What is wrong with the Kalam Cosmological Argument?

[9-10ths_Penguin]

Yes agree. That is my point infinite is not a number this is why you cant have a infinite number of balls nor an infinite number of seconds nor an infinite number of precursors. (As @Polymath257 claims)

So you disagree with the premises of Zeno's Paradox?

 

[Polymath257]

You have demonstrated that you think of infinity as a number and not as a process. That is why you are always wrong here. There is no "infinity" as a number there is only infinity as a process. That is why @Polymath257 was correct when he said 1 + 1 + 1 . . . is infinite. It is an infinite process that does not end and yet has a beginning. There is no "approaches infinity" as you used the term.

Not quite true. Infinity is not a real number, but there *are* infinite cardinal numbers. And the cardinals are what is relevant in the current context. Infinity is NOT just a process (old terminology-potential infinity). There are *actual* infinities in math and physics.

Infinite sums are standard fare in math and physics. There is nothing contradictory or wrong about them, but special care is required.

As @leroy likes to say, a *finite* sum of finite quantities is finite. but an *infinite* sum of finite quantities can be either finite or infinite.

Ultimately, most theists don't seem to have caught up with modern mathematics. Certainly WLC has not. There are *paradoxes* involving infinite quantities, but no *contradictions*. The paradoxes require one to learn the differences between finite and infinite, but that is the only real issue. many things that are true for finite quantities are false for infinite ones. But that is to be expected.

 

[Polymath257]

That is circular reasoning; we are trying to see if we can have “something infinite” in the real world you can´t solve the problem by invoicing “infinite intervals”

Why not? You are claiming a contradiction where there is not one. You are assuming before the argument comences that the infinite is impossible.

What you are saying is “we can have infinite seconds all you have to do is sum an infinite number of intervals” obviously this argument presupposes (rather than proves) that we can have” infinite something” in the real world.

It shows that you claim of a contradiction is wrong. I am not trying to prove that there is an infinite amount of time. I am trying to prove that it is not a contradictory concept. Whether there is or is not will depend on physic logic.

NO, No, that is potential infinite; which means that infinite is a limit that one “approaches” but never reaches.

In the real world if you add 1 ball + 1ball + 1ball etc you will always get a finite amount of balls

Ah, the old potential infinite vs actual infinite false dichotomy.

YOU were claiming that a sum of finite quantities will always be finite. I showed that an infinite sum can be infinite. You are seeing that as a process, not a finished result, thereby assuming that no actual infinity exists.

It is quite valid to take the limit and *define* that limit as the result of the infinite process.

Yes the issue is that you have to show that it’s possible to have” infinite something” in the real world.

I am merely trying to show that having an infinite amount of something isn't contradictory. it will be a matter of observation and physics to see if there is an actual infinity or not. It is NOT merely a matter of logic alone.

And, there is every reason to believe, for example, that space is infinite in extent. In the realm of quantum gravity, there is every reason to believe that time is infinite in extent going backwards.

These are not questions that can be resolved solely on the basis of philosophy or logic. The only way to tell is by observation and testing.

Both “1” and “0” occurred after the same amount of time, this is the very definition of simultaneous.

Same amount of time *after what*? There is no point in time that they are the same amount of time after.

Second, that is NOT the definition of simultaneous. To be simultaneous means to be at the same time.

I understand (and grant) that if you add a finite interval an infinit amount of times you will get “infinity” as a result.

Good! So it is not a contradictory concept!

Sure if you have an infinite number of sets with 3 balls, you will have infinite balls (3 x infinity = infinity)……….what I don’t gran is that you can have an “infinite something” in the first place ,

And yet, you have given no reason to think such is impossible.

Remember the original claim is that “we can’t have an *infinite something*” in the real world, any argument that presupposes the existence of infinity would be circular.

But it is equally circular to say that there cannot be an infinite something. It is a *logical* possibility. the question then becomes whether it is what actually happens in the real world. And *that* is a matter for physics, not philosophy.

And, from the physics standpoint, an infinite past is NOT an issue. In fact, it seems to be required in many quantum theories of gravity.

 

[Subduction Zone]

Yes agree. That is my point infinite is not a number this is why you cant have a infinite number of balls nor an infinite number of seconds nor an infinite number of precursors. (As @Polymath257 claims)

You can't "have it". That is true,but you have not shown that they cannot exist. You have only claimed that @Polymath257 is wrong but have not supported your claim properly at all.

 

[leroy]

It shows that you claim of a contradiction is wrong. I am not trying to prove that there is an infinite amount of time. I am trying to prove that it is not a contradictory concept. Whether there is or is not will depend on physic logic.

