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  Among synthetic judgements, where the predicate is not contained in the subject, there are many whose truth can be determined only by examining the items to which the judgement refers. If we say, ‘the cat is large’, deciding whether the judgement is true involves examining the cat. Some synthetic judgements are thus known a posteriori, and perhaps the majority of them are known in this way. Hume’s view is that they are all known a posteriori, since his view entails that all synthetic judgements are matters of fact.

  This is exactly where Kant disagrees with Hume. Kant wonders whether there are any judgements that are informative – that is, synthetic – which are nonetheless necessarily true – that is, known a priori. He consequently poses this question: ‘Are there any synthetic a priori judgements?’ It is a crucial and philosophically groundbreaking question, and Kant’s answer is positive. If one can identify any judgements of this sort, they would establish a solid and outstanding ground for one’s philosophy. Informative judgements that are necessarily true would tell us much, either about ourselves or about the world.

  We will say more about synthetic a priori judgements – in particular mathematical and geometrical judgements – when we consider Kant’s theory of space and time. The examples of mathematical and geometrical judgements that Kant offers are controversial, however, and it is difficult to appreciate from them the strength and importance of synthetic a priori judgements. We will use an alternative and more straightforward example of a synthetic a priori judgement which Kant also mentions. It is ‘all events are caused’.

  Contrast these two judgements: (1) ‘all effects are caused’ and (2) ‘all events are caused’. The first is analytic and is true a priori, merely by virtue of the meanings of the words. By definition, to be an ‘effect is nothing other than to be caused’. The statement is necessarily true, but it is also trivially true. It is an analytic a priori judgement.

  Now the judgement, ‘all events are caused’ is another matter. This judgement is thought-provoking. To be an ‘event’ does not logically entail being ‘caused’, for although it is remote and virtually unimaginable, it is not contradictory to assert that something could happen spontaneously, ‘out of nowhere’. For Kantian reasons that we will later see, every human being has a difficult time imagining this. Nonetheless, admitting the mere possibility of an ‘uncaused event’ is not the same as proposing an idea like ‘round square’, ‘wooden iron’, or ‘reddish green’. The idea of ‘uncaused effect’ may be a contradiction, but that of an ‘uncaused event’ is not.

  This is to say that ‘all events are caused’ is a synthetic judgement where the predicate is not contained in the subject. We learn something new through it. In fact, the judgement makes a strong philosophical claim, asserting that determinism is true. Kant adds importantly that there is a sense in which ‘all events are caused’ is necessarily true: it is necessary, he maintains, relative to how we need to think about the world as rational human beings, as he will later argue.

  This is why in our example above, it is so difficult to imagine an uncaused event. The thought goes against our rational grain. So here, then, is a prime example of a synthetic a priori judgement. If there is a human being, then we know beforehand, without examining how the world is, that the person will think scientifically and will regard every event as having a cause.

  We can summarize Kant’s theory of judgement in the following chart:

  A priori

  A posteriori

  Analytic

  ‘All effects are caused’

  –

  ‘The cat is an animal’

  ‘Bachelors are unmarried’

  Synthetic

  ‘All events are caused’

  ‘This effect is loud

  ‘5 + 7 = 12’

  ‘This event is profound’

  ‘The cat is brown’

  Key idea: Synthetic a priori judgements

  Located at the centre of Kant’s theory of knowledge, these judgements are both informative and necessarily true. Examples would be ‘all events are caused’ (as opposed to ‘all effects are caused’) along with judgements in mathematics and geometry which are not simply matters of definition. In the Critique of Pure Reason, one of Kant’s most important questions is ‘How are synthetic a priori judgements possible?’

  3 Intuitions and concepts

  Now that we have described Kant’s theory of judgement with its various kinds of S is P type judgements, we can look at judgements from a new angle. This is from the standpoint of what happens in our minds when we make a judgement of the form S is P.

  At one level, Kant’s conception of this mental activity is straightforward. First, working with the S is P format, he begins by considering our ideas of the S’s. The S’s are individuals, and Kant refers to our awareness of individuals as ‘intuitions’. The German word translated here into English as ‘intuition’ is Anschauung, which is worth dwelling upon for a moment.

  In German, the verb schauen means ‘to look’, and the prefix an means ‘at’. The verb anschauen means ‘to look at’. So the term Anschauung means ‘a-looking-at’ or a ‘view’. An associated term Weltanschauung means ‘world-view’ or world-outlook’. This all conveys the idea that typically, an ‘intuition’ refers to our direct perception of an ordinary individual thing, such as a table, chair, cup, window, car, or tree.

  Second, Kant considers our ideas of the P’s. These are predicates or general properties that we ascribe to individuals. Kant refers to them as ‘concepts’, which is the translation of the German word Begriff. This is also an informative word to examine. It is related to the verb greifen, which means ‘to hold’ or ‘to grasp’. The underlying thought is that a concept ‘holds things together’ and allows us to ‘comprehend’ a set of things in one grasp. We see this in the word ‘comprehend’ which literally means ‘hold together’. Another related word – an important one for Kant, as we shall see – is ‘synthesis’ which also means to hold together. So when we think of our ideas of the Ps, we have predicates, concepts, comprehension, synthesis, and grasping, all tied together linguistically in the idea of a concept.

