Philip Osborne

Interesting replies:

"How do you identify objects/entities across universes; i.e. how can you tell that the x in universe U is actually the "same" as the y in universe V ? Objects or entities do not come with name tags around their necks."

This problem would seem to apply whether or not we have a concept of necessary existence. I may not exist in all possible worlds, but I might exist in a nearby possible world, w. In that case, your argument, according to which it is impossible to identify me in w, applies. Thus, I cannot exist in any other possible worlds. But if that is so, then I cannot be in any other way than I am. If it is possible that I have green hair, then there is a possible world in which I have green hair. But your argument seems to imply that I cannot exist in any possible world, which would have the further consequence that it is impossible for me to have green hair. But this seems contradicted by the fact that I can easily go to a punk rock-type store and buy green hair dye. In short, your argument, if a sound criticism of necessary existence, would not only invalidate necessary existence but the whole notion of possible worlds. For this reason, I think it can be rejected.

"It is true by definition. In a cause-effect relation, the cause is that which comes earlier."

If it is merely true that causes come before their effects by definition, then I will use the notion of "cause*," which does not include this requirement. The point is that the question of causal asymmetry cannot be settled by an appeal to a definition.

"What test can tell us that X necessitates Y?"

I can't give a complete set of criteria off-hand; the point is that it can be done in principle, which means it is still possible to differentiate between X and Y even if Y does not temporally precede X. Here's an example: Suppose there is a candy vending machine, which usually dispenses candy when a coin is inserted in it. If I insert a coin, and a candy bar comes out, the token of the candy bar being dispensed necessitates that I put a coin in it; otherwise, it would be a different token. Yet it is possible for me to insert a coin into the vending machine and yet for no candy bar to come out. The insertion of the coin into the vending machine does not necessitate the effect.

"This appears true, what is a necessary dog with a contingent leg?"

Pace Clutch, I think that a necessary dog is impossible, but assuming that such a thing can exist, it seems clearly possible for a necessary dog to have the contingent property of biting the mailman's leg off, since being in the state of doing so is not an essential property of a dog.

"This "model", without any more description, would be useless in describing cause and effect. It could describe anything. Take modal axiom M, []p -> p."

Interesting objection, but if it is established that Lp is true, then p necessitates it. It is generally understood that if a fact is necessary, then every fact necessitates it. So if p is necessarily true (which is an assumption of your argument), then the actual truth of p necessitates the necessity of p. That seems to be the way your argument works, by saying that the necessity of p is the cause of p being true. But if the first part of the conditional is true, then the statement L(p => Lp) is also true, which means we have no asymmetric necessitation.

"This is a somewhat odd response, the first time I have heard it. If there can be no instinsic maximum of "goodness", how then, can we call God omnibenevolent? And couldn't God hypothetically simply create infinite times to acheive the infinitely best world, or somesuch?"

Although the things that make possible worlds good do not admit of an intrinsic maximum, this is not so for God. For instance, God may be able to do all that it is conceptually possible to do. It is conceptually impossible to be able to do more than this. Omnibenevolence may be defined as exercising perfect moral judgement under every possible state of affairs. It is conceptually impossible for a being to be more benevolent than this.

As for your many universes objection, I can't give a definitive answer to your response at this moment, but, for example, Alexander Pruss has given argument to the effect that the totality of all possible worlds cannot exist (as an argument against modal realism). Also, it may turn out that God did create many such worlds, which might be consistent with atheistic "many worlds" hypotheses.

"I cannot create the greatest state of affairs, so I will just settle for less?" I doubt it. Unless it was logically possible for God to create the greatest state of affairs, I doubt he would have created at all, as a factor of omnibenevolence.

I find it highly unlikely that God would think to himself, "Blast, there's no best possible word; I have no idea what to do!" An omnipotent God should not be flustered into total inaction simply because of the fact that there is no best possible world. This depends upon our conception of omnibenevolence, and what omnibenevolence would allow.

Sincerely,

Philip

HRG

There may be an entity in W which is called Philip O. by his friends and acquaintances, but why would it be you ?
Note that you are using the present tense here. IOW, your statement is not complete because it would require a time value: "At 12:00 PM, July 28th, 2002 CE, Philip O. has/has not green hair".
In this case, you would first have non-green hair, and then green hair. Many properties are not invariant under time translation; see above about the required specification of a time value.

