrarily (willkürlich) invented concepts for which it is not certain whether the object can be made (KrV, A729/B757). ‘Explication’, which seems to be the specification or spelling out of the content of an expression (Refl., XVI:577, 2922, 2923; XVI:579, 2931), is a less used term. It is very close to ‘exposition’ as the making distinct of a concept, although expositions can be given either of concepts or of appearances, while explications cannot be given of appearances. ‘Explication’ is often contrasted with ‘declaration’ (Refl., XVI:585, 2950). Finally, Erörterung is a term Kant will gloss as Exposition (JL, §105), and I do not take him to distinguish these.

^7. The possibility of reading the footnote in this way was suggested to me by Stephen Engstrom.

^8. Beyond the First Critique, most of the logical works, even the pre-critical ones, characterize precision through an analogy with putting a fraction into minimal terms (e.g. Bloomberg Logik, 24:263–264; Refl., 2979). The examples Kant gives of marks that would be excluded from such a definition in minimal terms include curved, or are often similar, excluding divisible from ‘the body is extended’ (Logik Pölitz, 24:575). All of which suggests that if he did intend precision in the weaker sense in the footnote, he was breaking with prior usage.

^9. The chemical formula for the element, however, comes closer to giving a boundary determination that allows the concept to stand at the head of all judgements about gold things. Nonetheless, the sub-atomic structure of certain samples of the element may lead to those samples exhibiting novel behaviour that goes beyond that which is fixed by its atomic structure. Accordingly, although an explanation of gold in terms of its atomic structure, which presumably fixes most of its macroscopic and mesoscopic properties, comes very close to fixing the precise boundaries of the concept, this too will not suffice, strictly speaking, for a definition. This would be no surprise to Kant, who thought empirical concepts were not definable (KrV, A727/B755).

^10. We find something similar in the case of invented concepts of objects of experience like Schiffsuhr, a clock precise enough for the computation of longitude. Such a thing had not been invented in Kant's day. Until we have built one, until we have proved that it can be produced in accord with the conditions of objects of experience in general, we do not know that this arbitrarily made concept has a really possible object (cf. KrV, A729/B757). It may, like a perpetual motion machine, not be physically constructible.

Kant will sometimes call specifications of how to make empirical objects, like instructions for building such a clock, definitions. One example is ‘the definition of cinnabar: mercury and sulfur sublimated produces cinnabar’ (Busolt Logic, 24:660). Such a definition, made out of empirical concepts, however, is not a counterexample to Kant's claim that empirical concepts cannot be defined. This is because these are technical concepts for making things, not the kind of empirical concept we might mistakenly want to define in an empirical science.

I think one way at this distinction is to note that although the matter for this definition is empirical, the definiendum is made apriori, since the concepts are put together through an act of will, not through an exposition of given appearances. Both Beck (1956, 184) and Dunlop (2011, 96), however, count this kind of invented concept as aposteriori made. I take this latter class, however, to contain only those concepts that we arrive at through hypothesis in empirical natural science, and which we test against appearances through observation (JL, 9:141). My reason is that I take the nature of the synthesis involved in the creation of the concept to be more important than the kind of matter combined, in determining whether a concept is apriori or a posteriori for Kant. Of course, I, nonetheless, allow that there is an important difference between Schiffsuhr and circle insofar as the matter of the concepts and the conditions on construction are empirical or apriori, respectively.

^11. One place where the kind of relation I have in mind comes out is in a passage of Kant's on biangles: ‘In the concept of a figure that is enclosed between two straight lines there is no contradiction, for the concepts of two straight lines and their intersection contain no negation of a figure; rather the impossibility rests not on the concept itself, but on its construction in space, i.e. on the conditions of space and its determinations; but these in turn have their objective reality, i.e. they pertain to possible things, because they contain in themselves a priori the form of experience in general’ (KrV, A220–221/B268). Circles, like biangles, are connected to space. But instead of this connection accounting for their impossibility, circles are possible. And in both cases, the possibility or impossibility of the figure in question depends ‘on the conditions of space and its determinations’ – whether the concept describes a possible limitation of space or not (cf. KrV, A619/B647). It is the relation between the concept circle or biangle, and space that I suspect is taken for granted in geometry, according to Kant. For one discussion of the topic in the secondary literature, which also situates it within a wider discussion of the transcendental exposition of space, see Shabel (2010, esp. 102–108).

^12. The relation of mathematics to appearances is studied in philosophy because the principles of mathematics are made possible through the principles of the pure understanding (KrV, A162/B202), the study of which belongs to philosophy. Specifically, Kant says that the application to experience of the principles of mathematics (which are derived from intuition, not the understanding) still always rests on the pure understanding (KrV, A159/B199). And the principle of the pure understanding in question is ‘all appearances are, as regards their intuition, extensive magnitudes’ (KrV, B202). He goes on to call this the ‘transcendental principle of the mathematics of appearances’ (KrV, A165/B206), and explain that this is the principle which ensures that mathematics governs appearances, objects of experience. So it is this principle, treated in philosophy, that ensures the objective validity of mathematics.

