The Problem with Cosmological Arguments?

[NowAgnostic]

Most every cosmological argument I have seen ends with a big leap, for instance Aquinas’ “…and this all men call God” or involves a special plead somewhere (e.g. insisting His actions need no cause, but everyone else’s do), or ends in modal collapse. Is there possibly a fundamental modal problem with them? They are attempting to argue from something contingent to something necessary. The arguments go like this:

Necessarily, if (some feature about the world), then some entity “god” exists.

But that doesn’t mean

If (some feature about the world) then some entity “god” necessarily exists.

That’s the classic modal fallacy. You would also need

Necessarily, if not (some feature about the world), then some entity “god” exists.

to show that “god” exists necessarily. But if you could show that, then you would have an ontological proof, not a cosmological one, for it wouldn’t matter if that feature was present in the actual world or not.

It’s rather fundamental in logic that one cannot argue from a contingent fact to a necessary one. How can cosmological arguments get around this? They can’t. It’s not possible for a contingent fact to entail a necessary one.

In fairness to cosmological arguments, especially some of the modern manifestations, what they attempt to show is that a world with only contingent entities to be impossible. Therefore the space of logically possible universes either consists of those with God (a necessary being) in them, or a null-world. But something exists, ergo God exists.

The flaw is very subtle. But to see it you need to ask why the null-world is an impossible world, exactly what contradiction is entailed? The only possibility of course is that “God does not exist” is itself a contradiction. Now, exactly what contradiction is entailed by a world with only contingent entities, but not when God is added to the mix? The only thing different between the two worlds is that God exists, so that shows the only contradiction entailed by the world with only contingent entities, again, is that “God does not exist”. But that’s of course just as much begging the question as to whether that really is a contradiction, or, conversely, a tautology if His existence is logically impossible, as if we argued the null-world entailed a contradiction.

So basically, either there’s a valid ontological argument or it’s bust.

 

[flyingfish]

It’s rather fundamental in logic that one cannot argue from a contingent fact to a necessary one.

Can you explain why this is so? Intuitively, it doesn’t make sense to me.

The flaw is very subtle. But to see it you need to ask why the null-world is an impossible world

Offhand, the “null-world” is an impossible world because it’s not a world.

Also, why is “Necessarily, if (some feature about the world), then some entity “god” exists.” not sufficient?

I see the distinction you are making, i.e. that if a “null-world” is possible then the argument (if contingent world exists) then (god exists) doesn’t lead to “god exists” in all cases.

But I don’t see the flaw in this argument + “contingent world does exist” to imply that god exists.

Explain better?

 

[angelsdefendus]

If it wasn’t so late I would go into this more, but I hope someone reads this and expands.

The whole cosmo- v. onto- dichotomy is flawed as a premise. It presupposes the ability to start “backwards” to explain the existence of God. I don’t think this is true… and therefore it is quite possible that modal logic cannot create that proof.

It is quite possible to go the other way… in the cosmo- argument, but most philo- folks wont go that way because they are so “stuck” on form.

I hope I typed enough to explain. There is a lot more to this, and I may not have given enough “meat” to do it justice.

 

[NowAgnostic]

Can you explain why this is so? Intuitively, it doesn’t make sense to me.

Well, a contingent fact obtains in at least one, but not all, possible worlds. Whereas a necessary fact obtains in all possible worlds. Whatever is entailed by that contingent fact is only entailed in those worlds where it is true.

Offhand, the “null-world” is an impossible world because it’s not a world.

That’s arguing semantics. An empty set is still a set.

Also, why is “Necessarily, if (some feature about the world), then some entity “god” exists.” not sufficient?

Because God, by definition, must exist necessarily. But whatever is shown in the consequent of the argument is not necessary but only contingent since the antecedent is contingent.

I see the distinction you are making, i.e. that if a “null-world” is possible then the argument (if contingent world exists) then (god exists) doesn’t lead to “god exists” in all cases.

Correct.

But I don’t see the flaw in this argument + “contingent world does exist” to imply that god exists.

Explain better?

Because god hasn’t been shown to exist necessarily, in all worlds.

