The first cause argument

[muhammad_isa]

There are many questions about infinite sets that are unresolved. But we aren't even close to those in this discussion.

You make it all about infinite sets, which it is not.
One can't make conclusions about the nature of our universe by set theory alone .. that's absurd. It is merely an excuse to say that it is possible that there might be an infinite amount of causes.

As I say, if that's what you believe .. fine. It has little to do with set theory. It's what you want to believe.
i.e. the cause of a being has a cause that has a cause .. and on and on..

A person doesn't have to know about set-theory to 'smell a rat'

 

[Polymath257]

You make it all about infinite sets, which it is not.
One can't make conclusions about the nature of our universe by set theory alone .. that's absurd. It is merely an excuse to say that it is possible that there might be an infinite amount of causes.

Not an excuse. It shows that there is no contradiction to an infinite number of causes.

As I have said before, I do not know whether or not time is infinite into the past. But simple philosophical argument *cannot* answer that question. It is *logically possible* either way. But *nobody* knows what is actually the case.

As I say, if that's what you believe .. fine. It has little to do with set theory. It's what you want to believe.
i.e. the cause of a being has a cause that has a cause .. and on and on..

A person doesn't have to know about set-theory to 'smell a rat'

The set theory shows that there is no contradiction to an infinite regress. So *some* sort of additional argument is required to establish the facts either way. No rat. Just looking at the possibilities.

 

[Link]

Set theory proves God actually (ultimate set) and would mean nothing can exist without him. OFF-TOPIC but true.

Go on.

 

[Polymath257]

You make it all about infinite sets, which it is not.

Well, actually, it *is* about whether there can be an infinite set of causes.

One can't make conclusions about the nature of our universe by set theory alone .. that's absurd.

I would agree. That is why I don't know whether time is infinite into the past or not. I do not know if there is an infinite regress of causes or not.

The set theory shows there is no contradiction inherent in either way.

But I would also say that it is absurd to think that philosophy alone can say anything about our universe either. At *some* point, it is going to be necessary to actually look at the universe and test to see which model fits the facts better.

It is merely an excuse to say that it is possible that there might be an infinite amount of causes.

No, it is looking at ALL of the logical possibilities and then seeing which fits the observational facts better.

As I say, if that's what you believe .. fine. It has little to do with set theory. It's what you want to believe.

Actually, the set theory is used only as a possible model. it shows that the question is a real one and that math and philosophy alone won't solve the issue.
E]i.e. the cause of a being has a cause that has a cause .. and on and on..

A person doesn't have to know about set-theory to 'smell a rat' [/QUOTE]

And what, precisely, is wrong with an infinite regress of causes? You seem to find it counter-intuitive. OK. Others don't find it to be so. OK.

Now, how will the issue be resolved? The only way I know of is to actually LOOK and see what happens in the real world.

And, at that point, we don't have the evidence to determine the facts of this particular question. So we have to wait for an answer until more data comes in.

 

[night912]

If you read the OP, you will see the argument.

Thanks.

Please address my point instead of avoiding it.

Thanks.

 

[Polymath257]

Set theory proves God actually (ultimate set) and would mean nothing can exist without him. OFF-TOPIC but true.

Go on.

In set theory, a universal set is self-contradictory.

 

[Link]

In set theory, a universal set is self-contradictory.

How? Can you show it. I took a class where we taught set theory, I don't recall this.

 

[Polymath257]

How? Can you show it. I took a class where we taught set theory, I don't recall this.

If there is a universal set, then the collection of all subsets of that set has a larger cardinality, but is also a subset of the universal set. That is a contradiction.

My guess is that you were taught what is known as naive set theory. And naive set theory is known to be internally inconsistent.

To get the real story, look into axiomatic set theory.

 

[Link]

If there is a universal set, then the collection of all subsets of that set has a larger cardinality, but is also a subset of the universal set. That is a contradiction.

Why does it have a larger cardinality?

