by Robert Wicks
Dig Deeper
Henry Allison, Kant’s Transcendental Idealism: An Interpretation and Defense, Part Two, Section 5 (Yale University Press, 1983)
Lorne Falkenstein, Kant’s Intuitionism: A Commentary on the Transcendental Aesthetic (University of Toronto Press, 1995)
Paul Guyer, Kant and the Claims of Knowledge, Chapter 16 (Cambridge University Press, 1987)
Arthur Melnick, Space, Time and Thought in Kant (Kluwer Academic Publishers, 1989)
Lawrence Sklar, Space, Time and Spacetime (University of California Press, 1977)
Study questions
1 Briefly characterize Newton’s conception of space and time, and explain why Kant found it objectionable.
2 Why is Kant’s characterization of space in an intermediary position between Newton’s and Leibniz’s characterizations?
3 Why does Kant believe that space and time are not concepts?
4 Why does Kant believe that space and time are not derived from sensory experience?
5 How does Kant argue that space and time are knowable a priori?
6 What does Kant mean when he says that all things intuited in space and time are only appearances? Of what are they appearances?
7 Why does Kant claim that if we depart from the human standpoint, then space and time represent nothing at all?
8 How does Kant use the structures of space and time to explain how synthetic a priori judgements in geometry and mathematics are possible?
9 Do you think that it is possible to think of space or time without any contents at all?
10 Why does Non-Euclidean geometry pose a challenge to Kant’s theory of space? How might Kant answer the charge that his theory of space is mistaken, because it is based on a Euclidean conception of space?
5
Aristotelian logic: the structure of the faculty of understanding
Kant’s views on space and time were philosophically revolutionary, but his insight reaches an even deeper level by using Aristotelian logic to explain how we further construct our world of daily experience. In this chapter we will see how Kant begins with twelve elementary logical forms of judgement, and how he extracts from them twelve pure concepts which serve to organize our given sensations. These are the ‘categories’ or pure concepts of the understanding. One of these categories is the concept of ‘causality’, which will help Kant explain in reply to David Hume’s scepticism, why we can indeed rely upon our scientific theories to predict the future.
1 Aristotelian logic
One of the leading ideas in the history of Western philosophy is that human beings are rational animals. They are, of course, also laughing animals and political animals, featherless, walking on two legs. Such features notwithstanding, along with self-consciousness, rationality has been the famously human essential characteristic in Western philosophical theorizing.
Kant inherits this tradition, but by the time he is writing in the late 1700s, philosophers regarded the idea of rationality as best expressed by the discipline of formal logic – a discipline that Aristotle first formulated which, like algebra, uses letters and symbols to refer to and to designate abstract connections between concepts, individuals, relations and the propositions that contain them as elements. We are already familiar with this style of thinking from the elementary formula S is P, which represents a judgement such as ‘the sky is blue’, or in this case more directly, the thought of a ‘blue sky’. We are all born as rational animals, and as such, the elementary forms of logical judgement – that is, Aristotelian logic itself – are present within us as a matter of human nature.
When Kant develops his theory of knowledge, he makes extensive use of the idea that our human nature is logical. Utilizing a kind of ‘faculty-based’ psychological model, to recall, he distinguishes two sectors of the mind that participate jointly in the formation of knowledge. The first is the faculty that receives sensations and organizes those sensations according to spatial and temporal forms, the faculty of ‘sensibility’, which we discussed in the previous chapter. The second is the faculty of ‘understanding’, which applies concepts to those sets of organized sensations, so we can apprehend the sets of sensations as things of a particular kind, which we will now consider.
The faculty of sensibility supplies the intuitions, or individuals, and the faculty of understanding supplies the concepts, which give meaning to the individuals which the faculty of sensibility has initially configured in space and time. Neither faculty stands alone: ‘concepts without content are empty, intuitions without concepts are blind’ (A51/B75), as Kant says. When these two faculties operate together harmoniously, elements from each faculty are effectively situated to combine with each other into judgements of the form, ‘this individual is of some particular quality’, following the elementary logical format, S is P. Through such an act of judgement, our consciousness registers the apprehension of, say, a ‘blue sky’.
Before any sensations are given, both faculties are assumed to have their own structures fully intact, knowable a priori, comparable to the structure of a car’s motor, before it is started. The structure of sensibility is constituted by the forms of space and time, which we can imagine as two endless and intersecting expanses of infinitesimal points, like empty containers, waiting for some sensory content to fill them. Kant refers to these formal infinite expanses as ‘manifolds’ of spatial and temporal intuition. They are merely sets of contentless points to be filled with sensations, soon to be given meaning through the application of concepts. In the last chapter, we saw how Kant specifies the structure of the faculty of sensibility in the section of the Critique of Pure Reason entitled the ‘transcendental aesthetic’. He specifies the structure of the understanding, or faculty of concepts, in his discussion of ‘transcendental logic’.
