Sunday, May 4, 2008

The Cosmological Argument

The Cosmological Argument is one of the classic arguments for the existence of God. There are actually a ton of variations on the cosmological argument. The general form is as follows:
  1. I exist.
  2. If there is something that exists, then God exists.
  3. Therefore, God exists.
Simple, right? If you accept the two premises, the conclusion logically follows. Of course, the major part of the argument is within the second premise. There are a variety of ways to try to justify the second premise. Here's the form that most people think of:
  1. Every object has a cause.
  2. Causal chains cannot be infinite.
  3. Therefore, if something exists, then it must be the result of a finite causal chain.
  4. The beginning of that chain is God.
The obvious objection here (the one that most people will think of) is that premise 1 applies to God. What caused God? However, this reasoning is specious. It's relatively easy to modify the argument so that no such contradiction appears.
  1. Every contingent object implies the existence of another object, namely, its cause.
  2. Causal chains cannot be infinite.
  3. Therefore, if a contingent object exists, then it must be the result of a finite causal chain, which can only begin with a non-contingent (or "necessary") object.
  4. That necessary object is God.
I hasten to add that "contingent" is sort of a technical word in philosophy. Contingent means that it is true in some possible worlds, but not in all of them. Necessary means that it is true in all possible worlds. For example, I am contingent, since I might not have existed, but 1+1=2 is necessary, because it absolutely must be true.

Now that we've gotten to a reasonably good formulation of the cosmological argument, we can question its premises.

The first premise assumes every contingent object has a cause. But is that really true? I'd question the very idea that causation is a truly fundamental concept. For example, it is possible to describe physical laws without the notions of cause and effect. Furthermore, you have to consider the full range of contingent objects. My keyboard is contingent, and has a cause, but what about more abstract things? Is time contingent, and does it have a cause? Is love contingent, and does it have a cause? Maybe you think so, maybe you don't.

The second premise assumes that causal chains cannot be infinite. But why can't they? Plenty of religions see the world as being in an infinite cycle, so what's logically impossible about that? If a particle is moving along in space, you can say that its arrival at any point B was caused by its previous position at point A. And then you could follow its path back indefinitely. Of course, in our universe, it is difficult to actually do this, because the path will eventually be traced back to the Big Bang. However, as a matter of science, I will say that the Big Bang is not certainly the beginning of the universe, and is almost guaranteed to be a mere wall past which our current understanding of physics is inconsistent. Near the singularity, Quantum Mechanics and General Relativity contradict each other, indicating that we need better theories before we can reliably determine that the Big Bang was truly a beginning.

But my above objections, while valid concerns, are not the real killers of the cosmological argument. The unsolvable problem in the cosmological argument is in step 4. This problem remains in every variation of the cosmological argument I've ever seen. Though we might prove the existence of a necessary being, why must it be God? Perhaps you'll say that the necessary being is God by definition. But if you've given God this new definition, there is no guarantee that it will have all the other traits normally attributed to God. Must the necessary object be conscious? Must it be good? Must it be omnipotent? Must it be singular rather than plural? Would it even make sense to worship, respect, or ponder this object? None of these are guaranteed, much less the idea that the necessary object listens to prayers, or sends prophets.

Personally, I think the necessary object is probably the world. Nothing unusual about that. The world is simply the ground of all possibilities. Without the world, things couldn't possibly exist within it. There you go.

32 comments:

DeralterChemiker said...

I don’t see how you can say that “the Big Bang is not certainly the beginning of the universe, and is almost guaranteed to be a mere wall past which our current understanding of physics is inconsistent.” Since you can’t see past the Big Bang, you have no knowledge whatsoever of what preceded it. All you have is prejudicial intuition, which may or may not be correct.

Also, you are assuming that if God exists, he or it must have the “traits that are normally attributed to God.” That is not necessarily true. You are simply knocking down a “straw man” that you yourself have set up.

Personally, I don’t see why one should be concerned about this. I am quite sure that God, if he or it exists, does not listen or respond to prayers, as any objective person must acknowledge on the basis of countless pieces of evidence. Therefore I see no need for worship, or any advantage in pursuing religious rituals. Nor do I see any harm in rituals, unless these rituals are harming other members of the human race. My loyalty is not to a God, but to the human race, and in acknowledging that loyalty I am merely following the dictates of my DNA.

miller said...