IOW, your example is about possibility within one and the same universe and says nothing about other possible universes (in the sense of philosophy).
See above. I do not reject possible worlds, but only the assumption that an automatic identification is possible. I submit that this identification must be done by defining properties; if there is a property PO such that you and only you fulfill it in U, and it similarly by exactly one entity in W, then it would be legitimate to identify you with this entity in W.

And which notion would that be, pray tell ?
How else, since we have to define "cause" first ?
This differs from the usual notion of cause: this notion requires that the cause determines the effect, and not vice versa. The cause of your candy bar would be the total state of the machine plus your coin.
Then - at least according to the usual definition - it cannot be the cause; at most one element of a set of contributing circumstances. Picking it out of this set and calling it the cause seems rather arbitrarily to me; why shouldn't I call the presence of candy within the vending machine the cause of candy ? It is "necessitated" in the same way as the coin.

Your definition would lead to strange results in cases where there is a 100% correlation between 2 events (event 1: an electron enters a tube - which is absolute vacuum and free from external fields - at end A; event 2: the electron exits at end B). As I understand your concept, both events "necessitate" each other; so which one is the cause, and which one the effect ?

I submit that everyone would say that 1 is the cause of 2, and not vice versa. Why ? 1 happened earlier.

Regards.
HRG.

Philip Osborne

"See above. I do not reject possible worlds, but only the assumption that an automatic identification is possible. I submit that this identification must be done by defining properties; if...."

But what does this have to do with the notion of necessary existence?

"And which notion would that be, pray tell?"

My notion is the model of asymmetric necessitation that I have given above.

"How else, since we have to define "cause" first ?"

The problem with appealing to a definition is that it is easy to fit your model of asymmetric causation into it, thus defining opposing viewpoints out of existence. My notion of cause* may have a different conception of the asymmetry of causation. Appealing to definitions cannot tell us whether causation is more useful than causation*.

"Then - at least according to the usual definition - it cannot be the cause; at most one element of a set of contributing circumstances. Picking it out of...."

The idea of asymmetric necessitation is that it is logically possible for the candy to be dispensed when the total state of the machine M and the coin C being inserted into the machine both obtain, yet it is logically possible for both M and C to obtain in the absence of the effect.

"Your definition would lead to strange results in cases where there is a 100% correlation between 2 events (event 1: an...."

100% correlation is not equivalent to necessitation. For instance, suppose you have a spinner with each point on the circle representing one of the real numbers, and the whole of the circle covering the entire range of real numbers. The tip of the spinner tapers to a point, so it can only point to a single point on the circle at a time. If I spin it, the chances of the spinner landing on exactly 3 are 1 in infinity, which basically comes to 0. Thus we can say P(spinner does not land on 3)=1. Nonetheless, this does not mean it is logically impossible for the spinner to land on 3.

"You are right that causes do not (logically) necessitate their effects. However, God intending that some event token e occurs *does* logically necessitate that e occurs, since God is omnipotent. From this...."

Your argument seems to be this:

1. If God existed, then there would be instances in which causes necessitate their effects (because causal relationships involving God's intentions are of this form).
2. Causes do not necessitate their effects.
3. Hence, God does not exist.

Your argument is valid, but I'm not convinced that theists would be obligated to accept the construal of omnipotence offered in (1). This is so especially in light of the fact that most theists do not consider God outside the laws of logic or the laws of causality. One could construe omnipotence in such a way that God's intentions give their effects a probability of 1 (which is not the same as necessitation; see above). For some, this might be an example of "making God in man's image." However, when the alternative is to be confronted by an impotent God, it seems acceptable.

Sincerely,

Philip Osborne

SRB

PO
100% correlation is not equivalent to necessitation. For instance, suppose you have a spinner with each point on the circle representing one of the real numbers, and the whole of the circle covering the entire range of real numbers...this does not mean it is logically impossible for the spinner to land on 3.

SRB
Such a spinner is unintelligible. It is not difficult to prove that there is in fact no such thing as a uniform probability density function (pdf) over the real numbers. Even if one allows infinitesimal probability densities, one can still prove that the integral goes off to either infinity or zero, violating the condition that every well formed pdf encloses an area of precisely 1.

SRB
"You are right that causes do not (logically) necessitate their effects. However, God intending that some event token e occurs *does* logically necessitate that e occurs, since God is omnipotent. From this...."

