Kant, Prolegomena to any Future Metaphysic

Section 13 if you cant help thinking that space and

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: as not bounded by anything; and this can only come from intuition, and could never be inferred from concepts. Thus mathematics is really grounded in pure a priori intuitions; they are what enable it to establish synthetic propositions as necessary and certain. [In this paragraph Kant speaks of a certain ‘transcendental deduction’ of certain concepts. A ‘deduction’ is a theoretically grounded or justified list; it is ‘transcendental’ in Kant’s main sense of that word if it is based on considerations about what makes some kind of a priori knowledge possible.] Hence our transcendental deduction of the concepts of space and time - ·that is, our establishing that whatever is given to us in experience must be in space and in time· - also explains the possibility of pure mathematics. If we did not have such a deduction, and could not take it for granted that whatever is presented our senses - whether outer (space) or inner (time) - is experienced by us only as it appears, not as it is in itself, we could still do mathematics but we would have no insight into what it is. Section 13 If you can’t help thinking that space and time are real qualities attached to things in themselves, try your intelligence on the following paradox. When it has defeated you, you may be free from prejudices at least for a few moments, and then you may be more favourably disposed towards the view that space and time are mere forms of our sensible intuition. If two things are completely the same in every respect of quantity and quality that can be known about each separately, you would expect it to follow that each can be replaced by the other in all cases and in all respects, without the exchange causing the slightest recognizable difference. That is indeed the case with two-dimensional figures in geometry, but not with three-dimensional ones: it can happen that two of them have a complete inner agreement yet also have an outer relation such that one cannot be replaced by the other. . . . What can be more like my hand, and more equal in all points, than its image in the mirror? Yet I can’t put such a hand as is seen in the mirror in the place of its original: for if the original was a right hand, the hand in the mirror is a left hand, which could never serve as a substitute for the other. Here are no inner differences that any understanding could think - ·that is, no difference that can be expressed in concepts· - and yet the differences are inner as far as the senses tell us, for the left hand can’t be enclosed in the same boundaries as the right (they are not congruent), despite all their equality and similarity. For example, the glove of one hand can’t be used on the other. So the two hands are intrinsically different in a manner that cannot be captured in concepts - it can only be shown through the fact that a spatial region that exactly contains one will not contain the other. 22 How can this be? Well, these objects are not representations of the things as they are in themselves, but are sensible intuitions, i.e. appearances, which come about through the relation to Ÿour sensibility of Ÿcertain things that are unknown in themselves. When this sensibility is exercised as outer intuition, its form is space; and the intrinsic nature of any region of space is fixed by how that region relates to space as a whole, the one big space of which it is a part. (The part is made possible by the whole: ·a small region of space can exist only if there is a larger region of which it is a part·. This never happens with things in themselves, but it can happen with mere appearances.) Thus, to make intelligible to ourselves the difference between similar and equal yet incongruent things (e.g. snails winding opposite ways), we must relate them to the right and the left hand. That means that it must be done through intuition; it can’t be done through any concept. ·That is, it must be done by showing, and can’t be done by telling·. Note I The propositions of geometry are not mere fantasies that might have nothing to do with real objects. Pure mathematics, and in particular pure geometry, is objectively valid, but only in application to objects of the senses. When we represent such objects through our sensibility, we represent them not as they are in themselves but only as they appear to us. So they must have any features that are conferred on them by the form of our sensibility and in particular they must be in space, because space is simply the form of all outer appearances. Outer appearances are possible only through sensibility, the form of which is the basis for geometry; so outer appearances must conform to what geometry says about them. If the senses had to represent objects as they are in themselves, the situation would be quite different. For then the facts about our representation of space would not provide a guarantee about how things are in reality. The space of the geometer - a mere representation - would be a fiction with no objective validity, for there would be no reason why things should have to conform to the picture that we make...
View Full Document

Ask a homework question - tutors are online