plantingaquinasus

Filled in your assertions is the supposition that an actual infinite can exist. If we assume that when you say the words "from eternity" you mean that an actual infinite amount of time elapsed before today. I'm sure you're familiar with the philosopical difficuties that have been proposed through the years that have given that idea serious doubt.

While I agree with you that it is possible that something can have a sustaining cause, this does not take away from the fact that the "stuff" being sustained in existence has the possibility of existing "from eternity" due to the philosophical difficulties having to do with the synonomous idea of an actual infinite.

I think the point that's being proved through your analogy of the music and the orchestra is flawed and in your own words, rest on multiple suppositions (which can be debated and argued and should not be taken as givens). When you say, "We can consistently hold that the music exists from eternity and also hold that the music has a cause, if we suppose that the orchestra exists from eternity."; "music existing from eternity" and "music having a cause" seem to be mutally exclusive. If something has existed from eternity then that would preclude the possibility of it having a cause. You base your statement on the
supposition the orchestra exists from eternity. But this all rests on the question of whether or not an actual infinite applies to the real world (and my statement rests on whether or not what you mean by "from eternity" correctly corresponds to an "actual infinite").

Also, when you say, "an orchestra performing at a concert is the sustaining cause of the existence of the music"; it does not follow that just because there is a sustaining cause of the music, then the music must exist from eternity. A sustaining cause is not the only cause we should consider in questions on origins (effecient cause). We would also have to consider (with respect to your analogy) if the sustaining cause would need an effecient cause (in this analogy's case it would seem so; for an orchestra is a contingent existent).

So it seems that our anology fails to do 1.) problems relating to your ambiguous meaning of "from eternity" relating (possibly) to the impossibility of an actual infinite existing and 2.)insufficient comparisons (orchestra being the sustaining cause of the music being analagous to God being the sustaining cause of the universe, but the orchestra being contigent and God being necessary) between God and the orchestra and 3.)failing to realize the nature of the sustaining cause and how it doesn't totally elimate the possibility of there existing an efficient cause to accompany it.

All issues aside, I'm 19 year old Christian and a sophmore in college and am excited to see someone near my age (but younger) interested in this field of study.

God Bless!!

[ July 22, 2002: Message edited by: plantingaquinasus ]</p>

Theli

Philip Osborne...

This line made me halt. How can something be outside the cosmos and cause it at the same time?
How can it be outside something wich doesn't exist yet?

SRB

Here are some objections to the main argument:

Objection #1
The proponent of the argument is committed to an inconsistent set of assertions. Recall that q is "The Conjunctive Positive Fact," the aggregate of all positive facts in the actual world reporting the existence of every contingent existent. One of the facts contained in q is "all of time exists." Now, a consequence of axiom 3 is that something cannot be brought into existence if it already exists, from which it follows that all of time cannot be caused to exist (since nothing can exist before all time). It follows that there is at least one fact mentioned in q which has no cause, from which it follows that axiom 2 is false.


Objection #2
The proof of corollary 1 is invalid, since it assumes without argument that contingency (of facts) is distributive. In other words it assumes that if a, b and c are contingently existing entities then it follows that their aggregate exists contingently. However, this is not obvious. It might be true that entities a, b and c can individually go out of existence or never come into existence, even though when they all exist together they do so necessarily. Some argument is needed to establish that contingency is distributive. Note that many theists hold the related belief that it is possible that God never existed, but that if he ever exists then he cannot go out of existence.


Objection #3
The proof of corollary 2 is invalid, since an existent could have more than one cause. Corollary 2 needs to be rewritten "q has one or more causes, x." One consequence of this change is that the conclusion of the argument should be modified to say that there are one *or more* necessary first causes of all contingent entities.


Objection #4
It is philosophically possible (WL Craig's efforts notwithstanding) that time is infinite and that everything that ever existed was caused to exist by a contingent existent in an infinite chain. Since this theory cannot obviously be ruled out, and since axiom 2 entails that this theory is false, axiom 2 is suspect and can be reasonably denied.


Objection #5
Axiom 2 becomes less plausible the further removed we become from everyday life. If Big Bang theory is true then in the situation at the origin of the universe the physical conditions were incomprehensibly different to what they are here and now. The physical regularities as we know them are thought to have broken down in those circumstances. Any inductive inferences about causal relations in such circumstances based on our everyday experiences are bound to be hopelessly weak, and that makes the support for a strong generalisation like axiom 2 hopelessly weak. Quite aside from Big Bang considerations, I also agree with others here that the existence of every positive fact is a very special and unusual sort of fact. Any inductive inferences about it will be very weak for that reason.