 

[Polymath257]

Why does it have a larger cardinality?

That is known as Cantor's theorem. See Cantor's theorem - Wikipedia

Given any set A, let P(A) be the set of all subsets of A. Then, there is *never* an onto function f:A-> P(A).

But, there is *always* an onto function from any set to any non-empty subset.

In the case where A is a purported universal set, P(A) would be a subset and that would give a contradiction.

If you want specifics, I can give them.

 

[Link]

That is known as Cantor's theorem. See Cantor's theorem - Wikipedia

Given any set A, let P(A) be the set of all subsets of A. Then, there is *never* an onto function f:A-> P(A).

But, there is *always* an onto function from any set to any non-empty subset.

In the case where A is a purported universal set, P(A) would be a subset and that would give a contradiction.

If you want specifics, I can give them.

This is just rephrasing same premise. Can you show why there is no onto function?

 

[Link]

Anyways, seems it might be mathematics ceases to have consistent coherency with ultimate set. I don't think it disproves it even if it was the case.

 

[Polymath257]

This is just rephrasing same premise. Can you show why there is no onto function?

Suppose that f:A->P(A) is any function.

Let B={x in A : x not in f(x) }

Then B is a subset of A and so is an element of P(A).

But if B=f(y), we would have y in B <--> y not in f(y) <--> y not in B, a contradiction.

Hence, f is not onto: B is an element of P(A) that is not the image of any element of A.

 

[Polymath257]

Anyways, seems it might be mathematics ceases to have consistent coherency with ultimate set. I don't think it disproves it even if it was the case.

Well, it is a standard reductio ad absurdum argument.

 

[Link]

I don't understand. I will look more into it and will see a professor to explain it. Are you saying you can't have universal set in a universal set?

 

[Polymath257]

I don't understand. I will look more into it and will see a professor to explain it. Are you saying you can't have universal set in a universal set?

I am saying that if A is a universal set (so it contains all sets), then, in particular, it contains all subsets of itself as elements.

In that case, the power set, P(A) would be a subset of A. That would mean that P(A) has a cardinality no more than that of A.

But, by the argument in my last post, P(A) always has a greater cardinality than A for *any* set A.

This would be a contradiction.

The usual resolution is to say that the collection of all sets isn't a set. it is a different type of thing: a proper class. proper classes can't be elements of other classes.

Naive set theory has a lot of contradictions. This is only one of the many.

The problem is in how sets are constructed: there have to be limitations on what is allowed to be a set. And those limitations will then disallow a universal set.

 

[Link]

Okay, thanks for that.

 

[KWED]

You make it all about infinite sets, which it is not.
One can't make conclusions about the nature of our universe by set theory alone .. that's absurd. It is merely an excuse to say that it is possible that there might be an infinite amount of causes.

As I say, if that's what you believe .. fine. It has little to do with set theory. It's what you want to believe.
i.e. the cause of a being has a cause that has a cause .. and on and on..

A person doesn't have to know about set-theory to 'smell a rat'

You only "smell a rat" because the concept means that you can't arbitrarily insert "god" into the infinite series, and you require an infinite god to be in there somewhere.
To those without such a pre-existing requirement, there is no rat to smell.

 

[muhammad_isa]

You only "smell a rat" because the concept means that you can't arbitrarily insert "god" into the infinite series..

That is not so.
I have an enquiring mind, and I have always found that there are reasons why things happen.
An infinite number of reasons for why something happens is not a satisfactory explanation, as @firedragon has already pointed out.

 

[Polymath257]

Can you provide some evidence of that?

Infinite regress - Wikipedia

Some infinite regresses are vicious and some are not.

"An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress.[1][5] For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious.[1][4] The mere existence of an infinite regress by itself is not a proof for anything.[5] So in addition to connecting the theory to a recursive principle paired with a triggering condition, the argument has to show in which way the resulting regress is vicious.[4][5] ]"