Could a God Change the Value of Pi?

[Werg22]

Yes, I am also sure that 2 + 2 = 4. That's a theorem.

 

[humanino]

a·b will always equal b·a. Right?

This is a very bad example. Commutativity is valid for real numbers, period.

There are objects beyond commutativity, no problem, we just did not know that at that time. But that has not changed the commutativity of real numbers, neither has it changed the value of \pi. By the same token, the fundamental principles of elementary logic are valid independently of the fact that one can construct other forms of logical systems, such as fuzzy logic for instance.

 

[OAQfirst]

This is a very bad example. Commutativity is valid for real numbers, period.

There are objects beyond commutativity, no problem, we just did not know that at that time. But that has not changed the commutativity of real numbers, neither has it changed the value of \pi. By the same token, the fundamental principles of elementary logic are valid independently of the fact that one can construct other forms of logical systems, such as fuzzy logic for instance.

Not the point I was making. What seemed impossible at one time was found quite possible later.

 

[humanino]

Not the point I was making. What seemed impossible at one time was found quite possible later.

Still wrong. Mathematical theorems are true and period. If we have one think on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

 

[baywax]

2+2 = 2+2

 

[Werg22]

Still wrong. Mathematical theorems are true and period. If we have one think on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

I'd like to add a little something to this. Theorems are true by sole virtue of us declaring the axioms of the theories in which they occur as true. An axiom is, however, not true in by itself - there is no truth to be acquired about undefined terms - but rather purely assumed to be true; i.e. we assign the truth value 1 to the axioms of a theory by convention. The convention is obviously not arbitrary; this allows us the great flexibility of separating between "true" and "false" statements in mathematics (true if valid, false if the contrary is valid), which gives way to the method of reductio ad absurdum.

 

[jostpuur]

A "god" can do whatever you want to pretend it can do. You can make any mythical creature capable of anything.

The whole "problem" is based on personal belief, myth, not a real thing. So based on what you want this 'god" to be capable of, the answer will be different.

You cannot make a mythical creature capable of changing the value of pi, unless you know what it means to change the value of pi. Nobody here knows what it means to change the value of pi, so there's one problem.

One possible interpretation for the word "God" in this context would be, that if we can figure out what it means to change the value of pi, then the procedure of changing its value exists in some sense, and we can say that the God could do it. Or at least that's the way I would like it. Then we don't need to yet solve what God is, and dealing with the pi is enough.

 

[Evo]

You cannot make a mythical creature capable of changing the value of pi, unless you know what it means to change the value of pi. Nobody here knows what it means to change the value of pi, so there's one problem.

One possible interpretation for the word "God" in this context would be, that if we can figure out what it means to change the value of pi, then the procedure of changing its value exists in some sense, and we can say that the God could do it. Or at least that's the way I would like it. Then we don't need to yet solve what God is, and dealing with the pi is enough.

If you have circles, I'd agree that the value of PI would be constant. Of course that means that your God cannot be all powerful.

A God could change the universe so that circles, etc... did not exist, then you would have no PI.

 

[humanino]

A God could change the universe so that circles, etc... did not exist, then you would have no PI.

You see, I am so closed minded I can't understand that. It does not matter that kids have no clue what a differential equation is, and it does not make them impossible if nobody knew about them. They are a logical construction, ready to be discovered by anybody willing to look at them. I can understand if you tell me, God could have prevented us from constructing the concept of circle. But making the construction impossible, I just don't see how it can make sense.

 

[peter0302]

Humanino you and I are on precisely the same page :)

And I beg to differ with those that say that the axioms of math are not necessarily true. What makes them axioms is the fact that they are self-evident. That is different than a postulate, which is an assumption not necessarily self evident.

For instance, it is an axiom that when you one thing together with another thing, you get two. In fact, that is essentially definitional. "2" is defined as what you get when you put "1" and "1" together. "3" is defined as what you get when you put "1" and "1" and "1" together. It is therefore self-evident that when you put "2" together with "1" you also get "3" because "2" is defined to be the same as "1" and "1".

