12-30-2005, 02:45 AM
Jester,Dec 30 2005, 12:10 AM Wrote:There is nothing, logically speaking, to prevent one infinite set from being "larger" than another, in the sense you describe. The set of all positive integers is twice the size of the set of all even integers. Russell proved that, IIRC. Yet, the more integers you assign to each set, the larger the (sum) difference between the two sets. Both sets, however, are infinite.So what is infinite can be larger than what is infinite? You find no contradiction in stating that a thing may be larger than itself?
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Jester,Dec 30 2005, 12:10 AM Wrote:Time is one of the dimensions of the universe.... Time is just a dimension. It is something required to locate an object. Motion is of no concequence.I had thought that there was some generally accepted early 20th century theory in physics that stated, roughly speaking, that place and time were relative and that motion was absolute. Let us not digress, though.
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Jester,Dec 30 2005, 12:10 AM Wrote:Motion is just a subset of "everything," and everything, insofar as I can tell, has a cause.I don't understand how everything can be claimed to have a cause, with one hand, while with the other claim that things exist without a first cause; since without a first cause there can follow no other cause, and thus things must exist as uncaused. For if no first cause exists, how can a second cause exist, or a third, or a fourth, or any higher number, let alone an infinite number? It would appear as if one who would reject a first cause for something as unreasonable, would then turn around and claim that no cause is an answer in better accord with reason.
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To return to the example of integers, if a set contains an infinite number of integers, mustn't in contain every quantity of integers smaller than the infinite? In other words, if a set of 100 items were examined, mustn't it also be found to contain 99 items, and 98 items, and so on? If a set of 100 items did not contain a first item, how could it contain a second? Thus, how if one claims a set of infinite items, can it not contain a first item?
In fine: If one assumes that everything has a cause, then it cannot be eternal, as before it was there was a cause that created it. The chain of cause cannot be infinite, or it would be eternal.