by means of an always evident synthesis. In experimental philosophy doubt and delay may be very useful; but no misunderstanding is possible, which cannot be easily removed; and in experience means of solving the difficulty and putting an end to the dissension must at last be found, whether sooner or later. Moral philosophy can always exhibit its principles, with their practical consequences, in concretoat least in possible experiences, and thus escape the mistakes and ambiguities of abstraction. But transcendental propositions, which lay claim to insight beyond the region of possible experience, cannot, on the one hand, exhibit their abstract synthesis in any à priori intuition, nor, on the other, expose a lurking error by the help of experience. Transcendental reason, therefore, presents us with no other criterion, than that of an attempt to reconcile such assertions, and for this purpose to permit a free and unrestrained conflict between them. And this we now proceed to arrange.* The antinomies stand in the order of the four transcendental ideas above detailed. sive synthesis. It follows because no part of any such hat an infinite series already time contains a distinctive conelapsed is impossible, and dition of being, in preference that consequently a begin to that of non-being (whether ning of the world is a ne- the supposed thing originate of cessary condition of its exist- itself, or by means of some ence. And this was the first other cause). Consequently, thing to be proved. many series of things may a beginning in the world, but the world itself cannot have a beginning, and is, therefore, in relation to past time, infinite. have As regards the second, let us take the opposite for granted. In this case, the world must be an infinite given total of coexistent things. Now we As regards the second statecannot cogitate the dimensions of a quantity, which is not given within certain limits of an intuition,* in any other way than by means of the synthesist of its parts, and the total of such a quantity only by means of a completed synthesis, or the repeated addition of unity to itself. Accordingly, to cogitate the world, which fills * We may consider an undetermined quantity as a whole, when it is enclosed within limits, although we cannot construct or ascertain its totality by measurement, that is, by the successive synthesis of its parts. For its limits of themselves determine its completeness as a whole. What is meant by successive synthesis must be tolerably plain. If I am required to form some notion of a piece of land, I may assume an arbitrary standard,-a mile, or an acre,-and by the successive addition of mile to mile or acre to acre till the proper number is reached, construct for myself a notion of the size of the land.-Tr. ment, let us first take the opposite for granted that the world is finite and limited in space; it follows that it must exist in a void 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, out of and beyond which no object of intuition, and consequently no can be correlate to which *Space is merely the form of external intuition (formal intuition), and not a real object which can be externally perceived. Space, prior to all things which determine it (fill or limit it), or, rather, which present an empirical intuition conformable to it, is, under the title of absolute space, nothing but the mere possibility of external phænomena, in so far as they either exist in themselves, or can annex themselves to given intuitions. Empirical intuition is therefore not a composition of pha nomena and space (of perception and empty intuition). The one is not the correlate of the other in a synthethe same empirical intuition, as matsis, but they are vitally connected in ter and form. 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 enumeration 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 a contemporaneously given whole. The world is conIf we wish to set one sequently, as regards extension of these two apart from the otherin space, not infinite, but en-space from phænomena-there arise closed in limits. And this was all sorts of empty determinations of external intuition, which are very far the second thing to be proved. from being possible perceptions. For example, motion or rest of the world in an infinite empty space, or a determination of the mutual relation of both, cannot possibly be perceived, and is therefore merely the predicate of a notional entity. OBSERVATIONS ON THE FIRST ANTINOMY. On the Thesis. On the Antithesis. In bringing forward these The proof in favour of the conflicting arguments, I have infinity of the cosmical sucnot been on the search for so- cession and the cosmical conphisms, for the purpose of tent is based upon the conavailing myself of special plead- sideration, that, in the opposite ing, which takes advantage of case, a void time and a void the carelessness of the opposite space must constitute the limits party, appeals to a misunder- of the world. Now I am not stood statute, and erects its unaware, that there are some unrighteous claims upon an ways of escaping this concluunfair interpretation. Both sion. It may, for example, proofs originate fairly from the be alleged, that a limit to the nature of the case, and the ad- world, as regards both space vantage presented by the mis- and time, is quite possible, takes of the dogmatists of both without at the same time holdparties has been completely ing the existence of an absoset aside. lute time before the begin The thesis might also have ning of the world, or an absobeen unfairly demonstrated, lute space extending beyond by the introduction of an erro- the actual world—which is neous conception of the infi- impossible. I am quite well nity of a given quantity. A satisfied with the latter part quantity is infinite, if a greater of this opinion of the phithan itself cannot possibly exist. losophers of the Leibnitzian. The quantity is measured by school. Space is merely the the number of given units-form of external intuition, but which are taken as a standard not a real object which can it-contained in it. Now no self be externally intuited; it number can be the greatest, is not a correlate of phænobecause one or more units can mena, it is the form of phænoalways be added. It follows mena itself. Space, therefore, that an infinite given quantity, cannot be regarded as absoconsequently an infinite world lutely and in itself something (both as regards time and determinative of the existence extension) is impossible. It of things, because it is not itis, therefore, limited in both self an object, but only the respects. In this manner I form of possible objects. Conmight have conducted my sequently, things, as phænoproof; but the conception mena, determine space; that given in it does not agree is to say, they render it possiwith the true conception of ble that, of all the possible an infinite whole. In this predicates of space (size and there is no representation of relation), certain may belong to its quantity, it is not said how reality. But we cannot affirm large it is; consequently its the converse, that space, as conception is not the concep- something self-subsistent, can tion of a maximum. We cogi- determine real things in regard tate in it merely its relation to size or shape, for it is in itto an arbitrarily assumed unit, self not a real thing. Space in relation to which it is greater (filled or void)* may therethan any number. Now, just as the unit which is taken is *It is evident that what is meant here is, that empty space, in so far greater or smaller, the infinite fore be limited by phænomena, will be greater or smaller; but but phænomena cannot be the infinity, which consists limited by an empty space merely in the relation to this without them. This is true of given unit, must remain always time also. All this being the same, although the abso- granted, it is nevertheless inlute quantity of the whole is disputable, that we must asnot thereby cognized. sume these two nonentities, The true (transcendental) void space without and void conception of infinity is that time before the world, if we the successsive synthesis of assume the existence of cosunity in the measurement of a mical limits, relatively to space given quantum can never be or time. completed.* Hence it follows, For, as regards the subterwithout possibility of mistake, fuge adopted by those who that an eternity of actual suc- endeavour to evade the consecessive states up to a given quence-that, if the world is (the present) moment cannot limited as to space and time, have elapsed, and that the the infinite void must deterworld must therefore have a mine the existence of actual beginning. things in regard to their di In regard to the second part mensions-it arises solely from of the thesis, the difficulty the fact that, instead of a senas to an infinite and yet elapsed suous world, an intelligible series disappears; for the mani-world-of which nothing is fold of a world infinite in ex-known-is cogitated; instead of tension is contemporaneously a real beginning (an existence, given. But, in order to cogi- which is preceded by a period tate the total of this mani- in which nothing exists) an exfold, as we cannot have the aid istence which presupposes no of limits constituting by them- other condition than that of selves this total in intuition, time; and, instead of limits we are obliged to give some of extension, boundaries of account of our conception, which in this case cannot pro *The quantum in this sense contains a congeries of given units, which is greater than any number -and this is the mathematical conception of the infinite. as it is limited by phænomenaspace, that is, within the worlddoes not at least contradict transcendental principles, and may there. fore, as regards them, be admitted, although its possibility cannot on that account be affirmed. |