On the Big Bang, you're right. We don't know what preceded it, because it goes into a realm in which current theories are inconsistent. Therefore we have no knowledge of whether it really was a beginning, or what. My prejudicial intuition says it was probably the beginning, but I would not say this with certainty.

On God, I did not assume that God has the traits normally attributed to him/it. I never said you can't call it God. I carefully avoided it, in fact, because I knew you'd object. I was just raising the obvious point that simply calling something a rose doesn't make it smell sweet.

And I also agree with you that one should not be concerned about this too much. But obviously, people are concerned. Now, if only I could get people as excited about critical thinking! I mean, this is just an application of critical thinking here, don't people know?

miller said...

One more thing to add. It's technically not a straw man if there are people out there who actually believe such a position.

Linda said...

Therefore I see no need for worship, or any advantage in pursuing religious rituals. Nor do I see any harm in rituals, unless these rituals are harming other members of the human race. My loyalty is not to a God, but to the human race, and in acknowledging that loyalty I am merely following the dictates of my DNA.

deralterchemiker, (now, that's a mouthful) :-)

May I point out that there are theists who agree with you on this? Also, loyalty is not a pre-requisite to being a believer.

Miller said,
Now, if only I could get people as excited about critical thinking!

We are! We are!

Anonymous said...

Abstractions that are not causally contingent are nevertheless ontologically contingent on some intelligent being that thinks of them. In this case, then, the first premise is still true; every contingent object implies the existence of another object.

This is why, in my opinion, Leibniz's version of the argument is more preferable: its domain isn't restricted to causal explanations, but rather all kinds of explanations.

Regarding the second premise, causal chains cannot be infinite because, firstly, an actual infinity entails the contradictory notion that a part is equal to the whole; for example, a book with an infinite number of pages would be such that the number of its odd-numbered pages are equal to the total number of pages in the book. Similarly, subsume some of the causal agents into a proper subset of the entire set of causal agents, and their respective cardinalities are equal--this is an absurdity.

Presuming that you are an atheist, I can't understand why the tenets of any particular religion would suffice for you as any sort of defense mechanism in what I presume is supposed to be an argument undermining religion in general. To answer your question, though, those Eastern religions contain logical absurdities.

As I am not a physicist, I can't really argue that the Big Bang was the true beginning of the universe, although everything I've read indicates that it is. But the argument, the way I see it, goes deeper than the beginning of our universe; rather, it is based upon truisms such as the Principle of Sufficient Reason, which transcends the physical universe.

That the first cause is God is based upon the notion that every cause must be more powerful than its effect, or else whatever power is had by the effect could not have come from its cause but must have just emerged out of nothing. The first cause is therefore omnipotent. Being omnipotent, the first cause is also omniscient, because a blemish in wisdom precludes maximal power (i.e., a being who possesses all of God's power and whose knowledge includes whatever is not known by God would be more powerful than God by virtue of what he knows). And then there are inferences to be made with regard to self-existence, immateriality, eternity, and so forth. But in the interest of brevity, I'll stop here. (Note, William Lane Craig gives some arguments for why the first cause would be God.)

Larry, The Barefoot Bum said...

Abstractions that are not causally contingent are nevertheless ontologically contingent on some intelligent being that thinks of them.

The comment as a whole is an impressive display of philoso-babble! Kudos!

miller said...

@anonymous,

I don't agree with the premise that all abstractions require a mind to think of them. But even if we accepted that, how does that align with the idea that "causes" are more powerful than their effects? It is easy to think about abstractions more powerful than ourselves. Come to think of it, does the concept of "power" even apply to all abstractions or inanimate objects? For an argument based on intuitive premises, this is very counter-intuitive.

Infinities do not entail that a part is equal to its whole. They entail that the cardinality of a part is equal to the cardinality of a whole. Anyways, if you read any introduction to infinite set theory, they bring up these absurdities, the point being that our intuition is wrong, not that infinities are wrong. I'm always amazed how Lane Craig gets that backwards.

Finally, on cosmology: At some point, the universe was small and dense enough that it was in the quantum gravity regime. As there is no theory of quantum gravity, what happens before that has long been in dispute. Lane Craig and others are in the habit of selectively citing one side of that dispute in a way that always struck me as dishonest. It's funny because, like you, I don't even think this is a necessary part of the cosmological argument. It's just pointless dishonesty.