In principle, Kant finds the structure of the understanding easy to describe. Recognizing that we are essentially rational animals, and that our rationality is expressed most generally and precisely in the discipline of formal logic, he adheres closely to the steadfast structure of Aristotelian logic, highly respected and unchanged substantially for two thousand years. Kant consequently utilizes the twelve elementary forms of judgement, stated in the logic books of his time, and bases his theorizing on this specific set of judgements. In the Critique of Pure Reason, he presents the following ‘table of judgements’, constituted by twelve basic logical structures which he believes all human beings, insofar as they are ‘rational animals’, use to think rationally:
Logical forms
Examples
A Judgements of quantity
1 Universal
All roses are red
2 Particular
Some roses are red
3 Singular
This rose is red
B Judgements of quality
1 Affirmative
This rose is red
2 Negative
This rose is not red
3 Infinite
This rose is non-red
C Judgements of relation
1 Categorical
This rose is red
2 Hypothetical
If this is a rose, then it is red
3 Disjunctive
Either this is red, or this is not red
D Judgements of modality
1 Problematic
This rose may be red
2 Assertoric
This rose is red
3 Apodeictic
This rose must be red
Kant attends mainly to the different logical aspects of our thinking as listed in the left-hand column above. Taking a look at the table, we can note that the same judgement, This rose is red, has four logical aspects, like different coloured lights that one can shine upon the judgement. The judgement is at once singular, affirmative, categorical and assertoric. These logical aspects – twelve of them in all, organized into four groups of three – occupy the centre of Kant’s attention when he theorizes. He uses them as a template throughout his philosoph
y as a way to lend a systematic form to his discussions.
Key idea: Table of judgements
This is a listing of twelve elementary logical forms of judgement, taken from the logic books of his day, through which Kant identifies the basic formats in which we think rationally.
Kant’s project in this particular section of the Critique of Pure Reason is to employ the above table of logical judgements as a guide to describing the fixed, universal structure of the faculty of human understanding. As we know, the understanding is a faculty of concepts that applies concepts to objects, individuals or ‘intuitions’ given to consciousness through the faculty of sensibility. The fixed structure of the understanding therefore contains a set of basic concepts that are always applied to given intuitions, informing them with a rudimentary organization, somewhat in the way a hot waffle iron informs the soupy batter into a hard, gridlike shape before one adds any syrup, butter, whipped cream or fruit.
Kant isolates the faculty of understanding and describes it in the abstract, independently of any sensory contents that might be given by the faculty of sensibility. Since he is characterizing the understanding as it is by itself, independently of sensory experience, the fundamental concepts that he identifies as constituting the understanding are empty, devoid of sensory content. Kant refers to them as formal or ‘pure’ concepts, just as the forms of space and time are originally empty. All in all, they are sets of formats for sensations.
Kant’s discussion of the fundamental concepts of the understanding proceeds initially with an account of how these concepts apply to the empty forms of space and time – the containers that receive the sensory impressions to begin with. With that established, the way is marked for the application of the pure concepts to specifically sensory-filled configurations in space and time, such as a lamp, window, wall or doorway.
To see how Kant informatively uses the table of judgements, it is important to understand how he defines the idea of a ‘concept’. For him, a concept is an expression of unity among a set of representations. The many points of light in a clear night sky, for example, can be comprehended together under the concept of a ‘star’. The concept ‘star’ allows us to apprehend all of the points of light as being of the same kind. In contrast, although they might also see the individual points of light, a dog or cat looking up at the same sky will not comprehend all of the points of light in this way, since neither animal has the concept of ‘star’.
Kant refers technically to a concept as the ‘common representation’ under which a unity of various representations is brought. By ‘representation’, he means either an intuition or a concept, so the common representation ‘star’ would bring together under itself the set of individual points of light, or intuitions, of the various individual stars.
The key thought is that a concept is an expression of unity amongst a set of representations. A set of pure concepts inherent to the faculty of understanding would thus be a set of unifying functions that organize whatever is given to the understanding by the faculty of sensibility. At the most basic level, the concepts of the understanding prescribe the most basic kinds of unity to space and time in the abstract, considered as sets of empty points, or ‘manifolds’. In such an abstracted situation, we would be talking about how the concepts of the understanding organize the structure of space and time with respect to any given object at all, or with respect to an ‘object in general’. Kant is interested here, not in the conditions for apprehending this or that kind of an object, but the conditions for apprehending any object. He is interested in the ‘conditions for the possibility of human experience’, as he describes it.
