26 Sep '16 22:51>
Originally posted by LemonJelloWith you now, yes twhitehead was doing exactly what you describe, which was slightly frustrating as I found myself drawn into defending an idea I'm not committed to...
Perhaps I was not clear, but I am not disputing that you can specify two members of the extended reals that yield the result you want (say, minus-infinity and zero). Rather, my point is that in the context of the original argument, it is probably excusable on the part of the objector if he takes this to be some sort of ad hoc stipulation.
To the exten ...[text shortened]... what you mean when you say that adding a beginning defeats the original purpose of the argument.
I think I get the problem with the argument now. Its purpose is to show that time must have begun at some point. Although the proponent may not realise it they have assumed the extended real numbers describe time, but they cannot as they cannot rule out the real numbers doing that - the idea being to establish a contradiction along the lines of 'otherwise we can't get to now and it is now'. So by adding this point at minus infinity the proponent is insisting on a starting point and begs the question. The argument needs to rule out the normal real numbers to do what the proposer is hoping for.
Although the original form of the argument seems not to work, I'm not sure it cannot be modified so that it does. Although the time between any specific points is finite, this interval can be made arbitrarily large, so although it takes so long to get to now I can always find a prior time where it takes longer and can keep doing that ad infinitum. Problem is I can't get my head around whether that's a problem for a model of the universe that stretches back indefinitely or not.