Anonymous said...

In what sense can an abstraction be more powerful than us? For example, I can conceive of the world's most intelligent human; I can perfectly imagine her answering even the most difficult questions on Jeopard, scoring perfectly on the GRE's, finding the cure for AIDS, and so forth. But the abstraction itself is not intelligent at all; in fact, it is neither cognitive nor sentient. At the very least, a thing having power cannot be inert, and this does not apply to abstractions. To use a more salient example, what causal power, if any, does the number "7" have?

I don't think it is Craig's contention that infinities are "wrong." A mathematical infinite is perfectly okay. Problems ensue only when such things are mapped onto reality, as in the example of the infinity-paged book. This is not an argument from intuition; that A's part is not equal to A's whole is a truism the denial of which results in a logical contradiction. Whether you say this of A's part or the cardinality of A's part, the result is the same.

miller said...

"In what sense can an abstraction be more powerful than us?"

It was your argument which brought up the concept of power; perhaps I should have waited for you to define it. If rain causes a river, does that imply that the rain is more powerful than the river, and what does that even mean? If cancer causes death, does that imply that cancer is more powerful than death, and what does that even mean?

"I don't think it is Craig's contention that infinities are "wrong." A mathematical infinite is perfectly okay. Problems ensue only when such things are mapped onto reality, as in the example of the infinity-paged book. This is not an argument from intuition; that A's part is not equal to A's whole is a truism the denial of which results in a logical contradiction."

You used the word "absurdity", which suggests an intuitive argument. If infinities are problematic, why do they make for such workable mathematical theories? More to the point, there are an infinite number of positions between my right hand and left. If this is problematic, why does it make for such workable physics theories?

Or do you contend that this is a potential infinity rather than an actual one? I cannot get a handle on the potential/actual infinity distinction, because it does not exist anywhere in physics or mathematics, and I've only ever seen it from William Lane Craig. As far as I can tell, he makes the distinction arbitrarily to suit his theological needs.

Anonymous said...

X is more powerful than Y just in case X has greater control than Y over what happens. So for instance, I am more powerful than a single fly, because with a stomp of my foot I am able to end the fly's existence. On the other hand, a fly has very little control over what I do. Further, flys cannot build houses, write poetry, discuss quantum mechanics and so forth. Rain doesn't cause a river; a river is caused by surfaces runoffs, drainage basins, laws of physics governing the cohesion of hydrogen atoms, and various other factors. You are conflating metaphysical notions of causation with colloquial usages of the term, or perhaps with ordinary material conditionals (e.g., if it does not rain, then there is no river).
That we cannot pinpoint exactly what causes something is an epistemological issue, however. The main issue here is that we have two exclusive alternatives, and one of them is necessarily. Either causes are more powerful than their effects, or the surplus of power possessed by the effect comes from nothing.
I used "absurdity" in reference to that which is logically contradictory. Sorry for not clarifying. Infinities are not problematic in mathematics--I've made that clear. They are not so because mathematics deals with abstract infinities. It does not deal with actual infinities; the positions between your two hands are abstract. (I'm not familiar with any physics theory based on the assumption that there are actually these concrete non-mental objects called "positions" which exist between your two hands.
The potential/actual distinction between infinites has existed in philosophy for thousands of years. I believe it is still accepted in most of philosophy. Read Aristotle's solution to Zeno's paradox.

miller said...

"Rain doesn't cause a river; a river is caused by surfaces runoffs, drainage basins, laws of physics governing the cohesion of hydrogen atoms, and various other factors."

So... are any of those more powerful than the river, in the sense of having greater control over what happens?

"You are conflating metaphysical notions of causation with colloquial usages of the term, or perhaps with ordinary material conditionals (e.g., if it does not rain, then there is no river)."

Gee, you're right. I also forgot to wait for you to define causation. ...

"I'm not familiar with any physics theory based on the assumption that there are actually these concrete non-mental objects called "positions" which exist between your two hands."

There is an electric field at every position. Is this a mental object only? All objects in physics are mental objects, which we posit as real. My point isn't even that they are real objects. My point is that they are conceivably real objects, contrary to your argument that actual infinities are impossible in the real world.

Anonymous said...

All of them put together are more powerful than the river, in the sense of having greater control over what happens.