PO
Your argument seems to be this:

1. If God existed, then there would be instances in which causes necessitate their effects (because causal relationships involving God's intentions are of this form).
2. Causes do not necessitate their effects.
3. Hence, God does not exist.

Your argument is valid, but I'm not convinced that theists would be obligated to accept the construal of omnipotence offered in (1).

SRB
On your conception of divine omnipotence there is a logically possible world where God intends that a universe exists but he somehow bungles matters and no universe comes into existence. Most theists (including Koons himself) rightly find such a consequence intolerable. Such bungling can hardly be considered compatible with divine omnipotence.

You claim that one can establish when event token e1 necessitates another event token e2 without assuming that e1 is temporally prior to e2. However, in all your illustrative examples you *do* specify that one event occurs before the other. The upshot of this is that you have not shown how one might make any sense of asymmetric simultaneous causation.

SRB

WJ

Automation!

"Well, actually, that was the point. I think "a necessity causing a contingency" is a flawed notion, because no aspect of a necessary being can be contingent, including causal actions. If a causal action cannot fail to be, then that which is caused is necessary as well."

In your view, and aside from the arguments of possibly a 'di-polar' God, what would be the logical inconsistency of a necessary Being, along with the notion of the 'percieved' illusion of free-will?

Walrus

[ July 29, 2002: Message edited by: WJ ]</p>

Philip Osborne

"Such a spinner is unintelligible. It is not difficult to prove that there is in fact no such thing as a uniform probability density function (pdf) over the real...."

I'm not exactly sure what this means, since I'm not an expert in math, but the essential question is whether or not something can have a probability of 1 and yet not be logically necessary.

"On your conception of divine omnipotence there is a logically possible world where God intends that a universe exists but he somehow bungles matters and no universe comes into existence. Most theists (including...."

First, it is not correct to characterize God as "bungling" anything. Suppose God's intention E causes state of affairs F to obtain. There is a logical possibility that E obtains and yet F does not obtain. If this state of affairs is instantiated, it is not because God somehow incorrectly performed E; it is simply the result of causal laws. Most theists do not hold God to be outside causal or logical laws. And theists might be willing to countenance that God's intentions can fail to produce the intended effect, providing that this event has a probability of 0, if they become aware of the deductive consequences of their beliefs. It seems to me that even if an omnipotent God does not necessitate His effects, He may still intelligibly be considered worthy of worship. If this is so, then Dr. Smith has failed to refute theism.

"You claim that one can establish when event token e1 necessitates another event token e2 without assuming that e1 is temporally prior to e2. However, in all your illustrative examples you *do* specify that one event occurs before the other. The upshot of this is that you have not shown how one might make any sense of asymmetric simultaneous causation."

Actually, you've gotten it backwards. I stated that effects necessitate their causes, not the other way around. But what is relevant to the atheistic cosmological argument is whether or not simultaneous asymmetric causation is possible, and it is not obviously true that I have to provide a non-controversial set of criteria that account for causal direction in order for it to be possible.

Sincerely,

Philip

[ July 29, 2002: Message edited by: Philip Osborne ]</p>

HRG

Because the definition of a necessary being requires the ability to identify beings across universe, so that we can say "x in U, y in V, z in W .... are actually all the same old x; thus x exists in all universes".
Of course, you can define causation to mean anything you want to. However, you then have to demonstrate which statements hold for this new concept of "causation in the sense of P.O."

Then either the universe is non-deterministic - which pretty much kills the exact cause-effect relationship - or M is not a full description of the state of the machine.
If not, then what is equivalent to necessitation - in the real world, that is ?
If you are talking about real spinners, it is meaningless to say that they land on 3. Spinners and real circles are objects with finite precision; thus you can only say that the spinner landed in a small, but finite interval around 3.

If you are talking about mathematical spinners, let's first discuss probability spaces, countable additivity of measures and null sets wrt to a given measure

IOW, we have to distinguish between reality and an (approximate) mathematical model of reality. Not all features of the model (like the existence of null sets - even uncountable null sets -, or the distinction between rational and irrational numbers) have their counterparts in reality.

Regards,
HRG.

P.S. For those who love strange mathematical beasties (all living in the interval [0,1] of the real numbers):

1) There exists an uncountable set with "probability" (i.e. measure) zero.

2) For any value p smaller than 1, there exists a nowhere dense set (i.e. it contains no open interval) with probability (as above) greater than p.