I’ll try to explain it another way. It’s a bit long-winded so please bear with me.

The cosmological argument is trying to argue as follows:

(Contingent beings exist) && ~(God exists) → a contradiction (let’s call it x).

Necessarily, ~x

Therefore

~((Contingent beings exist) && ~(God exists)) (MT) which means

~(Contingent beings exist) V (God exists).

But contingent beings exists, therefore God exists.

The question is what is x, the contradiction implied by the conjunction of contingent beings existing and God not existing. Note that because “God exists” is a necessary truth (assuming He in fact, does exist) the possibility is that the contradiction implied is nothing more than “God does not exist”. It’s like saying what is the contradiction implied by the conjunction of “the sky is blue” and “2+2=5”.

If the conjunction of A and B entail a contradiction, there are a number of possibilities as to how this could be so:

1. A itself entails a contradiction,
2. B itself entails a contradiction,
3. A entails ~B,
4. B entails ~A,

But which of these are applicable depends on the modal status of A and B. If A and B are contingent (not necessarily true or false), then they cannot in themselves entail a contradiction and thus one must look to 3 or 4. If A and B are both necessary one must look to 1 and 2. 3 or 4 **may **also be true (the conjunction of 2+2=4 and 2+2=5 since 2+2=4 entails 2+2 != 5) but A and B could also be completely unrelated, e.g. the conjunction of “2+2=4” and “all married men are bachelors” entails a contradiction but neither 3 nor 4 are the case.

What if A is contingent and B is necessary (the case under discussion)? Obviously we reject 1 and accept 2 as possibilities. Then, we can distinguish the hypothetical cases in which B is true from those in which B is false. If B is true the conjunction is true. 2 is false. 3 and 4 are false by definition. If B is necessary it holds in all possible worlds; its negation cannot possibly be entailed by anything (3). If A is contingent it holds in at least one, but not all, possible worlds, its negation cannot possibly be entailed existing in every possible world (4). So therefore for the the conjunction to be false B must be false. If B is false, 2 is true. What about 3 and 4? 3 is trivially true, or false, depending on how entailment is conceived, it’s a statement like “if apples are red, then 2 + 2 =4” - the consequent is necessarily true and thus does not follow as a logical consequence from the contingent antecedent. 4 is irrelevant because the antecedent is necessarily false - a necessarily false statement cannot entail anything. It’s like asking “if 2 + 2 = 5, then…” So what we see is that the only contradiction that really “applies” is that B itself is a contradiction.

To sum up, there are two ways of trying to put the CA:

1. If contingent beings exist, then God exists.

But God’s existence, being a necessary fact, cannot follow as a logical consequence from a contingent fact. Any consequence of contingent facts only holds in the worlds in which those facts hold. Again, it’s like saying, if apples are red, then 2 + 2 = 4.

Or one could try the contrapositive:
2) If God does not exist, then contingent beings would not exist. But contingent beings exist. Therefore, God exists (MT).

But nothing can be entailed by a necessarily false antecedent. Again, it’s like saying, if 2 + 2 = 5, then… or, if Socrates is a man and Socrates is not a man, then…

Hope this makes it clearer.

 

[punkforchrist]

There’s much to say about this, NowAgnostic, but I’ll just comment that, your thoughtful inquiry aside, the objection only applies to Leibnizian versions of the cosmological argument. Other cosmological arguments (Thomistic and kalam) don’t involve logical necessity/contingency.

 

[NowAgnostic]

There’s much to say about this, NowAgnostic, but I’ll just comment that, your thoughtful inquiry aside, the objection only applies to Leibnizian versions of the cosmological argument. Other cosmological arguments (Thomistic and kalam) don’t involve logical necessity/contingency.

Agreed, they do not show a logically, but only a metaphysically necessary, being. But then the further question arises, can a logically contingent being be God?

 

[James_S_Saint]

Agreed, they do not show a logically, but only a metaphysically necessary, being. But then the further question arises, can a logically contingent being be God?

NowAgnostic, Metaphysics is not separate from logic.

The connection being stressed in both the cosmological argument and the ontological argument is the presumption of logic and definitions.