Objection #6
There is supposed to be inductive support for axiom 2, but consider how, once permitted, such inductive considerations pull in different directions. Consider that every individual existent in our experience that was uncontroversially caused to exist had a contingent cause. To be consistent, the defender of the argument must concede that this provides us with good inductive evidence that *every* individual existent has a contingent cause. However, this conflicts with the proposition that the argument is sound, and so presumably constitutes inductive evidence that axiom 2 is false. For this reason it is hard to see why inductive considerations, even if we permit them, support axiom 2 over its negation.

SRB

WJ

Hi Phil/Plant!

Great post and lots of great responses. I'd like to briefly explore questions of existence (consciousness) relative to perhaps axiom #2. I too am a Christian and believe thru cosmological inference and analogy that God is a necessary Being and necessarily exists.

My question (about conscious existence) to both of you relates to contingency and necessity. Firstly, do you consider the will (v. intellect and reason) as an existing thing, to be necessary or contingent? Or said another way, how does the will interact with the intellect and the ability to reason?

Again, great post!

Walrus

Philip Osborne

I find that my responses are getting longer and longer.

"There's nothing in the idea that you can say, Oh, no -- that's not the sort of cause I was hoping for, so it can't be *that*...'"

Let us suppose first that an essential property of a lump of coal is that it possibly can be caused to exist. Let us also suppose that causes do not necessitate their effects. "a" is the statement, "something causes a lump of coal to exist." "b" is the statement, "a lump of coal exists." Using the S5 system of modal logic, we can construct the following proof that there are no necessary lumps of coal.

1. a =&gt; ~Lb (Causes do not necessitate their effects)
2. L(a =&gt; ~Lb) (Necessitation axiom on 1)
3. Ma =&gt; M~Lb (Theorem of S5: L[p =&gt; q] =&gt; [Mp =&gt; Mq])
4. Lb =&gt; LLb (Modal axiom S4)
5. M~Lb =&gt; ~Lb (Contrapositive of 4)
6. ~Lb (Modus ponens, 3, 5)

As long as it is reasonable to suppose that all lumps of coal could possibly have been caused to exist, none can be considered necessary. One could respond, "A necessary lump of coal couldn't be caused to exist," but this simply attacks the conclusion of the argument, without either engaging any of its premisses or even attempting to render intelligible the notion of a lump of coal that cannot, in principle, have a cause of its existence (keeping in mind such a cause need not be a sufficient condition for the existence of the coal). This follows for any arbitrary feature of our world.

I am indeed aware that you attempted some backfilling to shore up "Axiom" 2. I saw nothing that defused the familiar...."

Let us suppose at least that I am right that aggregates normally have causes, but that you are right in supposing that this does not solve the alleged fallacy of composition (your expression that you are not persuaded doesn't seem to carry much weight). In that case, we can construct a variation on my argument. I am going to assume every fact involves at least one individual and one property of that individual. By Axiom 3, if something is caused, this cause must involve at least one other individual. I am going to call any cause which involves only contingent beings a "positive cause."

1. Assume there is at least one positive fact x.
2. This fact has a cause, y. (By Axiom 2)
3. If y is not a positive cause, then we are through with the argument. So assume it is positive.
4. Since there is at least one positive cause of x, there is a sum or aggregate of all positive causes of x, which I will call "BC(x)."
5. BC(x) has a cause, H. (by Axiom 2)
6. Assume the causal relation is transitive. If a is a cause of b, and b is a cause of c, then a is a cause of c.
7. By 7, H is a cause of x.
8. Suppose, H is positive. In that case, H overlaps with BC(x), since H is a cause of x.
9. Causes and effects do not overlap.
10. Hence, H is not positive.

By excluded middle, and the assumption at the beginning of the argument that every fact involves at least one individual, we must assume that H expresses the causal action of a necessary being.

"Your argument is entierly consistent with the atheistic cosmological principle; Some facts about the universe could be described as positive whereas some...."

I have already conceded that not every fact in the universe is positive. This is not inconsistent with the supposition that the aggregate of all positive facts requires a cause which involves a necessary being, so it is unclear how your objection is to work. Of course, according to the Genesis account of creation, however one interprets it, everything God creates can be expressed in terms of a positive fact. So it would seem to me that the argument is Biblically acceptable.

