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| I: On the Thesis? In exhibiting these conflicting arguments I have not tried to avail myself of mere sophisms for the sake of what is called special pleading, which takesadvantage of the want of caution of the opponent, and gladly allows his appeal to a misunderstood law, in order to establishhis own illegitimate claims on its refutation. Every one of our proofs has been deduced from the nature of the case, and no advantage has been taken of the wrong conclusions of dogmatists on either side. I might have apparently proved my thesis too by putting forward, as is the habit of dogmatists, a wrong definition of the infinity of a given quantity. I might have said that the quantity is infinite, if no greater quantity (that is, greater than the number of given units contained in it) is possible. As no number is the greatest, because one or more units can always be added to it, I might have argued that an infinite given quantity, and therefore also an infinite world (infinite as regards both the past series of time and extension in space) is impossible, and therefore the world limited in space and time. I might have done this, but, in that case, my definition would not have agreed with the true concept of an infinite whole. We do not represent by it how large it is, and the concept of it is not therefore the concept of a maximum, but we conceive by it its relation only [432] to any possible unit, in regard to which it is greater than any number. According as this unit is either greater or smaller, the infinite would be greater or smaller, while infinity, consisting in the relation only to this given unit, would always remain the same, although the absolute quantity of the whole would not be known by it. This, however, does not concern us at present. The true transcendental concept of infinity is, that the successive synthesis of units in measuring a quantum, can never be completed.1 Hence it follows with perfect certainty, that an eternity of real and successive states cannot have elapsed up to any given (the present) moment, and that the world therefore must have a beginning. With regard to the second part of the thesis, the difficulty of an endless and yet past series does not exist; for the manifold of a world, infinite in extension, is given at one and the same time. But, in order to conceive the totality of such a multitude of things, as we cannot appeal to those limits which in intuition produce that totality by themselves, we must render an account of our concept, which in our case cannot proceed from the whole to the determined multitude of the parts, but has to demonstrate the possibility of a whole by the successive synthesis of the parts. As such a synthesis would constitute a series that would never be completed, it is impossible to conceive a totality either before it, or through it. For the concept of totality itself is in this case the representation of a completed synthesis of parts, and such a completion, and therefore its concept also, is impossible. [347] II: On the Antithesis [431]? The proof of the infinity of the given series of world, and of the totality of the world, rests on this, that in the opposite case an empty time, and likewise an empty space,would form the limits of the world. Now I am quite aware that people have triedto escape from this conclusion by saying that a limit of the world, both in time and space, is quite possible, without our having to admit an absolute time before the beginning of the world or . |
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