Many proposals, not including definitions, presume the reader to use what the author used for concepts. That is a natural weakness for any argument.

Ontological arguments declare definition. But in so doing, they get accused of inventing the definition just for sake of manufacturing an favorable argument.

In both cases, logic is assumed although seldom clearly and rigidly adhered to. The ontological argument emphasizes the logic whereas the cosmological argument emphasizes the apparent evidence and presumes logic to be obvious, though it seldom is to many readers.

In most cases there is more error on the part of the reader, but it only takes one small imperfection on the part of the author to allow for an adversary to attack.

 

[flyingfish]

Well, a contingent fact obtains in at least one, but not all, possible worlds. Whereas a necessary fact obtains in all possible worlds. Whatever is entailed by that contingent fact is only entailed in those worlds where it is true.

Okay, I was bothered a lot by your idea of a “null world” (I still don’t think a null world is a world).

But as I understand your argument works just as well if you say that the the cosmological argument fails to prove the existence of a necessary being if it is possible for nothing at all to exist.

One question that I have, is why must “necessary being” be defined as a being that must exist in any world that could have arisen.

For example, why can’t it be understood that any world that exists must necessarily have a starting point, but that this starting point is not necessarily the same one. i.e. A god must exist, but which kind of god would be different for each possible world?

 

[NowAgnostic]

NowAgnostic, Metaphysics is not separate from logic.

Nothing is separate from logic. Everything, at the very least, assumes law of identity, excluded middle, and non-contradiction. Yet any other kind of “necessity” is not logical necessity - it is only “necessity” according to a certain accessibility relation and thus can be described as “non-necessity” in a different relation.

 

[James_S_Saint]

Nothing is separate from logic. Everything, at the very least, assumes law of identity, excluded middle, and non-contradiction.

Well, we might the minority in such a belief. But if you take that even more seriously to heart than you do already and assume that perhaps ALL others (on all sides) merely have trouble not accepting anything that isn’t of logic, then everything begins to fall into place - everything. The right people are sometimes the wrong people and the wrong people are sometimes the right people.

 

[NowAgnostic]

Okay, I was bothered a lot by your idea of a “null world” (I still don’t think a null world is a world).

OK, I guess we’ll just have to agree to disagree. I still think an empty set is a set.

But as I understand your argument works just as well if you say that the the cosmological argument fails to prove the existence of a necessary being if it is possible for nothing at all to exist.

Right. If it is possible for nothing at all to exist, then it is in fact impossible for a necessary being to exist. And it could only be impossible for nothing at all to exist because a necessary being exists.

One question that I have, is why must “necessary being” be defined as a being that must exist in any world that could have arisen.

Because a necessary being is, by definition, a being whose non-existence is a logical contradiction. Just like 2+2=4 must be true in any world that could have arisen.

For example, why can’t it be understood that any world that exists must necessarily have a starting point, but that this starting point is not necessarily the same one. i.e. A god must exist, but which kind of god would be different for each possible world?

Then each god would be a logically contingent god. The logically necessary fact would be that a god exists, but which god exists would be logically contingent

 

[flyingfish]

OK, I guess we’ll just have to agree to disagree. I still think an empty set is a set.

I agree with you about a set, but an empty set still has the framework of a set so it’s not the same as there being nothing at all (you could say, put things in this set if you wanted to). Another way to see that an empty set is not the same as nothing is that an empty set differs from an empty sequence.

What is an empty world? Is it the existence of physical laws then without space, time, matter and so on to fill it out? It doesn’t make sense. An empty world can’t even have that framework, it’s a nothing.

Right. If it is possible for nothing at all to exist, then it is in fact impossible for a necessary being to exist. And it could only be impossible for nothing at all to exist because a necessary being exists.

Makes sense.

So the point you are making is that CA attempts to show that it’s impossible for nothing to exist (via a necessary being), and you’re saying it can never do that?

Then each god would be a logically contingent god. The logically necessary fact would be that a god exists, but which god exists would be logically contingent

Does this kind of god still serve the purpose that the CA is supposed to serve? (i.e. get rid of the infinite regress) Or must we then wonder why god A and not god B, and must there be a metagod that necessarily determines this?