No, No, No I am not saying that your model is contradictory ……..….(your model is not married bachelor)

My objecting is that your model is metaphysically impossible….. (analogous to imaginary numbers, or negative dogs)

The concept of “3i+2 dogs” is logically coherent (no contradictions) but it is metaphysically impossible to have something like that in the real world, (independently of any laws of physics that might excist)………………. So my objection is that the concept of “infinite precursors” is metaphysically impossible, not that the concept is “contradictory”

The reason is simple, the number of precursors is given “by the number of intervals (A)” *” the number of precursors on each interval (B)”

SO if:

1 A and B are finite then the product is finite

2 If any of them is infinite, then you are using circular reasoning because you are presupposing ininite to prove infinite

 

[leroy]

You can't "have it". That is true,but you have not shown that they cannot exist. You have only claimed that @Polymath257 is wrong but have not supported your claim properly at all.

Well if I was unable to support my claim properly, then perhaps you can help me with it. After all we both agree on this point.

We both agree on that infinite is not a number, and therefore you can’t have an infinite number of precursors. and (@Polymath257 woudl claim otherwise)

So perhaps you can help me by formulating a better argument in support of that claim.

 

[Polymath257]

We both agree on that infinite is not a number, and therefore you can’t have an infinite number of precursors. and (@Polymath257 woudl claim otherwise).

OK, but you *can* have an infinite *collection* of precursors.

The word number here is a red herring.

 

[Polymath257]

No, No, No I am not saying that your model is contradictory ……..….(your model is not married bachelor)

My objecting is that your model is metaphysically impossible….. (analogous to imaginary numbers, or negative dogs)

The concept of “3i+2 dogs” is logically coherent (no contradictions) but it is metaphysically impossible to have something like that in the real world, (independently of any laws of physics that might excist)………………. So my objection is that the concept of “infinite precursors” is metaphysically impossible, not that the concept is “contradictory”

Wrong again. 3i+2 is NOT a cardinal. it is a complex number.

The reason is simple, the number of precursors is given “by the number of intervals (A)” *” the number of precursors on each interval (B)”

Not quite (you are assuming the number of precursors is the same for every interval), but OK.

SO if:

1 A and B are finite then the product is finite

Yes, a finite sum of finite quantities is finite. I will happily grant you this.

2 If any of them is infinite, then you are using circular reasoning because you are presupposing ininite to prove infinite

No, I am showing how the assumption of a infinite set is NOT contradictory. In other words, I am showing that you cannot assume that things are only finite.

*You* are the one making a circular argument (assuming everything must be finite to get that everything is finite). A priori, you cannot make that assumption. My claim is NOT that an infinite amount actually exists (that is a matter for observation and testing). My claim is that you cannot *assume* everything is finite since an infinite amount is not a self-contradictory. I claim that there is no metaphysical principle that implies the non-existence of an infinite past.

So what *metaphysical* principle does the existence of an infinite past contradict? Don't assume that everything is finite in the statement of that principle: it has to be a *conclusion*.

 

[Subduction Zone]

Well if I was unable to support my claim properly, then perhaps you can help me with it. After all we both agree on this point.

We both agree on that infinite is not a number, and therefore you can’t have an infinite number of precursors. and (@Polymath257 woudl claim otherwise)

So perhaps you can help me by formulating a better argument in support of that claim.

Lord knows that I have tried. And so have others. When a person refuses to learn there is no help at times.

 

[leroy]

So what *metaphysical* principle does the existence of an infinite past contradict? Don't assume that everything is finite in the statement of that principle: it has to be a *conclusion*.

The sum of any finite amount gives you a finite amount……………..the idea of an eternal past contradicts this principle.

 

[Polymath257]

The sum of any finite amount gives you a finite amount……………..the idea of an eternal past contradicts this principle.

No, the principle is that a sum of finitely many finite amounts gives a finite amount. The result you stated isn't correct: a sum of infinitely many finite quantities can be infinite. And the *correct* principle doesn't contradict an infinite past.

You are, in essence, assuming that ALL sums have only finitely many terms, which you have not proven.

And, in fact, there is also a principle that a sum of anything with an infinite quantity will be infinite.

 

[leroy]

And, in fact, there is also a principle that a sum of anything with an infinite quantity will be infinite.

GRANTED, but how do you get that infinity in the first place?

The age of the universe is given by:………Today’s seconds (finite number) + Yesterdays secocds (finite number) + the day before yesterday (finite number) etc……. therefore the age of the universe is give by a sum of finite numbers.