Causation is the production of an effect.

All objects in physics are physical objects, or are you claiming that gravity and planetary motion are merely figments of my imagination?

Actual infinites are impossible in the real world--unless you can show me a book with an infinite number of pages, or a hotel with an infinite number of rooms, or a basket with an infinite number of eggs, and so on. Can you?

Anonymous said...

I have no idea about electric fields. Are there an infinite number of them? If so, can you refer me to any physicists who vindicate this so as to undermine further the credibility of physicists who presume themselves philosophers and thus tread upon issues the discussions of which they have no business participating in?

miller said...

I'm not sure that surface runoffs, drainage basins, water cohesion, or rivers have any control over anything. But I've learned my lesson; I should wait for you to define "control".

I'm also unclear on how cancer does not cause death under your given definition, but I think we've all had enough of this. I'll drop the point.

"All objects in physics are physical objects, or are you claiming that gravity and planetary motion are merely figments of my imagination?"

No, I think gravity, planetary motion, and electric fields are real. I just thought you might deny the reality of electric fields (you didn't), and my response is to point out that it doesn't even matter if they are not real, just that they could be real. Your argument suggests that they couldn't possibly be real objects.

"Actual infinites are impossible in the real world--unless you can show me a book with an infinite number of pages, or a hotel with an infinite number of rooms, or a basket with an infinite number of eggs, and so on. Can you?"

Under standard cosmology, the universe is infinite in extent, and uniform on the largest scales. We cannot see this, because of the finite speed of light and finite time since the big bang. This implies an infinite cardinality of stars. This may or may not be true, but are you willing to reject it on purely philosophical grounds? I'm not.

I just don't think actual infinities can be logically contradictory in reality, but okay in mathematics. Logic applies just as much in mathematics as in reality, if not more so. Infinities are built into much of our understanding of reality. Real numbers, derivatives, integrals, are all based on infinite sets. It's just not a big deal, you know?

(Judging from the length of this last comment, you are getting sick of this. So let that be my concluding remark. You may have the last word.)

Anonymous said...

I don't want this to be your last comment. I'd like the discussion to continue. The only reason that I was being condescending is that I felt like you were. If this is just your way, then I apologize. But please, let the discussion continue. I'm enjoying this.

Anyway, I really don't know how to define "control." I can only give you examples of one thing controlling something else. I'm sure we could draw out this debate for eons if we continually ask one another to define words, only to then request definitions of other words included in the definition just posited.

I really don't know enough about biology to know how death works. But this is an issue of causal epistemology, and I don't claim to know every single cause of every single effect.

Here's the bottom line which you need to address: Individual things have certain potencies--there are certain things that they can and cannot do. Now, for those things that they can do, from where do they obtain those abilities? Are such abilities self-created, or are they given by something else? Since the former is not logically possible (your attributes cannot just emerge out of nothing, after all), this pretty much solidifies that all causes are more powerful than their effects.

Now, my argument is not simply that actual infinities do not exist in reality; I'm saying that they *cannot*. Evidently, you are saying that they can, and you use the example of electric fields. I have no idea about electric fields, but if they are defined as an actual infinity of something, then my answer is the same; they canot possibly be real objects.

I don't know a lot about standard cosmology, but I was under the impression that the universe is gradually inflating; therefore, it cannot be infinite in extent, or else something that is infinitely long is possibly longer than it already was. I'm also not seeing why this would imply a particular amount of stars. Are stars required in order for our universe to exist?

Anyway, I am rejected this on purely logical grounds. I think when physicists encounter a contradictory notion, then they need to rethink their theory and start over. A universe infinite in extent with an infinite number of stars is logically impossible, because that would entail the contradictory notion that some proper subset of A has a cardinality smaller than that of A.

Actual infinites are not okay in mathematics. They are not okay anywhere. They are contradictory in math, science, philosophy and everywhere else. The point is, the set of natural numbers is not *actually* infinite; it's only potentially infinite. The reason mathematicians don't use this term is that they're generally not interested in philosophical issues, but I'm sure they would be willing to grant that numbers are only abstract concepts.

Please continue with the discussion. Thanks.

miller said...

Very well, just one more comment, because I don't think I have much more to say.

I'm surprised that you are saying:
1) Electric fields, which exist at an infinite number of points, cannot be real objects.
2) Uniform cosmology cannot be true on purely logical grounds.
3) Actual infinities are not possible in mathematics.

