Hi,
As to cause and effect and effects needing a cause, that simply leads to an infinite regression. One must either accept that, postulate a 'first cause', or give up some part of casualty. All three are perfectly acceptable philosophical grounds. But that is not the only viable viewpoint. There are many other possibilities: our 'universe' may be a bubble in something that is infinite in time; the curvature of our universe might have been sufficiently great prior to the initial expansion that time was curved onto itself so that it was infinite but bounded; our universe might still be a gravitationally bound object that expands, contracts, rebounds and goes on like that forever in both the past and future. Frankly, we haven't been doing science long enough to have more than a notion or two.
--Pete
wakim,Dec 30 2005, 05:33 PM Wrote:I won't quibble; I grant this.Yes. Consider the set of positive and negative integers: {. . ., -2, -1, 0, 1, 2, 3, . . .}. Without getting into advanced set theory, this set is countably infinite and yet (assuming the axiom of choice) it has no 'first' or 'last' element. A simpler example, {all flatware in your house} is a finite set that has, a priory, no ordering principle -- any element of that set could be designated 'first', or if you prefer, no element can be.
The question was, if I recall, whether a set than contains some quantity of elements, whether infinite in magnitude or not, could exist that did not contain a first element?[right][snapback]98353[/snapback][/right]
As to cause and effect and effects needing a cause, that simply leads to an infinite regression. One must either accept that, postulate a 'first cause', or give up some part of casualty. All three are perfectly acceptable philosophical grounds. But that is not the only viable viewpoint. There are many other possibilities: our 'universe' may be a bubble in something that is infinite in time; the curvature of our universe might have been sufficiently great prior to the initial expansion that time was curved onto itself so that it was infinite but bounded; our universe might still be a gravitationally bound object that expands, contracts, rebounds and goes on like that forever in both the past and future. Frankly, we haven't been doing science long enough to have more than a notion or two.
--Pete
How big was the aquarium in Noah's ark?