Originally posted by vistesd
Please, lay that out for me. Even if you have before (or cut & paste). That certainly has philosophical implications...
Agerg will probably answer this better, but sometimes different explanations in concert help make things easier to understand.
Of course it is possible that it will just confuse things further but hey ho ;-)
It has to do with there being classes of infinity.
The lowest/smallest of which being what's called the countably infinite.
Countable infinity implies as the name suggest that you could (hypothetically) count it.
So if you had an infinite number of apples you could number each apple with an integer and as the integer numbers go on forever
you can keep doing so for ever counting the apples.
Indeed the base example of a countable infinity are the integer numbers.
Now you might be thinking well anything you have must be countable, you just assign a number to each object and there
are infinite numbers so you will never run out.
Unfortunately this is where I introduce the real number line.
So lets say I want to count the real numbers from 1 to 2.... that shouldn't be too hard should it.....
However there are an infinite number of real numbers between 1 and 2. (inclusive)
but were still ok as there are an infinite number of integers to muse to count them...
except that there are more real numbers between 1 and 2 than there are integers.
The way I show that is like this.
The first number is 1 so I can label that with the integer 1.
lets say the next is 1.1 and label that with the integer 2....
Except that can't be right because there are numbers between 1 and 1.1
so lets say its 1.01...
Except that there are numbers between 1 and 1.01....
In fact there are an infinite number of numbers between any real number and any other real number.
Any number I try to nominate as my second number I can find an infinite number of real numbers between the two.
It isn't possible to match up a countable infinity with the real number line because there will always be an infinite number
of real numbers between any two you pick.
So in fact you can see that the real number line is infinitely bigger than the integer number line, despite the fact that the
integer number line is infinite.
And that in fact the real numbers between any to integers outnumber the total number of integers by infinity...
What has this to do with doing everything if you exist forever....
Well it depends on what infinities you are using.
Time is usually considered to be granular and is thus countably infinite.
And thus if god can only do a finite number of things per time unit, the things he can do in an infinite amount of time are still countably infinite.
However if god can do a non-countably infinite number of things then he not only need not have done them all, but he can't possibly have done them all.
That said I find the idea that god can do a non-countably infinite number of distinct things to be absurd.... but that is a different argument.
EDIT: Agerg I would be interested in any comments/corrections you have on my description of the problem (I went with as non-technical as possible
as I suspected you would go down the technical route)