These are not theorems that require assumptions; these are axiomatic / definitional constructs that cannot be falsified under any circumstances because they are self-evident.

What if God said "When you put one thing together with another thing, a third thing will magically appear"? Well that'd be quite a feat, but it would not change the above.

 

[OAQfirst]

Still wrong. Mathematical theorems are true and period. If we have one think on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

I think we need to skip back and reexamine what I was saying. Werg22 wrote, "We're not even sure if two objects are brought together give 4 in our universe. We just know that we haven't observed otherwise." I replied, "You'd have a pretty hard time finding anyone without the confidence enough in that equation to not be willing to bet one's life on it. So I'd say just about everyone is sure." If there is an exception to 2+2=4, then wouldn't the rules of the universe be jeopardized? That's why I draw a certainty. I probably shouldn't have used quaternions as an example to support the other view, as I was just playing Devil's advocate. So to get back to my original point, I am sure 2+2=4. And I'm sure most everyone else has the same impression.

 

[baywax]

If there is an exception to 2+2=4, then wouldn't the rules of the universe be jeopardized? That's why I draw a certainty. I probably shouldn't have used quaternions as an example to support the other view, as I was just playing Devil's advocate. So to get back to my original point, I am sure 2+2=4. And I'm sure most everyone else has the same impression.

Not me.

2 apples plus 2 apples = 1 trillion cells + 1 trillion cells + 5 or more seeds (per apple).

The number of pixels in the digitally imaged number "2" plus the same = approx. 26


etc... (eg. 2 oranges + 2 oranges = marmalade)

 

[Werg22]

An axiom is self-evident? Only in the case we are in the realm of material axiomatics, in which case the subject matter of the theory is a physical concretion with definite properties. In formal axiomatics, an axiom is nothing but a statement declared as true about some undefined, primitive terms of the theory. Example:

My theory will consist of a set of objects S, and a dyadic relation R and a binary operation # on S. Here are my axioms:

1. a R b -> b R a
2. a R b and b R c -> a R c
3. a # b = b # a
4. There exists a unique element 0 such that a # 0 = a for every a
5. a R b and a R c -> a R (b # c)

Now tell me a little, which one of these, exactly, is self-evident to you?

I think we need to skip back and reexamine what I was saying. Werg22 wrote, "We're not even sure if two objects are brought together give 4 in our universe. We just know that we haven't observed otherwise." I replied, "You'd have a pretty hard time finding anyone without the confidence enough in that equation to not be willing to bet one's life on it. So I'd say just about everyone is sure." If there is an exception to 2+2=4, then wouldn't the rules of the universe be jeopardized? That's why I draw a certainty. I probably shouldn't have used quaternions as an example to support the other view, as I was just playing Devil's advocate. So to get back to my original point, I am sure 2+2=4. And I'm sure most everyone else has the same impression.

There is no one in their right mind that functionally doubts that when two groups of two objects are brought together we obtain four. That is not the point. 2 + 2 = 4 is, repeating myself once again, is a theorem of arithmetic! Whether or not the interpretation of 2, + and 4 to real objects make it a true proposition or not is none of the pure mathematician's concern!

 

[Evo]

Ok, if a God can't create a Universe where circles would not exist, then this thread is completely pointless and should be deleted, correct?

 

[OAQfirst]

@Werg22: Then would you be kind enough to expand on your reply in post #26?

 

[Evo]

@Werg22: Then would you be kind enough to expand on your reply in post #26?

May I ask what the point is in discussing what everyone agrees is impossible? Because I don't see it.

I have tried making this obvious in every way I know aside from just saying "No" and closing the thread after the first post.

 

[peter0302]

Simply because you do not understand/appreciate the topic does not justify locking the thread which has (I am happy to see) generated quite a lot of interest.