Another word that Kant uses to express the idea of a unifying function is ‘synthesis’, since this conveys the idea of taking up a set of individuals and connecting them together into a unity. He also uses the word ‘combination’ to express the same idea. Kant’s German word for this is Verbindung, which signifies ‘binding together’, as in a community, society, union or association. He consequently describes the pure concepts of the understanding as various modes of synthesis or combination. In sum, the pure concepts of the understanding are various modes of synthesis of the manifolds of intuition provided by the forms of space and time.
This is a technical way to express Kant’s idea, but the underlying thought is as follows. Considering the human mind – not in connection with any specific sensory experience, but only in relation to the formal structures it has prior to any sensory experience – to be like a computer fresh from the factory, or a car immediately rolling off the assembly line, we have two faculties, the faculty of sensibility and the faculty of intuition, each with its respective formal structure. The structure of sensibility gives us two empty containers, space and time, constituted merely by sets of points that constitute an endless expanse. These forms are empty, like cups without any liquid in them, or sheets of paper with no writing. They are nonetheless constituted by a ‘manifold’, which is a set of points that waits to be filled with sensory content and further organized.
Conjoining with space and time, we have the understanding – a complementary faculty of pure concepts that works with sensibility to organize the more specifically configured manifold of space and time, once it receives some sensory information. As a faculty of ‘concepts’, the understanding projects twelve different ways in which objects in general, given in space and time, are organized both with respect to their individual constitution and with respect to their interrelationships with other objects.
Note how we are still not yet referring to any specific sensory objects such as the silver lamp, or ballpoint pen, or leafy tree, but are still speaking in the abstract, of any objects whatsoever that could be given as possible configurations in space and time, prior to their being actually given. We are thinking about the structures that must operate within any possible human experience, quite universally. The investigation is about how the mind operates at the most fundamental level, as if we were talking about how the various parts of a car’s motor are related to each other, prior to turning on the motor.
To some people, this style inquiry could sound premature, or backwards, or impractical, or unrealistic. It might even sound too cautious and fearful, as if to avoid drowning, Kant is trying to learn first, how to swim ‘in theory’ before touching the water. These kinds of criticisms have sometimes been levelled at Kant’s method.
If, however, we consider the work of engineers, it stands that if the exact engineering specifications of a car’s parts are indeed known, one can calculate how fast it will drive before it is even built. This is the kind of inquiry, by analogy, in which Kant is engaging. Like an engineer who is building a spacecraft, and who can calculate before the spacecraft is launched, how it will be able to perform, Kant, thinking like a scientist, is trying to specify how the mind works in general before it knows anything specific. He is aiming to specify for any given human, including the humans that have not yet been born, exactly how powerful the human mind is.
In the Critique of Pure Reason, Kant is keen to establish once and for all, how powerful human reason actually is, because some philosophers have maintained optimistically that we can know fully about the ultimate realities of the universe, such as whether God exists, while others have maintained sceptically that we cannot even be sure whether or not the sun will rise tomorrow or that the water will boil again when we heat it.
2 The pure concepts of the understanding
How, then, does Kant use the table of logical judgements to characterize the fundamental activity of the understanding and to answer this difficult question about the human mind’s power? How does he use this table to extract a corresponding list of pure concepts that the understanding uses to organize the spatio-temporal manifold for the sake of experiencing any object at all? The answer is that Kant ‘reads off’ of each kind of logical judgement a pure concept that matches the meaning of the judgement. Some of the correspondences are easy to see. Some are less obvious.
Let us consider one of the clear cases to illustrate what Kant has in mind. On the table of judgements, among the judgements of ‘relation’, there is the logical form of the ‘hypothetical judgement, sometimes called a ‘conditional’ judgement. The format is if A, then B, as in ‘if the water’s temperature is 100ºC, then the water will boil’ or as in ‘if one smokes too many cigarettes, then one will damage one’s lungs’. Through these examples it is easy to see that the elementary form of logical judgement, if A, then B, when applied to the world’s factual details, expresses the concept of ‘causality’. Since we are rational beings and think inherently in terms of the format if A, then B, we also thereby think in terms of the concept of causality, rather inevitably.
In his extraction of pure concepts such as ‘causality’ from the table of judgements, it should be more evident now, how Kant uses the discipline of formal logic to develop a theory of the structure and limits of human experience. These pure concepts, or ‘categories’, of the understanding, amount to the various ways in which the human mind organizes, or binds together, the spatio-temporal manifold. Kant asserts that there are no other ways, and that these are the necessary ways, since we are logical beings who have no choice but to think according to basic logical forms, just as a cat has no choice but to think like a cat, or a dog, like a dog.
Here is the list of pure concepts or ‘categories’ of the understanding that Kant sets out. It follows the table of judgements exactly.
General logic:
Transcendental logic:
