20 May '14 17:35>
Originally posted by moonbusIt makes as much sense as 'all the integers' which is reasonably interpreted as 'the set of integers' which although infinite, is perfectly valid to talk about.
"all the digits of pi" -- does this actually make sense?
....not even the greatest possible number of digits.
Now that doesn't make sense. What is 'the greatest possible number'?
One can speak of "all the even numbers" insofar as there is some calculable mode or equation which generates (any quantity of) even numbers--e.g., the iterative function "times two", for, in that case, we have the _function_ to grasp onto.
We do not however need such a generative function. We can quite happily talk about set such as the Integers, the Even numbers, the Real numbers, the Rationals the Irrationals etc based on their properties rather on generative functions.
It may be that an omniscient being sees the function in some way that we don't, but I don't think that entails seeing "all the numbers"--because being omniscient does not change the fact that there is no such number as "all of them."
Well this comes back to the question of what it is to 'know'. Do you 'know' an number if you have to calculate if prior to answering? Do calculators for example 'know' sine and cosine tables (to a certain precision) if they use a formula to calculate it each time one is requested?
Could God make pi to be a rational number? I don't know.
I do know. He couldn't.
Maybe in some non-Euclidean non-flat non-contiguous space such a thing would be possible.
No, it wouldn't, because pi is defined in Euclidean, contiguous, flat space. In some other geometry it is some other number, not pi.