The answer to your question:

Ok, if a God can't create a Universe where circles would not exist, then this thread is completely pointless and should be deleted, correct?

is that no one has suggested that god cannot create a universe in which circles do not exist. I have explicitly stated that that is fine. My question is whether god can create a universe in which the _idea_ of a circle cannot exist, which also implicitly asks whether mathematical ideas can be altered by any higher power or if they themselves are the highest power.

It is a perfectly legitimate philosophical question and I think that your locking threats miss the point and are uncalled for.


Weg22:
We're talking about the difference between an axiom and a postulate. Mathematical axioms are self-evident. What you're listing are postulates.

 

[Evo]

No one has agreed that it is possible from a valid scientific viewpoint, even bending the rules to allow for a mythical supreme being, which I did not have to allow, I tried to help you see if you could "construct" a "god" that would have such powers, but no one agreed such a god could be created.

To quote just one of many that have said no to your question.

But the question "does general relativity changes the value of \pi ?" has always been considered a "wrong" question. A mathematical constant does not depend on how we actually measure it. In the case at hand, euclidean circles still are euclidean, even if they would not be realized geometrically in our Universe, the constant stays itself. That's why I don't see how the original question is any different from "could God contradict Itself ?" (a well-known question, such as Q: "what was God doing before time ?" A: "preparing Hell for those who would wonder !")

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[jostpuur]

Funny, I'm disappointed with some of the views expressed here to the effect of "it's simple because God can do anything." No, that's a cop out. I'm asking about whether we have identified logical truths through math that are as powerful as any religious belief or perhaps even moreso. This is philosophy, not religion.

I didn't get clear to me if there was misunderstanding between us, but to me it seems we were annoyed by the same thing. Your original post deals with a genuine philosophical question, and then people come in posting simple truths like "yes" or "no" in a hope, that they would make the problem seem easy and already solved.

 

[jostpuur]

If you have circles, I'd agree that the value of PI would be constant. Of course that means that your God cannot be all powerful.

A God could change the universe so that circles, etc... did not exist, then you would have no PI.

Ok, if a God can't create a Universe where circles would not exist, then this thread is completely pointless and should be deleted, correct?

That is not obvious. The real question is that could God create a universe where circles existed, and where pi had a different value. This is the difficult question, which I believe is little bit too difficult for humans, but which is suitable for a topic of a philosophical discussion.

 

[jostpuur]

It does not matter that kids have no clue what a differential equation is, and it does not make them impossible if nobody knew about them. They are a logical construction, ready to be discovered by anybody willing to look at them.

We don't know why these logical constructions, which are not invented by humans, but are already waiting to be discovered by humans, exist. So to me it seems possible, that the logical constructions, which are only waiting to be discovered, could also be different, or work differently. I don't believe we have any tools available to prove the opposite.

 

[peter0302]

I didn't get clear to me if there was misunderstanding between us, but to me it seems we were annoyed by the same thing. Your original post deals with a genuine philosophical question, and then people come in posting simple truths like "yes" or "no" in a hope, that they would make the problem seem easy and already solved.

Precisely right, jostpour.

Evo, you seem to be one of the aforementioned people. Do what you want, it's your forum, but don't act like you're doing me any favors by keeping a thread open which - contrary to your implication - adheres to your guidelines.

 

[Evo]

That is not obvious. The real question is that could God create a universe where circles existed, and where pi had a different value. This is the difficult question, which I believe is little bit too difficult for humans, but which is suitable for a topic of a philosophical discussion.

That has already been answered as no.

See humanino's post below as an example of what is correct.

Still wrong. Mathematical theorems are true and period. If we have one thing on this Earth we know is true, it's mathematical theorems !

IF A THEN B

It might appear to us later that A is unnecessary. But

IF A THEN B

remains true. Even if A is false.

Any further speculation is overly speculative and without sound science, which violates the guidelines.

I've given the thread numerous chances to either ponder if a supernatural diety could create a universe where the OP's question might work, but no one offered an example of one and in this Universe, the anser is no.