  At the level of actual thinking processes when we ‘know’ something, the format S is P indicates a mental fusion of intuitions (the S’s) with concepts (the P’s). Just as the form of judgement S is P involves a unity of two different kinds of grammatical or logical elements, neither of which constitutes a judgement when taken individually, Kant maintains that intuitions and concepts are also two different kinds of elements in our awareness, neither of which alone provides knowledge. For there to be crisp, determinate knowledge of the world around us, an individual must be presented to our consciousness, and then a concept must be applied to that individual, or intuition, so that we can identify the kind of thing we are perceiving.

  When Kant considers how the mind must work in order to apply concepts to given individuals for the sake of obtaining knowledge of the world, he creates a psychological model that mirrors the S is P format. Using the logical format as his guide, and having associated intuitions with the S’s and concepts with the P’s, he hypothesizes that there is a section of the mind – a ‘faculty’ – that apprehends the individuals and ‘presents’ them to consciousness, and another section of the mind that contains our concepts, and which harmonizes with the individual-presenting section, thus allowing us to apply a concept to the given individual.

  In other words, Kant supposes that there is a compartment of the mind that contains the S’s and another, complementary compartment of the mind that contains the P’s. Just as S and P are combined in a judgement, the two mental faculties operate together: the faculty that presents and contains the S’s combines with the faculty that contains and applies the P’s to the S’s. From the elementary structure of judgement, Kant thus derives a theory of how the mind works when it knows things. He first refers to intuitions and concepts that correspond the S’s and the P’s and which combine in our minds when we make a judgement, and
then he refers to two sections of the mind that contain respectively, the intuitions and the concepts, and which themselves interact harmoniously to allow intuitions and concepts to be brought together.

  Kant refers to the faculty that presents individuals to consciousness as ‘sensibility’ and the faculty that applies concepts to the presented individuals as ‘understanding’. Parallel to and structurally matching the S is P interrelationship at the ‘theory of knowledge’ level, we have the interaction between the two cognitive faculties of sensibility and knowledge, which are both equally valued and interdependent. Kant describes this situation in the following excerpt from the Critique of Pure Reason:

  Neither of these qualities or faculties is preferable to the other. Without sensibility, objects would not be given to us, and without understanding, they would not be thought by us. Thoughts without content are empty, intuitions without concepts are blind. Therefore it is equally necessary to make our concepts sensuous, i.e., to add to them their object in intuition, as to make our intuitions intelligible, that is, bring them under concepts. These two powers or faculties cannot exchange their functions. The understanding can intuit nothing, the senses can think nothing.

  (A51/B75)

  We can now describe the more detailed structures of the faculty of sensibility and the faculty of understanding. The faculty of sensibility will be structured according to the forms of space and time. The faculty of understanding will be structured according to a set of basic logical forms. After describing the respective structures of these two faculties, we will work through Kant’s explanation of how the understanding’s logical structure combines with the sensibility’s spatio-temporal structure. This is a challenging task for Kant, since he comes to realize that aside from their similarities, the understanding and the sensibility have some strong differences to overcome, if they are to be brought into harmony.

  Following Kant’s sequence of exposition in the Critique of Pure Reason, and also following the path of an object that is given to us in experience, to which we subsequently apply a concept to say what kind of thing it is, we will first consider the structure of sensibility, and second, the structure of the understanding. This brings us to the subject of our next chapter: Kant’s theories of space and time, which he describes as “forms” of sensibility that we can know a priori.

  Dig Deeper

  Henry Allison, Custom and Reason in Hume: A Kantian Reading of the First Book of the Treatise (Oxford University Press, 2008)

  Tom Beauchamp and Alexander Rosenberg, Hume and the Problem of Causation (Oxford University Press, 1981)

  Paul Guyer, Knowledge, Reason and Taste: Kant’s Response to Hume (Princeton University Press, 2008)

  Wayne M. Martin, Theories of Judgement: Psychology, Logic, Phenomenology (Cambridge University Press, 2006)

  Eric Watkins, Kant and the Metaphysics of Causality (Cambridge University Press, 2005)

  Study questions

  1 How would you define ‘empiricism’? In a sentence, how would you state the empiricist theory of linguistic meaning?

  2 Using the empiricist theory of linguistic meaning, how would you explain the meaning of the words ‘sphinx’ and ‘God’?

  3 Using the empiricist theory of linguistic meaning, how would you explain the meaning of the word ‘causality’? Why might this present a problem for the foundations of scientific thinking?

  4 What did Kant think of the empiricist conception of causality?

  5 Briefly characterize Hume’s distinction between ‘relations of ideas’ and ‘matters of fact’. How well does this fit with Kant’s distinctions between ‘analytic’ and ‘synthetic’ judgements?