I don’t know, to be honest the only way any of this makes sense to me is that there is only one thing that must necessarily exist, and that time and therefore causation is only something we perceive as a segment of the one thing, not something that actually is.

 

[James_S_Saint]

What is an empty world? Is it the existence of physical laws then without space, time, matter and so on to fill it out? It doesn’t make sense. An empty world can’t even have that framework, it’s a nothing.

Are you talking about a “world” void of logic as well??

All you need is logic to bring about all real existence. But if you are thinking of an illogical world, then nothing you say about it is valid, including any proposal that it could exist.

 

[flyingfish]

Are you talking about a “world” void of logic as well??

All you need is logic to bring about all real existence. But if you are thinking of an illogical world, then nothing you say about it is valid, including any proposal that it could exist.

Right, I think if something has logic then you can’t call it a “null world”. It’s a world that has logic (might well have a very alien type of logic with say 12 different truth values).

And I think a world with logic wouldn’t serve the OP’s purpose, because then you might ask whence the logic, why this type of logic, and then you could use the argument. You’d need a true nothing.

 

[James_S_Saint]

Right, I think if something has logic then you can’t call it a “null world”. It’s a world that has logic (might well have a very alien type of logic with say 12 different truth values).

That is the true deep fallacy. There isn’t an option for what is logical. Logic really only has one principle without which it isn’t logic - non-contradiction of identity, “what is cannot also be what isn’t”. Aristotle stated 3, but in reality his first isn’t about reality itself but the use of logic in language and his 3rd is exactly incorrect, the opposite is true (where there are 2, there is ALWAYS a third).

But note even in stating that he who laid out the most used laws of logic was incorrect, I must have some kind of higher rule by which to go. How could I prove him wrong if he is defining what is right? I can prove him wrong because he wasn’t defining “logic”, but attempting to reveal what was already there.

Logic is not an invention, but a discovery. It never changes, it can never change, in any “possible world”.

 

[flyingfish]

That is the true deep fallacy. There isn’t an option for what is logical. Logic really only has one principle without which it isn’t logic - non-contradiction of identity, “what is cannot also be what isn’t”. Aristotle stated 3, but in reality his first isn’t about reality itself but the use of logic in language and his 3rd is exactly incorrect, the opposite is true (where there are 2, there is ALWAYS a third).

But note even in stating that he who laid out the most used laws of logic was incorrect, I must have some kind of higher rule by which to go. How could I prove him wrong if he is defining what is right? I can prove him wrong because he wasn’t defining “logic”, but attempting to reveal what was already there.

Logic is not an invention, but a discovery. It never changes, it can never change, in any “possible world”.

You can accept that as an axiom, but you can’t logically prove that the logic that makes sense to us is the one, true, and only possible logic.

I would suspect that what is logical is strongly tied to the fundamental laws of physics, and that if those were to change, so would logic. Must the laws of physics be this way and no other way? No one knows. It’s like asking why something rather than nothing. There is no answer.

For that matter, the logic that seems to make sense to us might only make sense to us because of the environment our brains evolved in. en.wikipedia.org/wiki/Quantum_logic

But I am derailing

 

[punkforchrist]

Agreed, they do not show a logically, but only a metaphysically necessary, being. But then the further question arises, can a logically contingent being be God?

Swinburne seems to think so.

 

[James_S_Saint]

You can accept that as an axiom, but you can’t logically prove that the logic that makes sense to us is the one, true, and only possible logic.

I would suspect that what is logical is strongly tied to the fundamental laws of physics, and that if those were to change, so would logic. Must the laws of physics be this way and no other way? No one knows. It’s like asking why something rather than nothing. There is no answer.

I’m certain that the “logic” that makes sense to you is not the “one, true, only possible logic”. What makes sense to any one person is not merely an issue of logic, especially if they don’t really know how to use logic in the first place. What does calculus prove to someone who never got past the 3rd grade?

The laws of physics are derived by the laws of logic, not the other way around, despite what the Quantum Magi want people to believe for sake of their lust to be God.