More generally, can God do something impossible? E.g., can God make a rock so heavy even he can't lift it? Either way you answer, there is something God can't do. Peter Geach used to parody this line of thinking by proposing (facetiously) that God is so omnipotent, he could make himself exist even if he didn't. Just goes to show that the concept of omnipotence is incoherent.
Originally posted by moonbusAlso if God is omnipotent, then perhaps that means everybody else is impotent.
More generally, can God do something impossible? E.g., can God make a rock so heavy even he can't lift it? Either way you answer, there is something God can't do. Peter Geach used to parody this line of thinking by proposing (facetiously) that God is so omnipotent, he could make himself exist even if he didn't. Just goes to show that the concept of omnipotence is incoherent.
Originally posted by JS357"A Rational Number is a real number that can be written as a simple fraction (i.e. as a ratio of two integers)."
Well the problem I see is that you have to use the exact values of irrationals like 1/3 and 1/7 to calculate it. Maybe that says the same thing.
"An Irrational Number is a real number that cannot be written as a ratio of two integers (i.e., a simple fraction)."
http://www.mathsisfun.com/rational-numbers.html
http://www.mathsisfun.com/irrational-numbers.html
pi belongs to the irrationals.
Personally, I always favored the imaginary numbers. (Those are the ones which make mathematicians' cheque books balance!)
Originally posted by RJHindsThe question is whether or not an omniscient being knows the exact number - and of course what it means to 'know'.
.....because no one seems to know the exact number....
A computer could calculate any tell you, any arbitrary digit of pi you asked it for. But no computer can simultaneously store all the digits of pi.
I believe sonship has claimed in the past that infinities cannot exist in reality, so I guess this means that he believes that God cannot know all the digits of pi.
"all the digits of pi" -- does this actually make sense? The point about an infinite series is that it doesn't consist of _a_ number of digits at all, not even the greatest possible number of digits. We grasp such series not in their quantity, so to speak, but rather in the functions which generate them.
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.
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."
Could God make pi to be a rational number? I don't know. I can't imagine that it could be done without changing a lot of other things along with it. Maybe in some non-Euclidean non-flat non-contiguous space such a thing would be possible.