  6 How does Kant use the S is P format to distinguish between (1) analytic and synthetic judgements, (2) intuitions and concepts, and (3) sensibility and understanding?

  7 What are the two main characteristics of a priori knowledge?

  8 Why are synthetic a priori judgements philosophically valuable? Why is ‘all events are caused’ a synthetic a priori judgement?

  9 What is the difference between an ‘intuition’ and a ‘concept’?

  10 What two faculties must be in harmony when we make a judgement that combines an intuition and a concept?

  4

  Space and time: the structure of the faculty of sensibility

  Among the most influential arguments in Kant’s philosophy are those which conclude that space and time are, as far as we can know, nothing more than features of the human mind which organize sensory inputs. This chapter will consider these arguments, and explain how they answer the crucial Kantian question, ‘How are synthetic a priori judgements possible?’ We will also describe some developments in the study of geometry after Kant’s death which, for some, cast contemporary doubt upon Kant’s position.

  1 Newton and Leibniz on space and time

  Space is like ourselves: although we live with ourselves constantly and with great familiarity, when we ask who or what we essentially are, the question usually leaves us dumbfounded. How a condition so close to us can be so inexplicable, is the puzzle surrounding space as well. To unveil space’s deepest truth, one might imagine travelling to the far corners of the universe, but no matter how far one travels, resolving that mystery is no different from fathoming the distance between one’s eyes and the words on this page.

  Writing over 1500 years ago in his Confessions, St. Augustine felt the same way about time: ‘What then is time? If no one asks me, I know: if I wish to explain it to one that asks, I know not…’ (Book XI). For some thinkers and for most people, space and time are as real as can be; for others, they are illusions on a cosmic scale. For Kant, space and time reside between these extremes.

  To appreciate Kant’s comprehension of space and time, it helps to understand the accounts against which he was reacting, namely, those of Isaac Newton (1642–1727) and Newton’s contemporary, Gottfried Wilhelm Leibniz (1646–1716). Although expressing diametrically opposed views on the nature of space and time, it is a historical curiosity that during the late 1600s, Newton and Leibniz discovered calculus as a mathematical method within years of each other.

  Newton regarded space and time as realities independent of the human mind: there is an absolute, immovable and inflexible space within which all locations are originally plotted, and an absolute, uniformly moving time within which all movements take place. Both space and time are empty containers, existing prior to all material content, so he believed.

  Although Kant realized its usefulness for scientific studies – a usefulness he hoped to preserve within his own view – he saw Newton’s theory of absolute space and time as threatening to morality and human freedom. If space and time are absolute, then mathematical, geometrical and causal relationships would apply within the universe absolutely. Our world would be a single, predictable, mechanical world, devoid of freedom.

  Moreover, if space and time are absolute, and if one believes in God, then space and time would have to be among God’s features. The spatio-temporal world, with all of the imperfection and pain it contains, would then be either wholly or partially equated with God himself – a pantheistic proposition which at the time, was sounding more like atheism than theism. Kant rejected this equation in favour of a more traditional conception, where God is set beyond and independent of time and space. He consequently sought a way to conceive of time and space that would preserve their scientific effectiveness, but which would keep space and time separated from the absolute order of things. His way to do this, as we shall see, was to conceive of them as being merely modes of human awareness.

  Contrasting with Newton’s more natural conception of space and time, Leibniz’s account makes sense only in reference to his extraordinary metaphysical outlook, inspired by his work in mathematics. According to Leibniz, the universe is composed of a set of simple substances, where each substance is an independent soul with a set of God-given perceptions. The souls are not located in space or time. Time and space are only the orderings
of the respective perceptions within each of these spiritual points.

  Neither do the simple souls interact with each other. Each is an isolated, self-enclosed, ‘windowless’ whole. Each soul’s set of perceptions is nonetheless synchronized with all of the others, like an arrangement of movie theatres along a street, all of which play a similar movie, and where each movie contains a segment that represents what is happening simultaneously in the other movies. God, as the supreme soul and centrally controlling movie projectionist, one could say, coordinates this set of souls in a pre-established harmony. Another name for simple soul is ‘monad’, which Leibniz uses to characterize these substances, or fundamental spiritual points that constitute the universe.

  To imagine Leibniz’s view of space (and by analogy, of time), consider two blindfolded people playing chess against each other using only verbal communication, each of whom has in mind an image of the chessboard upon which they are playing. No ‘real’ chessboard exists in an objective, external space independently of their imaginations, but there is a meaningful coordination between the two chessboard pictures that each imaginatively constructs.

  Since each simple soul has a set of perceptions, or ‘objects’ as its contents, space and time become nothing more than sets of relationships between these perceptions or objects. On Leibniz’s view, the souls and their objects come first, and space and time appear as secondary structures derived in reference to the perceptual contents of the simple souls. Within this outlook, space and time are merely relationships, or orderings, between perceived objects, so without supposing some objects with which to start (i.e., without some initial, God-given perceptual contents of the simple souls), there would be no space or time.