"You have given no argument, however, which gives us any reason to believe that something that might account for existence...."

I have expressed my "assumption" in terms of Axiom 3, "Causes and effects do not overlap." This axiom is the reason the cause must be ontologically distinct fro its effect, but it is hardly "informal." This is an extension of Hume's principle that causes and effects must be "seperate existences," and that nothing can cause itself to exist.

"On the level of minimalism, QM does not have any actual causal mechanism. Nonlocality, for example, can’t be described...."

At least from my knowledge of QM, it is not necessarily so that there are absolutely no causes whatsoever, but that causes are indeterministic and are not sufficient conditions for the existence of their effects. If this is so, it is entirely consistent with my argument, since I have not stated that causes are sufficient conditions for their effects.

"btw, I nominate Philip for the most coherent Christian philosopher on this BB."

Thanks for the compliments. I appreciate that, especially from people with opposing points of view.

"Wrong! q is not well-defined. q makes about as much sense as a square circle (which is to say none at all)."

I'm sorry, but at this point, the notion of what is "well-defined" is not well-defined. What are your criteria for something being well-defined, and how does my system for identifying individual positive facts violate these criteria? I'm beginning to think it is a subjective notion, i.e. q is not well-defined because you don't understand it.

"Could you please explain why?"

Because I'm asking for the cause of the conjunction. Even if the conjunction is infinite, it is not its own cause, by Axiom 3.

"Unproven assertion."

(See above.)

"This does not in any way, shape, or form address whether or not such a singular CPF would be well-defined."

It seems to me that it does give a system for determining whether or not a singular CPF is well-defined, because it gives us a system for determining whether or not a given fact is individual. For any aggregate of facts, if one member creates a truth-functional repitition, that fact is not invididual. This system may be cumbersome, but it tells us that every individual positive fact can in principle be seperated from every non-individual positive fact, which is enough to consider the notion "well-defined." Also, this singular CPF is not a "set of all sets," so that objection fails.

"Filled in your assertions is the supposition that an actual infinite can exist. If we assume that when you say the words "from eternity" you mean that an actual infinite...."

I was only trying to suggest that the argument is not inconsistent with an eternal universe, not that it demands the universe be eternal. Your points are well-taken.

"insufficient comparisons (orchestra being the sustaining cause of the music being analagous to God being the sustaining cause of the universe, but the orchestra being contigent and God being necessary)"

As I've said, God's causal action may be contingent; it is only God's existence that is necessary.

"How can it be outside something wich doesn't exist yet?"

"Outside" is not used in the physical sense. It means not sharing a common part with q. Assuming God exists, God does not share any common parts with anything that does not exist, and so, according to this usage of "outside," can be said to be outside all such things.

"Objection #1:"

Your argument makes the hidden assumption that causes must be temporally prior to their effects. But this assumption is not obviously correct, so you will have to provide stronger argument for it.

"Objection #2"

We must assume that contingency is maintained under distribution because to do otherwise would lead to absurd modal consequences. An aggregate necessitates all of its parts. In other words, if the aggregate of a, b, and c exists, it necessarily follows that a, b and c exist. First, suppose that a-c are individually contingent, which is true by hypothesis. Now suppose the aggregate of a-c is necessary. Since L(p =&gt; r) =&gt; (Lp =&gt; Lr) is a valid argument form, and substituting p for the aggregate and r for the seperate individuals, supposing, as you have, that Lp is true, we see that Lr is true. But Lr contradicts our hypothesis that a, b, and c were individually contingent. Additionally, your argument seems to assert that whether or not a thing is necessary can be contingent upon whatever conditions it happens to exist in. But this violates the S4 axiom of modal logic, which states that Lp =&gt; LLp.

"Objection #3:"

You are right that the conclusion is "at least one cause exists." I never implied that we could cite one and only one cause on the basis of the argument. However, when we know only of the existence of one necessary being, whereas to postulate others would not be supported by evidence, the law of parsimony obligates us to choose the option with less theoretical entities. In other words, one necessary being is more parsimonious, and hence more probable, than many such beings.

"Objection #4:"

Your argument amounts to the claim that it is possible for the infinite chain to exist without cause. But this is merely to claim that Axiom 2 is false without argument.

"Objections #5-6:"

Admittedly, I am not terribly familiar with Big Bang cosmology (which is why I favor the traditional argument from contingency in the first place), but it is important to keep in mind that I have not stated that causes necessitate, or have to provide sufficient conditions for their effects. Suppose sufficient conditions exist for the creation of a rabbit's ear; also suppose that instead of only the rabbit ear coming into existence, the whole rabbit comes into existence. According to the weak sense of causation I am using in my argument, we can still say that the rabbit has a cause of its existence.