I feel you are biting the bullet, so to speak.

William Lane Craig identifies actual infinities with aleph-null, which is a perfectly consistent concept within mathematics. It's well-accepted that the cardinality of an infinite set can be equal to the cardinality of a proper subset. No contradiction has ever been derived from this. As for real objects in the real world, they might not be as imaginitive as mathematics, but I don't see why they couldn't be.

Anonymous said...

I think I made a mistake. I just realized it. Therefore, I'm going to throw in the towel and declare you the winner of the debate.

Thanks for your time.

Charles said...

In mathematics, the cardinality of an infinite set can be equal to that of a proper set. But this becomes problematic as soon as you map that onto reality. Real objects do not have numbers attached to them; e.g., "12" is not an intrinsic property to a dozen eggs in the Super Market. It's just how we conceptualize them. This is why Zeno's paradox is fallacious: it falsely assumes that there really are half-points between two locations, when in reality the half-points are just imagined by us to be there.

miller said...

Charles,
I feel that your comment is missing a supporting argument. But thanks for explaining.

Charles said...

I guess a supporting argument could be this: If you assume that numbers are real properties of the universe, then you would have to assume that there are an infinite number of half points between any two distances. But if that was the case, then we wouldn't be able to move, because nobody can traverse that many half points. We do move, however, and therefore there are not really an infinite number of half points between any two distances.

miller said...

"...nobody can traverse that many half points."
Care to justify this statement? Seriously, I want to hear more.

Charles said...

Sure. Every time we move, an instant of time passes by. It follows that if we traverse an infinite number of half-points (or for that matter, an infinite number of inches, feet, miles, kilometers and so on), then we would exist eternally (that is, for an infinite amount of time). So the argument is thus stated:

(1) If everytime we move we traverse an infinite number of half-points, then we exist eternally.

(2) We do not exist eternally.

(3) Therefore, we do not traverse an infinite number of half-points everytime we move.

You could also posit that if a necessary condition for reaching a point in space includes reaching its half-point, and there are an infinite number of half-points, then there's a infinite regress of motion conditions unfulfilled.
So, on the one hand, we know that there's not an infinite number of half-points by virtue of our finite existence, and on the other hand, we empirically observe that the conditions for movement are fulfilled.

miller said...

What if there are an infinite number of instants within a finite length of time, just as there are an infinite number of positions within a finite distance?

Charles said...

That's like asking if there could be 12 miles between two bookshelves that are only 12 feet apart.

miller said...

Not really. A mile is longer than a foot. An instant has zero length. You can cram as many instants into a minute as you like. Or can you explain the impossibility of this?

Charles said...

"You can cram as many instants into a minute as you like."

Theists agree on this point. Any distance--whether temporal or otherwise--can be divided indefinitely without limit. The question is, do those mathematical points have any reality beyond our conceptualizations, or as you put it, beyond our cramming of them?

"An instant has zero length"

If you are defining "instant" as a moment without temporal length (which is basically the same as a space with no dimensions), then I'm inclined to agree that instants can be infinite in number. Indeed, that nothing can be infinite in number--at least in the concrete sense--has been my contention from the outset.

Again, if we traverse an infinite number of distances, then how come human beings are ceasing to exist?

miller said...

So, answer my earlier question. Why can't we traverse an infinite number of positions in a finite amount of time? Each position corresponds to an instant, and you just admitted that we can have an infinite number of instants in a minute.

Charles said...

No, I said that we can divide lengths of time indefinitely without limit, and that if you define "instant" vacuously as a temporal distance of zero length, then "instant" refers to nothing.

My answer is the same: traversing an infinite number of positions would take all of eternity to accomplish, and we are not eternal beings.

miller said...

Well, it seems that you are justifying the claim that lengths cannot be divided infinitely with the assertion that time cannot be divided infinitely. And how are you justifying this assertion? I can't disagree with you until you actually make a complete argument.

Charles said...

I didn't say that time cannot be divided infinitely, nor did I say that of lengths. In fact, I said the exact opposite. I said that mathematical points have no existence beyond our conceptualizations. Do you have any evidence that they do?

miller said...

I don't think you're ever going to provide a clear and complete argument, Charles.

Charles said...

I've given you two of them.