Kant Page 6

  On this particular point, Kant disagrees. He maintains that the objects in space and time cannot exist independently of space and time. To him, the reverse is true: first, we have in our minds the empty containers of space and time, and then, our sensory experience fills space and time with objects that it gives to us.

  Leibniz argues furthermore, though, that since God does not need space and time to perceive things, space and time cannot be absolute beings. He also notes that God would have no reason to construct a world in either a predominantly left-handed or predominantly right-handed way, so left-handedness and right-handedness must also be illusory. His views on space and time are unconventional, but Leibniz does have some challenging arguments to support it.

  Kant’s view is that since we cannot know whether or not God exists to begin with, it is difficult to say whether there are any perceptions that are independent of space and time in the universe. He also observes that we cannot translate a left-hand glove into a right-hand glove – these are incongruent counterparts – so any conception of space needs to recognize the reality of left-handedness and right-handedness, and hence, must recognize a more ‘objective’ conception of space and time than that Leibniz proposed.

  2 Kant: space and time as a priori intuitions

  Kant offers a series of arguments which establish an intermediary position between Newton and Leibniz. Unlike Newton’s conception of absolute space, Kant maintains that as far as we can know, space and time are only functions of the human mind that give order to our perceptions. Unlike Leibniz, Kant recognizes that space and time must be prior to the objects that are contained in them, thus lending space and time a reality that is independent of their material contents.

  Kant initially points out that space and time are not concepts, but are individualistic entities. He observes that when we refer to space and time, we think of them as ‘wholes’ that have ‘parts’. The many parts of space constitute the entirety of space, and the many parts, or moments, of time constitute the infinity of time.

  This whole/part relationship is of a different order from the relationships that hold between a concept and its instances. Consider the concept of ‘blue’ or ‘blueness’. There are many blue things in the world, but we do not conceive of each instance of blueness literally as a part of some endless, cosmic sheet of blue, as if this sheet had been cut into parts with a scissor and pasted onto objects to make them look blue. Neither do we conceive of blue as a large pot of paint in a world beyond which it diminishes in volume as the number of blue objects in the world increases.

  The relationship between a concept and its instances is different in kind from the relationship between a whole and its parts. Note how the concept of blue would stay the same, even if all of the blue items in the world disappeared. This is not true about the parts of space or time. Were all of the parts of space or time to disappear, so would space and time themselves. Kant consequently denies that space and time are concepts, and refers to them instead as ‘intuitions’, that is, as individuals.

  Key idea: Space and time are intuitions, not concepts

  Kant maintains that space and time are wholes composed of parts. As such, they are individuals, associated with the faculty of sensibility, rather than being generalized abstractions which issue from the faculty of understanding.

  The intuitions of space and time, Kant claims furthermore, are only formal structures, and are knowable a priori. To understand this, we need to recall his theory of knowledge. We have seen how the most elementary form of our knowledge can be expressed abstractly as the judgement S is P, where S is an individual and P is a concept. Since individuals are different in kind from concepts, to account for the possibility of such judgements, Kant postulates two distinct areas or ‘faculties’ within the mind that interact, as described in the previous chapter. One faculty, ‘sensibility’, contains the intuitions, and another faculty, ‘understanding’, contains the concepts. For there to be any knowledge of the form S is P, these two faculties must interact harmoniously, so that sensibility can supply the S’s and understanding can supply the P’s to form judgements. When we discuss Kant’s aesthetic theory, we will revisit this idea of two faculties working together in harmony to produce judgements.

  As mentioned, Kant does not believe with the British empiricists that the mind is totally blank at first. His view is that a human being has the faculties of sensibility and understanding from the start, and that each faculty has its own particular structure, knowable a priori. The structure is there in the mind before any experience occurs, present initially to give order to the incoming sensations. Now with regard to the faculty of sensibility, Kant reasons as follows:

  It is clear that it cannot be sensation again through which sensations are arranged and placed in certain forms. Therefore, although the matter of all phenomena is given us a posteriori, their form must be ready for them a priori in the mind, and must therefore be capable of being considered apart from all sensations.

  (A20/B34)

  Space and time are not abstracted from sensory experience in the manner of empirical concepts, but must be presupposed as a condition for having any experience at all. Otherwise, given sensations would have no place or time to be. That there is such a spatio-temporal order, and indeed a necessary one, is clear to Kant: sensations are ordered in sequences, one after the other in time, and one next to the other in space, following the laws of mathematics and geometry.

  Kant elaborates his view in a series of arguments, of which two exemplary ones are as follows:

  Space is a necessary a priori representation, forming the very foundation of all outer intuitions. It is impossible to imagine that there should be no space, though we might very well imagine that there should be space without any objects to fill it. Space is therefore regarded as a condition of the possibility of appearances, not as a determination dependent upon them. It is an a priori representation which necessarily precedes all outer appearances.