^13. Introducing his topic Kant says: ‘I understand by a transcendental exposition the explanation of a concept as a principle from which insight into the possibility of other synthetic a priori cognitions can be gained. For this it is required 1) that such cognitions actually flow from the given concept, and 2) that these cognitions are only possible under the presupposition of a given way of explaining this concept’ (KrV, B40). In the surrounding exposition, the concept in question is space, and the other synthetic a priori cognitions are those of geometry. I take the first paragraph of the exposition (the one spanning B40–B41) to be concerned with establishing this connection between our representation of space and our cognition in geometry.

^14. Another place where the dependence of geometry on philosophy for securing the relation between its constructions and space comes to the fore is in Kant's discussion with Eberhard. For example, in one suggestive remark Kant says, ‘the question, however, as to how this single infinite space is given, or how we have it, does not occur to the geometrician, but concerns merely the metaphysician’ (20:420–421; Kant and Allison 1973, English trans., 176). I take the surrounding context to fill out this remark in the direction I am suggesting.

^15. Before leaving the discussion of completeness, precision, and originality, I should note that my focus has been on the account of definitions given in the First Critique. In the works on logic, Kant approaches definitions from a slightly different angle. For example, in the Jäsche Logic he says, ‘a definition is a sufficiently distinct, and precise concept [zureichend deutlicher und abgemessener Begriff]’ (JL, §99; cf. KrV, B759). I take the differences between the terms used in the logical works and the First Critique to be largely insignificant, but in the Logic there is a shift in focus and perhaps a loosening. ‘Abgemessen’ I take to be the Germanic equivalent of the Latinate ‘Präcision’. ‘Zureichend deutlichkeit’ will have two sides, sufficient extensive and intensive distinctness (cf. JL, Intro §VIII, esp. XI:62–63). The former will roughly correspond to exhaustiveness, while the latter will be closely linked to originality. In shifting to talking about sufficiency of distinctness, Kant is de-emphasizing the explanatory elements of the definition – its originality and exhaustivity – and focusing on the logical form granted through these elements. Furthermore, in the context of general logic, which will govern all sciences, because sufficiency is relative to a use, we can perhaps see the point coming to the fore that what exactly is required for strict definitions is particular to a science, insofar as what will count as sufficient may be different in different sciences.

Another reoccurring theme in the logical works is the requirements or perfections of definitions which sometimes track the four headings of the functions of thinking (cf. JL, §107, 9:144; Busolt Logik, 24:658–660; Refl., 16:588–600; Wiener Logik, 24:921–922; Pölitz Logik, 24:574–575; DW-Logik, 24:759–760; Philippi Logik, 24:458; Blomberg Logik, 24:263ff). Some requirements these give, which do not get explicitly touched on in the Critique, are that definitions should not be tautologies, they should not be circular, and they should not explain the obscure by the equally obscure.

^16. Beck distinguishes ‘nominal’ and ‘logical’, using ‘logical’ as the name for specifically analytic nominal definitions. I do not see evidence for thinking this follows Kant's usage. Although it is true that Kant will often say ‘logical nominal definition’, what we have here are two adjectives describing the same kind of definition, not a specific kind of nominal definition. Kant tends to use ‘logical’ when he wants to emphasize that the definition is of a thing's concept, or specifies a logical essence, and tends to use ‘nominal’ when he wants to emphasize that the definition is of a name or a word, and although he will use both to contrast with ‘Real-’ or ‘Sach-Erklärungen’, ‘Nominal-’ or ‘Namen-Erklärungen’ seems to be his preference. Nonetheless, I do not think these preferences in use constitute a distinction in kind as Beck does.

^17.Refl., XVI:609–610, 3001, 3002, 3003.

^18. For example, on the one hand, at B757, he seems to rule them out entirely – ‘thus there remain no other concepts that are fit for being defined than those containing an arbitrary synthesis which can be constructed a priori, and thus only mathematics has definitions’ – on the other, a page later, at B758, he suggests that they are possible and that ‘in philosophy the definition, as distinctness made precise, must conclude rather than begin the work’.

^19. Although in the pre-critical 1772 Philippi Logik, Kant seems to think that body, unlike other empirical concepts, is general enough to be defined (24:457).

^20. There are two terms that get translated into English as ‘principle’: Grundsatz and Princip. Kant usually uses Grundsatz narrowly to speak of fundamental principles that can be formulated into judgements, and which can be laws of nature. Princip, however, often means something closer to Aristotle's arche or ‘starting points’, and can include faculties or concepts, as well as Grundsätze.