Philip Osborne

"Because the definition of a necessary being requires the ability to identify beings across universe, so that we can say "x in U, y in V, z in W .... are actually all the same old x; thus x exists in all universes"."

It's not clear that for a necessary being to exist, we must be able to identify it. We also need to be able to identify contingent beings across possible worlds, so your objection does not uniquely deal with necessary beings.

"Then either the universe is non-deterministic - which pretty much kills the exact cause-effect relationship - or M is not a full description of the state of the machine."

One of the motivations behind the thesis of asymmetric necessitation is that if we suppose that causes do necessitate their effects, we would be lead into an inflation of causes. In fact, M and C would not be sufficient conditions for the dispensing of the candy bar. We would have to include, as a part of the cause, the absence of conditions logically incompatible with M and C, such as X, Y, Z, etc. If it is countenanced that M and C are sufficient for a causal explanation of whether or not the candy bar is dispensed, we will have to reject the notion that causes necessitate their effects.

"If not, then what is equivalent to necessitation - in the real world, that is?"

a necessitates b if and only if in every possible world in which a obtains, b obtains also. This may seem like 100% correlation, but is not necessarily so for the real world. For instance, it is possible for there to be a 100% correlation between a and b in the actual world and yet for there to be possible worlds in which a obtains but b does not obtain.

Sincerely,

Philip Osborne

Automaton

On what are you basing this judgement? Why is the possibility of having necessity entity selective, and why some entities and not others? Of course I deny that a necessary dog exists in any possible world (and thus is impossible), because this would mean that it does, in fact, exist in every possible world. I'm assuming you accept this as well, but why do you arbitrarily distinct God from this reasoning?
But in some possible worlds there will be Dx (dog biting the mailman's leg off), and in the rest will be Dy (dog not biting the mailman's leg off). These are distinct entities, two different forms, albeit sharing the attributes of a dog. Neither occupies all possible worlds, thus no instances of the dog are necessary. But all instances of the dog must be necessary for the dog to be actually necessary.
So []p -&gt; (p -&gt; []p)? Whatever axiom you are thinking of, it's news to me. Care to provide a formal proof?
Generally understood by who?
[quote]So if p is necessarily true (which is an assumption of your argument), then the actual truth of p necessitates the necessity of p.[/quotes]Again, why?
[]p -&gt; p would be a cause-effect relationship if your "model" of causation were true.
Expanding that, it becomes []p =&gt; [][]p, or []p =&gt; []p. So what?
Please give me a reason.
Perfect moral judgement is still an instrinsic maximum.
What does this have to do with creating-then-destroying universes infinitely?

If say, an incredibly evil world was the only logically possible one God could create, would he see fit to create it, or would he just remain inactive? Since, according to you, the only world God can create is less than perfectly good, as a condition of perfect moral judgement, God would not see fit to create it.

HRG

How else could we say that the x in U is the same as the y in V ? As said, beings do not carry name tags around their necks.

To claim that x is a necessary being, you would have to show that for every V there is a y in V such that all properties which hold for x in U also hold for y in V.
Of course it is an objection against the whole necessary/contingent distinction for beings. I'd have thought it trivial that a claim that a property P is ill-defined includes that Not-P is ill-defined, too.
Sure. That's what happens when you try to formulate a metaphysical notion of causation, instead of the (testable) notion of correlation.

But when I say that the machine is in state M, this includes the absence of any condition which is logically inconsistent with M.

Of course, an additional problem arises for your PoV when the same effect can be the result of different causes, thus doesn't necessitate a single one.

[quote]
If it is countenanced that M and C are sufficient for a causal explanation of whether or not the candy bar is dispensed, we will have to reject the notion that causes necessitate their effects.
[quote]

Well, if you look at actual causation in the real world - instead of a metaphysical abstraction, you'll find out that all causation is only approximative.
What does "possible" mean in this context ? Logically possible (i.e. not self-contradictory) ? Physically possible ?

I could argue that there is just one world which is physically possible: the one we are inhabiting. If we have never observed Y, Y is prima facie physically impossible; that's how we derived the law of conservation of energy, f.i.

Only if you play around with sets of probability zero (which don't exist in the real world), as in your spinner example.

In any case - how do I test for the existence or not of this alternative world ? Does "possible" mean anything but "Philosopher A can conceive of its existence" ?

Regards,
HRG.