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Updated: May 6, 2025
The capacity of the mind is not infinite; consequently no idea of extension or duration consists of an infinite number of parts or inferior ideas, but of a finite number, and these simple and indivisible: It is therefore possible for space and time to exist conformable to this idea: And if it be possible, it is certain they actually do exist conformable to it; since their infinite divisibility is utterly impossible and contradictory.
The fact of the vast diffusion of some odors, as that of musk or the rose, for instance, has long been cited as the most remarkable illustration of the divisibility of matter, and the nicety of the senses.
For example, we cannot conceive of an end to divisibility of space; and therefore we cannot conceive how we can reach a given point. Now, practice gives the lie to this conclusion, and if some rationalist should follow his reason here, he would conclude that he can never get a piece of food into his mouth; or, in other words, the logical conclusion would lead to starvation.
We cannot, therefore, escape the responsibility of at least a critical solution of the questions of reason, by complaints of the limited nature of our faculties, and the seemingly humble confession that it is beyond the power of our reason to decide, whether the world has existed from all eternity or had a beginning whether it is infinitely extended, or enclosed within certain limits whether anything in the world is simple, or whether everything must be capable of infinite divisibility whether freedom can originate phenomena, or whether everything is absolutely dependent on the laws and order of nature and, finally, whether there exists a being that is completely unconditioned and necessary, or whether the existence of everything is conditioned and consequently dependent on something external to itself, and therefore in its own nature contingent.
To take his favorite example, we can not conceive the infinite divisibility of matter, and we can not conceive a minimum, or end to divisibility: yet one or the other must be true. As I have hitherto said nothing of the two axioms in question, those of Contradiction and of Excluded Middle, it is not unseasonable to consider them here.
For the infinity of the division of a phenomenon in space rests altogether on the fact that the divisibility of a phenomenon is given only in and through this infinity, that is, an undetermined number of parts is given, while the parts themselves are given and determined only in and through the subdivision; in a word, the infinity of the division necessarily presupposes that the whole is not already divided in se.
There is no more reason for stopping at one point than at another; why not go on? What could end space? As to the infinite divisibility of space, have we not, in addition to the seeming reasonableness of the doctrine, the testimony of all the mathematicians?
The scene which suddenly unveiled itself to the eyes of the two Seers crushed them with a sense of its vastness; they felt like atoms, whose minuteness was not to be compared even to the smallest particle which the infinite of divisibility enabled the mind of man to imagine, brought into the presence of the infinite of Numbers, which God alone can comprehend as He alone can comprehend Himself.
It certainly seems that, as a body must be cogitated as substance in space, the law of divisibility would not be applicable to it as substance.
Evidently there is either something wrong with this doctrine of the infinite divisibility of space, or there is something wrong with our understanding of it, if such absurdities as these refuse to be cleared away. Let us see where the trouble lies. WHAT IS REAL SPACE? It is plain that men are willing to make a number of statements about space, the ground for making which is not at once apparent.
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