  (A24/B39)

  Time is a necessary representation which underlies all intuitions. We cannot take away time from appearances in general, though we can well take away all appearances from time. Time therefore is given a priori. In time alone is all reality of appearances possible. These appearances may all vanish, but time itself (as the universal condition of their possibility) cannot be eliminated.

  (A31/B46)

  These two complementary arguments allow us to appreciate the Kantian philosophical method of separating layers of any given phenomenon to reveal its underlying structures. Here, he observes that given some object, we can imaginatively separate the space and the time in which the object is situated for independent consideration. Once we perform this abstraction, we can see that without the spatio-temporal form, there can be no object to perceive. The object depends upon the spatio-temporal form, but the spatio-temporal form does not depend upon the object. This is the crux of the argument. The spatio-temporal form is therefore independent and prior to the objects within it.

  For Kant, we can think of time in general without specifying any particular events, and we can think of space in general without specifying any objects contained in it. Empty space and empty time are conceivable, and moreover, are such that we must conceive of them as the very conditions under which we can have any experience at all. With such reflections, Kant maintains that space and time are within us before we experience any objects.

  Insofar as space must be presupposed as the condition for any outer experience, and insofar as time must be presupposed as the condition for any experience, Kant refers to them as knowable a priori. They are forms of the mind prior to sensory experience that each human has identically, and that order our sensations into a common and objective form. He refers to space and time in technical terms as a priori forms of sensibility.

  Kant draws amazing conclusions from this examination of space and time, which bear long reflection:

  …everything which is perceived in space and time, therefore all objec
ts of an experience possible to us, are nothing but appearances, that is, mere representations which, such as they are represented, namely, as extended beings, or series of changes, have no independent existence outside our thoughts.

  (A490-491/B518-519)

  …space and time [are] determinations and relations which are inherent in the form of intuition only, and therefore in the subjective nature of our mind, apart from which they could never be ascribed to anything at all.

  (A23/B37-38)

  It is therefore only from the human standpoint that we can speak of space, extended objects, etc. If we depart from the subjective condition under which alone we can have outer intuition, that is, so far as we ourselves may be affected by objects, the representation of space means nothing whatsoever.

  (A26/B42)

  Time is therefore simply a subjective condition of our (human) intuition…and in itself, apart from the subject, is nothing.

  (A35/B51-52)

  We deny that time has any claim on absolute reality, so that, without taking into account the form of our sensuous condition, it should by itself be a condition or quality inherent in things …

  (A35-36/B52)

  …the things we perceive are not in themselves what we perceive them as being, nor are their relations in themselves such as they appear to us, so that, if we remove the subject or the subjective form of our senses, all qualities, all relations of objects in space and time, indeed space and time themselves, would disappear.

  (A42/B59)

  3 How are (some) synthetic a priori judgements possible?

  We described earlier how Kant’s theory of judgement augments Hume’s elementary distinction between ‘relations of ideas’ and ‘matter of fact’ with the additional distinction between knowing a judgement to be true a priori, versus knowing it to be true a posteriori. The result is to generate a new kind of judgement, previously unheard of, that informatively adds some new content to the subject – i.e., the judgement is synthetic – but is knowable to be true independently of experiencing the objects to which that judgement refers. From the standpoint of philosophical theorizing these judgements are desirable, for they are informative and yet necessarily true.

  We previously used as an example of a synthetic a priori judgement, ‘all events are caused’. This contrasts with ‘all effects are caused’, which is true as a matter of definition, where the judgement’s truth can be determined merely by analysing the relationships between the meanings of the terms. We also noted how Kant listed some other judgements as synthetic a priori, namely, those in geometry and mathematics. We are now able to provide Kant’s answer to the grand question of how synthetic a priori judgements in geometry and mathematics are possible.

  It is obvious to Kant that geometry is the science of spatial relationships, and that as its body of knowledge it has a set of necessarily true propositions. These include the statement that on a flat surface, the sum of the interior angles of a triangle equals 180º. Also included is the statement that on a flat surface, parallel lines never meet.

  These statements do not seem to be mere matters of definition, as if one could change the relationships arbitrarily and decide that on a flat surface, parallel lines will eventually meet! Kant’s challenge is to explain how such statements can be necessarily true, if they are not arbitrary matters of definition.

  His answer, as we can now imagine, is that the synthetic a priori quality of space itself is being expressed and presented in the synthetic a priori quality of the statements that describe space’s geometrical relationships. The synthetic a priori propositions of geometry are possible, because space itself is knowable a priori as a feature of the human mind – one that informs our sensations with an ‘outer’ empirical reality. Geometry expresses the very nature of space. Kant states accordingly that ‘our explanation is thus the only explanation that makes intelligible the possibility of geometry, as a body of a priori synthetic knowledge’ (A25/B41).