Your argument that contingent things normally have contingent causes is intriguing, but is undermined once we see that the First Cause can be contingent, so long as the being involved in it exists necessarily. Also, your restricted causal principle may be an example of special pleading. For instance, I may create the revised causal principle, "Every positive fact has a cause except for facts after January 1, 2005." In our experience, we have never seen a fact that was caused after January 1, 2005, so presumably, all of our evidence for the causal principle also provides evidence for the principle that after January 1, 2005, no fact will have a cause, but everything before that did. But it seems plainly obvious that this parodied causal principle is less acceptable than the standard one.

"My question (about conscious existence) to both of you relates to contingency and necessity. Firstly, do you consider...."

I guess one could say that free will in the Libertarian sense may be a sufficient condition for reason and intellect, though not necessary. For instance, a deterministic reasoning process could still produce true conclusions. The fact that I think the sky is blue may be a result of a direct causal chain from the fact that the sky is blue, but this reasoning process still seems reliable enough. It would be difficult to go further into this topic without straying to far from the original intent of this thread. But thanks for the kind remarks.

At this point, I feel that we are starting to cover old ground. So unless something very pressing comes up, this will probably be my last response for this thread.

Sincerely,

Philip

[ July 23, 2002: Message edited by: Philip Osborne ]</p>

Silent Dave

I finally came back to this thread to reply to Philip's points, only to find that everyone else had done it for me. I see that the argument has already been dealt with very nicely, so there's little else for me to say.

I'd like to second what Synth said, however. A theist of such philosophical sophistication is rare for a college graduate, to say nothing of a high schooler. I think Philip's going places, folks . . .


Dave

Koyaanisqatsi

I say "yea" Philip Osborne!

Welcome to the viper's pit...now strap yourself in!

Synaesthesia

Hey Philip,

Although assuming that any infinite set of causes requires a cause rules out very real possibilities, my intuition is that there really is something to what you are doing with the infinite regress. I have doubts that normal causation can ever be sufficient to ‘explain’ existence. Perhaps there is nothing that can explain existence, but I suspect that we will at some point have to look deeper than chains of causes.

In a system that is in some form deterministic, the cause will actually necessitate some effect. This remains true even in a pseudo-deterministic system like a wavefunction.

In other words, we can have a chain of specific, contingent events, but THAT a chain of events occurs is non-contingent. This would allow an infinite regress in which each temporal ocurrence is necessarily preceded by a certain class of ocurrence. No external cause outside the regress is required because the aggregate would be necessary.

Simply because each fact in BC(x) is positive does not logically entail that BC(x) is itself positive. As long as it is possible that every event is necessarily preceded by another event of some kind, to assume that that effects as a class are contingent rules out possibilities. The conclusion of a logical argument based upon that assumption is consequently thrown in doubt.

Secondly, as I pointed out before, H could easily be a part of a physical universe unless we question-beggingly detach it from nature.

If the universe has facts which are not positive, nothing outside of the universe is logically required to explain or ultimately cause the universe. (If an explanation is possible.) The central purport of the cosmological argument is defeated.

If the universe contains facts that are not positive, there is no logical requirement that they be caused at all. Additionally, it is not impossible that non-positive facts are not caused, so they could, for example, form some sort of closed loop of causation. Here we already have two case where a self-sufficient universe doesn’t even need to violate the letter of Hume’s Principle. Even within the confines of your argument, the universe can be self-sufficient.

Regards,
Synaesthesia

[ July 23, 2002: Message edited by: Synaesthesia ]</p>

Goliath

Philip Osborne,

I had said:

To which you responded:

Your condescending and holier-than-thou tone is not appreciated one bit, xian.

I have spent the last 7 years in college, and I have spent the majority of those studying Mathematics. Consequently, I know a little something about set theory.

Tell me, Mr. Osborne, how long have you been studying mathematics?

Now, if I have understood you correctly thus far, you have said that an aggregate, or sum of facts, is simply a set containing all facts. You have then stated that the CPF, or q, is the set of all sets. It is well known that there is no such thing as the set of all sets. Such a thing has been proven not to exist. That is what I mean when I say that q is not well-defined.

Now, either drop q from your argument entirely, or explain how I have misunderstood what q means.