^21. The original ten: substance, quality, quantity, relation, action, affection, time, place, position, and state; as well as the post-predicaments: opposition, priority, simultaneity, motion, and possession.

^22. Time, place, position, priority, and simultaneity.

^23. It should be noted that Kant's notion of ‘action’ is not our modern notion of intentional action (e.g. fixing a water heater). This is especially clear when he talks of the actions of our cognitive faculties. What he means by ‘act’ is, rather, the more traditional philosophical, scholastic sense of the term, as in, ‘When one substance modifies another, the first acts on the second’. The ‘acts’ of the understanding will be modifications of our intellect – of the order possessed by the whole of our cognition.

^24. While Kant tends to use Analyse mainly to speak of the analysis of concepts, he will use Zergliederung to mean both the analysis of a faculty and of a concept. In this way, I think the situation is similar to that of Grundsatz and Princip (see footnote 20).

^25. After presenting his table of categories, Kant distinguishes them as ursprünglich stammbegriffe – original root (or stem) concepts – from derived (abgeleitete) pure concepts of the understanding, which he calls predicables. In this way, the categories are a class of pure concepts of the understanding – those that are elementary. In the first instance, however, Kant has the categories in mind when speaking of these pure concepts, and I will follow this usage here.

^26. Kant explains what he means by functions as ‘the unity of the act of ordering different representations under a communal [gemeinschaftlichen] one’ (KrV, A68/B93). We need not get bogged down in the intricacies of the relation between the unity of an act and an act.

^27. I will not dwell on the metaphysical deduction of the categories from the functions of thinking in judgement, although to really see how the original, precise, and exhaustive exhibition of the categories is working, this would have to be done. The issues here, however, are vast and many interpreters have dealt with these topics in greater detail than I could in this short essay. In what follows, I will only be briefly raising those points relevant to my case, and it goes without saying that even on these, much more could be, and has been, said.

^28. In other work I hope to develop a fuller account of these two aspects of the categories and their roles in making both cognitions and their objects possible.

^29. The predicate concepts of a disjunctive judgement stand in a conceptual community with one another under the subject concept (cf. KrV, A74/B99). Paradigmatic examples will be ‘Every triangle is either right, acute, or obtuse’, ‘Every cat is either a calico, or a non-calico’, or ‘Every animal is either a mammal, a reptile, a fish, … ’. In these cases, all of the predicates, when taken together, will exhaust the sphere of the divided subject concept and if, e.g. some triangle is right then it is not acute.

^30. Here and at B128, Kant is giving an explanation of the categories, which are concepts. Accordingly, these can seem like ‘higher order’ explanations, explanations about concepts rather than objects. I do not think Kant thinks about distinctions between ‘orders’ as we do, and he tends not to discuss concepts of concepts or judgements about concepts as such. Regardless, I do not think the general ‘explanation’ of the categories at B128 (or the one here) gives a strict (i.e. complete, precise, and original) definition of the categories, but only points the way towards them, by indicating how these concepts work. For, as we saw in the supposedly decisive passage, strict definitions must be adequate to their object (KrV, A728/B756), and in defining the categories what is at issue with their strict nominal or real definitions is the way in which an object is thinkable or cognizable through them. In this way, these definitions will indicate what is specific to each of them, and explanations of how they generally function will be inadequate.

^31. More examples are buried in his discussion of the real definitions of the categories on the preceding pages: leaving persistence out of substance we have ‘the logical representation of the subject, which I try to realize by representing to myself something that can occur solely as subject (without being a predicate of anything)’, in the pure category of cause we will only find ‘that it is something that allows an inference to the existence of something else’, and the pure concept of community will only contain the thought of ‘reciprocal causality in the relation of substances to each other’ (KrV, A242–243/B300–301).

^32. For the rest – substance, cause, community, possibility, existence, and modality – Kant does not sketch a real definition of the schematized versions in making his argument, although it seems clear that he thinks he could. Instead, he contents himself with making the case that (at least for substance and cause) without their schemata, not only would we lack all knowledge of the conditions under which the pure category can be attributed to any sort of thing but also that no consequences can be inferred from it, since we cannot know whether we can determine any object through it. At another place, in his elucidation of the postulates, he does claim that these postulates offer definitions or explanations (Erklärungen) of possibility, actuality, and necessity (KrV, A219/B266). Although I think these plausibly are proper real definitions, I do not take this passage to be decisive.

^33. For other examples, I think we would need to stray farther from the text in bringing together what I take to be Kant's logical definitions at A246 and the real specifications that came before at A242/B300. For this reason, I will leave considering what these might look like to the reader.