  In a similar way, he explains the synthetic a priori quality of mathematical propositions such as 2988 + 8749 = 11,737. (His own example is the more elementary 7 + 5 = 12.) Here, one cannot arrive at the sum 11,737 by examining the meanings of ‘2988’, ‘plus’, and ‘8749’, as we are able to do, for example, in deciding that the statement ‘this bachelor is unmarried’ is true. In the latter case, we only need to examine the meaning of the word ‘bachelor’. In contrast, Kant says in relation to 7 + 5 = 12, ‘we may analyse our concept of such a possible sum as long as we will, still we shall never discover in it the concept of twelve’ (B16). Mathematics, he concludes, is composed of informative synthetic judgements, rather than uninformative analytic ones.

  Kant also maintains that mathematics is grounded originally upon the basic number sequence ‘1, 2, 3, 4,…’. Realizing that the passing of time implicitly contains such an enumeration (and we can add that as a continuous ‘flow’, the structure of time implicitly contains the continuum of numbers as well), Kant maintains that time expresses itself in the structure of the number line. Arguing in parallel, since time is knowable as an a priori feature of the human mind that gives order to our sensations, mathematics is also knowable a priori. Since both space and time prescribe orderings to our sensations before we have any sensations, they have a synthetic quality, telling us a priori how our experience must be structured.

  Key idea: Why mathematics and geometry work in the daily world

  Since space and time organize sensory information that is given to us, and since geometry and mathematics articulate the very structures of space and time, our experience must always have a geometrical and mathematical form.

  4 Some objections to Kant’s theory of space and time

  Kant’s theory of space and time is innovative, if not revolutionary. It is also controversial. Perhaps the most fundamental objection issues from the abstractive, scientific style of thought he uses to identify the nature of space. Kant asks us, in effect, to consider any ordinary object, imagine that it is not there, and to continue this process of dissolution until all of the objects in the physical world are imaginatively set aside, leaving us to think exclusively about the pure, empty space in which the objects had been situated, as devoid of all content, and as a form on its own. Kant believes that it makes sense to think of space in this fully detached and evacuated way, while admitting that we can never experience space as such. It remains unclear, though, whether we can actually construct a conception of such a space.

  Another objection stems from the overall state of knowledge when Kant was living. For Kant and his generation, ‘logic’ meant Aristotelian logic and ‘geometry’ meant Euclidean geometry. This led him to assert accordingly that ‘space has only three dimensions’ (B41), never imagining that there could be higher dimensions of space, or spaces that are described by alternative geometries. One can consequently ask whether human experience needs to be organized according to the rules of Euclidean geometry as Kant could only believe.

  One reply to this objection is to define a more generally Kantian position acknowledging space as a form of the human mind, but adding that this form is completely general, inclusive of all higher dimensional and non-Euclidean spaces. Some people claim to experience a kind of enhanced consciousness in the apprehension of higher dimensional spaces, but if one follows this Kantian line of thought, the implication would be that when people claim to experience higher, non-Euclidean dimensions of space and perhaps even a kind of enlightenment thereby, that they would be equally as far from the absolute truth as before, since space in general, of whatever dimension, yields knowledge that remains human, all-too-human.

  Spotlight: Non-Euclidean geometry

  During the 1800s, non-Euclidean geometries challenged the universal validity of the Euclidean system that had prevailed for the previous 2000 years. The pioneers were Nikolai Lobachevsky (1792–1856) and Bernhard Riemann (1826–1866) who developed geometries based on hyperbolic and spherical surfaces respectively. The geometry of a spherical surface is ea
sy to visualize, since we can picture the spatial relationships as if we were piloting an airplane across the earth’s surface, or travelling along the surface of a bubble.

  Suppose we were to fly in a large triangle starting from the North Pole straight down to a point on the equator, and then straight along the equator for some distance, then making a right angle to turn northwards to return directly to the North Pole. In doing so, we will have traced a great triangle, where the two of angles touching the equator together measure 180º. Adding the third angle at the North Pole yields a triangle whose interior angles amount to more than 180º. This contradicts the Euclidean maxim that the sum of the interior angles of a triangle must equal 180º.

  This reason for the discrepancy is that although the non-Euclidean space in the example is a thin, two-dimensional surface, like that of a bubble, and like that of a Euclidean plane, it is not flat, but curved. Questions consequently arise concerning the validity of Kant’s claim that space – and he was indeed thinking of only of ‘flat’ space – is necessarily true as the only possible geometry. Subsequent theoretical physics has shown that the geometry of non-Euclidean, curved space more accurately represents the space of our physical universe.