Note: Page references refer first to pages in Politis (1991), then to the A and B editions of Kant's original publication, as referenced in Politis (1991).
p. 50 [A23/B37]
1. Space is not an empirical concept which has been derived from outward experiences. For in order that certain sensations may relate to something outside me (that is, to something which occupies a different part of space from that in which I am); in like manner, in order that I may represent them not merely as outside of and next to each other, but also in separate places, the representation of space must already exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phenomena through experience; but, on the contrary, this external experience is itself only possible through the said antecedent representation.
2. Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. We never can imagine or make a representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possiblity of appearences, and by no means as a determination dependent on them, and is a representation a priori, which necessarily supplies the basis for external appearances.
3. Space is not discursive, or as we say, general concept of the relations of things, but a pure intuition. For in the first place we can only represent to ourselves one space, and when we talk of divers spaces, we mean only parts of one and the same space. (p. 52 [A25/B39]) Moreover, these parts cannot antecede this one all-embracing space, as the component parts from which the aggregate can be made up, but can be thought only as existing in it. Space is essentially one, and multiplicity in it; consequently the general concept of spaces depends solely upon limitations. Hence it follows that an a priori intuition (which is not empirical) lies at the root of all our concepts of space. Thus, moreover, the principles of geometry -- for example, that 'in a triangle, two sides together are greater than the third' -- are never derived from general concepts of line and triangle, but from intuition, and this a priori, with apodeictic certainty.
4. Space is represented as an infinite given quantity. Now every concept must indeed be considered as a representation which is contained in an infinite multitude of different possible representations (as their common characteristic), which therefore, comprises these under itself; but no concept, as such, can be so conceived, as if it contained within itself an infinite multitude of representations. Nevertheless space is so conceived, for all parts of space, even to infinity, exist at once. Consequently, the original representation of space is an intuition a priori, and not a concept.
p. 52 [A26/B41]
Space is nothing else than the form of all appearances of the external sense, that is the subjective condition of sensibility, under which alone external intuition is possible.
p. 54 [A29/B45]
1. Time is not an empirical concept. For neither co-existence nor succession would be perceived by us, if the representation of time did not exist as a foundation a priori. Without this presupposition we could not represent to ourselves that things exist together at one and the same time, or at different times, that is, contemporaneously, or in succession.
2. Time is a necessary representation, lying at the foundation of all our intuitions. With regard to appearances in general, we cannot think away time from them and represent them to ourselves as out of and unconnected with time, but we can quite well represent to ourselves time void of appearances. Time is therefore given a priori. In it alone is all reality of appearances possible. These may be all annihilated in thought, but time itself, as the universal condition of their possibility, cannot be so annulled.
3. On this necessity a priori is also founded the possibility of apodeictic principles of the relations of time, or axioms of time in general, such as: 'Time has only one dimension', 'Different times are not co-existent but successive' (as different spaces are not successive but co-existent). These principles cannot be derived from (p. 55 [A31/B46]) experience, for it would give neither strict universality, nor apodeictic certainty. We should only be able to say 'So common experience teaches us', but it must be so. They are valid as rules, through which, in general, experience is possible; and they instruct us respecting experience, and not by means of it.
4. Time is not a discursive, or as it is called, general concept, but a pure form of sensible intuition. Different times are merely parts of one and the same time. But the representation which can only be given by a single object is an intuition. Besides, the proposition that different times cannot be co-existent, could not be derived from a general concept. For this proposition is synthetical, and therefore cannot spring out of concepts alone. It is therefore contained immediately in the intuition and representation of time.
p. 69 [A50/B74]
Without the sensible faculty no object would be given to us, and without the understanding no object would be thought. Thoughts without content are empty; intuitions without concepts, blind. Hence it is as necessary for the mind to make its concepts sensible (that is, to join to them the object in intuition), as to make its intuitions intelligible (that is, to bring them under concepts).
p. 317 [A424/B352]
Thesis:
The world has a beginning in time, and is also limited with regard to space.
Proof:
Let us assume that the world has no beginning in time; up to every given moment of time, an eternity must have elapsed, and therewith passed away an infinite series of successive states of things in the world. Now the infinity of a series consists in the fact, that it never can be completed by means of a successive synthesis. It follows that an infinite series already elapsed is impossible, and that consequently a beginning of the world is a necessary condition of its existence. And this was the first thing to be proved.
As regards the second, [that space has limits] let us assume the opposite. In this case, the world must be an infinite given whole of coexistent things. Now we cannot think the magnitude of a quantity, which is not given within certain limits of an intuition, in any other way than by means of the synthesis of its parts, and the whole of such a quantity only by means of a completed synthesis, or the repeated addition of unity to itself. Accordingly, to think the world, which fills all spaces as a whole, the successive synthesis of the parts of an infinite world must be looked upon as completed, that is to say, an infinite time must be regarded as having elapsed in the ennumeration of all coexisting things; which is impossible. For this reason an infinite aggregate of actual things cannot be considered as a given whole, consequently not as co-existing. The world is consequently, as regards extension in space, not infinite but enclosed in limits. And this was the second thing to be proved.
Antithesis:
The world has no beginning, and no limits in space, but is, in relation both to time and space, infinite.
Proof:
For let us assume, that it has a beginning. A beginning is an existence which is preceded by a time in which the thing does not exist. On the above supposition, it follows that there must have been a time in whichthe world did not exist, that is, an empty time. But in an empty time the origination of a thing is impossible; because no part of any such time contains a distinctive condition of being, in preference to that of non-being (whether the supposed thing originate of itself, or by means of some other cause). Consequently, many series of things may have a beginning in the world, but the world itself cannot have a beginning, and is, therefore, in relation to past time, infinite.
As regards the second statement, [that space has no limits] let us first assume the opposite -- that the world is finite and limited in space; it follows that it must exist in an empty space, which is not limited. We should therefore meet not only with a relation of things in SPACE, but also a relation of things TO SPACE. Now, as the world is an absolute whole, beyond which no object of intuition, and consequently no correlate to which can be discovered, this relation of the world to an empty space is a relation to NO OBJECT. But such a relation, and consequently the limitation of the world by empty space, is nothing. Consequently, the world, as regards space, is not limited, that is, it is infinite in regard to extension.
Thesis:
Every composite substance in the world consists of simple parts; and there exists nothing that is not either itself simple, or composed of simple parts.
Antithesis:
No composite thing in the world consists of simple parts; and there does not exist in the world anything simple.
Thesis:
Causality according to the laws of nature, is not the only causality operating to originate the appearances of the world. A causality of freedom is also necessary to account for these appearances.
Antithesis:
There is no such thing as freedom, but everything in the world happens solely according to the laws of nature.
p. xlix Introduction
The ontological argument attempts to establish God's existence from the concept of God alone: the concept of God is the concept of the most perfect being; but the concept of God would not be the concept of a most perfect being if it were not the concept of something existing; therefore God must exist.
p. 8
"The priority for the use of the term [phenomenology] in a scientific context would seem to go to Immanuel Kant, at least according to mere date of publication. For it was in his Metaphysische Anfangsgründe der Naturwissenschaft of 1786 that he applied it to the last of his four branches of the science of matter, dealing with "motion or rest only in relation to their appearance to us."