 

[Polymath257]

GRANTED, but how do you get that infinity in the first place?

Get it from what? You are assuming it is something that needs to be 'gotten' from something else. Like the universe itself, it 'just is' (in this scenario). With no start, there is no need for an overall cause.

In other words, the universe did not 'begin to exist': it always existed. By your own assumptions, it thereby doesn't need a cause.

The age of the universe is given by:………Today’s seconds (finite number) + Yesterdays secocds (finite number) + the day before yesterday (finite number) etc……. therefore the age of the universe is give by a sum of finite numbers.

How many finite numbers? If there is an infinite past, there would be an infinite collection of such numbers, which would give an infinite sum.

 

[leroy]

Get it from what? You are assuming it is something that needs to be 'gotten' from something else. Like the universe itself, it 'just is' (in this scenario). With no start, there is no need for an overall cause.
.

I am not asking for an overall cause of the universe, just for an explanation for how did you get infinity in the first place.

I am claiming that you can’t have infinite seconds … and you answer seems to be “yes all you have to do is start with infinite and then add any finite numbers that you want”

Obviously that is circular reasoning, that is like saying “yes you can have “i+2” dogs all you have to do is start with i and then add 2 dogs. “

Another metaphysical impossibility is that “now” is the consequence of infinite precursors. But since an infinite number of precursors will never occur………we can not arrive at “now”…. Nbut we arrived at now, therefore the number of precursors is finite.

 

[Polymath257]

I am not asking for an overall cause of the universe, just for an explanation for how did you get infinity in the first place.

Since no cause is there, there is no 'reason why'. Again, that is part of my point.

I am claiming that you can’t have infinite seconds … and you answer seems to be “yes all you have to do is start with infinite and then add any finite numbers that you want”

Obviously that is circular reasoning, that is like saying “yes you can have “i+2” dogs all you have to do is start with i and then add 2 dogs. “

No, I am showing one of the necessary conditions for this to happen. You have yet to give a reason why it can't happen past assuming that only finite processes are involved.

The difference is that i is not a cardinal and so 'i dogs' does not make any sense. But, the concept of 'infinitely many dogs' makes perfect sense. The only question is whether it actually applies to the real world.

Another metaphysical impossibility is that “now” is the consequence of infinite precursors. But since an infinite number of precursors will never occur………we can not arrive at “now”…. Nbut we arrived at now, therefore the number of precursors is finite.

And, once again, this was the point of my model (which you agree is consistent). it shows *how* you can 'arrive at now' and *still* have 'infinitely many precursors'.

You beg the question by saying 'an infinite number of precursors will never occur'. Why not? Remember, there is no starting point (as in the model).

I agree that no actual time interval can be finite (between two times), but that is true in my model even though there are infinitely many precursors.

 

[leroy]

Since no cause is there, there is no 'reason why'. Again, that is part of my point.



No, I am showing one of the necessary conditions for this to happen. You have yet to give a reason why it can't happen past assuming that only finite processes are involved.

The difference is that i is not a cardinal and so 'i dogs' does not make any sense. But, the concept of 'infinitely many dogs' makes perfect sense. The only question is whether it actually applies to the real world.



And, once again, this was the point of my model (which you agree is consistent). it shows *how* you can 'arrive at now' and *still* have 'infinitely many precursors'.

You beg the question by saying 'an infinite number of precursors will never occur'. Why not? Remember, there is no starting point (as in the model).

I agree that no actual time interval can be finite (between two times), but that is true in my model even though there are infinitely many precursors.

This is becoming circular, but I appreciate your honest engagement,

In summery I think there are 2 metaphysical impossibilities with the idea of an infinite past

1

A) Any sum of finite numbers will give you a finite number

B) The age of the universe necessarily is the result of a sum of finite numbers (and finite intervals)

C therefore the age of the universe is finite.


2


A) If today is preceded by an infinite amount of seconds, “now will never occur”

B) Today “occurred”

C) Therefore today is not preceded by an infinite amount of seconds

I am aware of your objections and I know exactly which premises would you reject and why so there is no need to repeat the same arguments again.

You beg the question by saying 'an infinite number of precursors will never occur'. Why not? Remember, there is no starting point (as in the model)

.
I don’t see why is this relevant, it is still true that your model requires that you were born after an infinite amount of seconds


As a bonus I would argue that any 2 random points (or seconds) *(the key word is random)* would be infinitely apart, but simultaneous at the same time, (which seems contradictory)

So it seems to me that in order to avoid the contradiction you would have to deny the possibility of having a random point, but that would be odd and it seems to me that you would open a new can of worms if you bite this bullet.