20 May 14
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.
20 May 14
"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. "
Do the digits of pi constitute such a set, independent of the function which generates them? If so, then, presumably, an omniscient being could know them all, one by one. If not, then knowledge of the function is all there is to know about it.
20 May 14
Originally posted by moonbusAn omniscient being could see all the digits of pi in the same way that I can see all the even numbers.
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."
e.g. Ask god what is the 1,678,952,000,000th decimal place
I don't see that as a philosophical problem
Of course he couldn't tell you how many digits he knew! 😉
21 May 14
1 edit
Originally posted by moonbusYes.
Do the digits of pi constitute such a set, independent of the function which generates them?
If so, then, presumably, an omniscient being could know them all, one by one.
But only if it has infinite storage capacity (if storage is what it means to 'know' ). Some people have claimed that infinities cannot exist in reality.
23 May 14
Originally posted by wolfgang59Of course god could change the value of pi. To any number. If he is truly omnipotent. And if he really wants to.
Can an omnipotent being change the value of pi?
Just a thought.
Surely omnipotence cannot be extended to changing universal truths?
Heck, even I could turn the number around. If I want to. But I don't tell how.
23 May 14
1 edit
Originally posted by FabianFnasPlease don't! If you do, every circle in the world would collapse into a black hole and THEN where would we be?
Of course god could change the value of pi. To any number. If he is truly omnipotent. And if he really wants to.
Heck, even I could turn the number around. If I want to. But I don't tell how.
You DO know it's only the circumference that keeps the whole thing from collapsing don't you?
23 May 14
Originally posted by sonhouseExactly this is the reason for me not wanting to change the pi, not even the slightest.
Please don't! If you do, every circle in the world would collapse into a black hole and THEN where would we be?
You DO know it's only the circumference that keeps the whole thing from collapsing don't you?
But I can! But I don't want to.
23 May 14
Originally posted by sonhouseLook how FabianFnas changed his tune. Now he claims to agree with you. If I had said the same thing, he would come up with something to disagree about it.
Please don't! If you do, every circle in the world would collapse into a black hole and THEN where would we be?
You DO know it's only the circumference that keeps the whole thing from collapsing don't you?