Oh, and next time, try a reply sans the attitude.

Sincerely,

Goliath

SRB

"Objection #1:"

PO
Your argument makes the hidden assumption that causes must be temporally prior to their effects. But this assumption is not obviously correct...

SRB
There are reasons to doubt the coherence of asymmetric simultaneous causation (e.g. it leaves us with no criterion for distinguishing causes from effects). However, even if such objections are ignored, the inductive support for the nonexistence of asymmetric simultaneous causation is at least as strong as the inductive support for axiom 2. All instances of simultaneous causation that have ever been seen or proposed are symmetric (i.e. such that both entities are involved as both a cause and an effect).

Either the inductive support for axiom 2 is weak or else the inductive support for objection #1 is strong. Either way there is a serious problem here.


"Objection #2"

PO
We must assume that contingency is maintained under distribution because to do otherwise would lead to absurd modal consequences...

SRB
Apparently there is some confusion about just what sort of modality is employed in your argument. Typically, in cosmological arguments a contingently existing entity is taken to be one such that it exists and it is logically possible that it goes out of existence. A necessarily existing entity is one such that it exists and it is not contingent [this understanding is implied in my formulation of the objection]. Apparently, you take an entity X to exist contingently iff "X exists" expresses a logically contingent truth, and take an entity X to exist necessarily iff "X exists" expresses a logically necessary truth. With this clarified, I withdraw objection #2, but point out that God's necessary existence is more usually understood as I proposed it. The other understanding is almost exclusively held by proponents of the Ontological Argument, of whom there are relatively few. Most theists conceive of God's necessary existence as being something that is very different to necessary existence as used in your argument.


"Objection #3:"

PO
...one necessary being is more parsimonious, and hence more probable, than many such beings.

SRB
Simplicity of theories is a praiseworthy goal in the sciences, but the probabilistic argument you mention is a failure. An analogy demonstrates why. If we have a box and lack background information about the contents, save that the box contains at least one object, we can scarcely dismiss the hypothesis that the box contains more than one object on the grounds of simplicity.


"Objection #4:"

PO
Your argument amounts to the claim that it is possible for the infinite chain to exist without cause. But this is merely to claim that Axiom 2 is false without argument.

SRB
The infinite chain cannot possibly have a cause since, by hypothesis, every existent in the chain is caused by another existent in the chain. It seems to me that axiom 2 amounts to the claim that this theory is false, without sufficient reason. It is quite incredible to suppose that simple enumeration can establish that the given theory is false.


"Objections #5-6:"

PO
...it is important to keep in mind that I have not stated that causes necessitate, or have to provide sufficient conditions for their effects. Suppose sufficient conditions exist for the creation of a rabbit's ear; also suppose that instead of only the rabbit ear coming into existence, the whole rabbit comes into existence. According to the weak sense of causation I am using in my argument, we can still say that the rabbit has a cause of its existence.

Your argument that contingent things normally have contingent causes is intriguing, but is undermined once we see that the First Cause can be contingent, so long as the being involved in it exists necessarily.

SRB
I pointed out that if Big Bang theory is true then in the situation at the origin of the universe the physical conditions were incomprehensibly different and so inductive inferences about such circumstances are bound to be very weak. Quite aside from Big Bang considerations, I also noted that the existence of every positive fact is a very special and unusual sort of fact. Any inductive inferences about that fact will be very weak for that reason. I don't see that you have anywhere addressed those points. You point out that it would be special pleading to say that every positive fact has a cause except for facts after a date such as January 1, 2005. Quite right, but on January 1, 2005 the universe will likely not be the size of a pinhead, with utterly different physical conditions, as found at the Big Bang.

You suggest that the particular inductive objection I presented may not be a problem for you. You may be right there, but there are similar inductive considerations that can be mustered against your position. For example, (i) every existent that we are familiar with that causes events to happen is not logically necessary, therefore there probably is no logically necessary existent that causes events; (ii) every case of causation we are familiar with is not asymmetric simultaneous causation, therefore there probably is no asymmetric simultaneous causation.

Your inductive considerations in favour of axiom 2 are, in effect, lined up against these inductive considerations. Even if we accept these (dubious) inductive considerations wholesale, the evidence against axiom 2 is at least as strong as the evidence in its favour.

[Incidentally, if you take these inductive arguments seriously, four similar arguments can be adduced to show that there probably is no omnipotent, omniscient, all good and completely rational person. That's because all persons we uncontroversially are acquainted with lack each of these properties].

SRB