Omnipotence

[Robin]

That's fine. The set of omnipotent values is then {all powerful activities, not all powerful activities.}

It is not really a well defined set is it? How do you define an "all powerful activity"? What do you exactly mean by "an omnipotent value". What is your definition of omnipotence? Do you accept the Thomist definition linked in the OP? Or do you have another definition? The most popular definition does not refer to "all powers" but "all intrinsically possible powers". The question about the unbreakable object was to determine if there was a disambiguation for "intrinsically possible", now you are referring back to omnipotence as though it had already been defined. You really can't see the circularity here?

That which resists all power necessarily lies in the set of all power values.

Again "That which resists all intrinsically possible powers...". The question being begged is whether the ability to break any object is an intrinsically possible power.

Could an omnipotent entity break itself? Either the answer is no or the question is nonsensical in which case the power to break any object is an impossibility or a nonsense.

Can an omnipotent entity (using the Thomist definition) break a promise? No, in fact all this means is that an omnipotent entity has the ability to make a promise. Can an omnipotent entity promise that some object will never be broken? Either the answer is yes or the question is nonsensical, if nonsensical then the Thomist definition is nonsensical so you need to provide another.

If the answer is yes (since an all-powerful being has the power to keep the promise) then there are no circumstances whatever under which the object can be broken, The ominpotent entity could not do so even if it wanted to because to do so would mean the omnipotent being was wrong. It would be illogical to term an object that cannot be broken under any circumstances as "breakable". So it is unbreakable.

So either there can be an unbreakable object or the Thomist definition of omnipotence is nonsensical.

 

[stamenflicker]

Robin,

quote:
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Originally posted by stamenflicker
That's fine. The set of omnipotent values is then {all powerful activities, not all powerful activities.}
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It is not really a well defined set is it? How do you define an "all powerful activity"? What do you exactly mean by "an omnipotent value". What is your definition of omnipotence? Do you accept the Thomist definition linked in the OP? Or do you have another definition? The most popular definition does not refer to "all powers" but "all intrinsically possible powers". The question about the unbreakable object was to determine if there was a disambiguation for "intrinsically possible", now you are referring back to omnipotence as though it had already been defined. You really can't see the circularity here?

So now you want to use language? Now you want a definition? OK... omni- "all;" potent - "power" All-power. So the set of all power values is then {all power, not all power}. What now? How is that any different from true is the set of values {true, false}? If you want to follow this line of reasoning, then fine. Let's rehash Russell all over again... nothing can be known outside of the theory of types. i.e. your need for a definition. Constructing a limit that ranges over itself is ungrammatical. You need to become a nominalist, because that is in essence what you are arguing. Actually you want to be a nominalist when it comes to omnipotence, but not anything else. Thats where the logic breaks down.

Could an omnipotent entity break itself? Either the answer is no or the question is nonsensical in which case the power to break any object is an impossibility or a nonsense.

Can an all-true equation invalidate itself? Either the answer is no or the question is nonsensical in which case the truth to invalidate is an impossibility or a nonsenese. I'm arguing that neither omnipotence nor truth is a logical impossibility, however in your sentence it is instantly ungrammatical and therefore nothing can be known about it.

Also, the base requirement for omnipotence is not logically necessary as existence.

No, because by saying an X "is a" Y you are saying they are equivalent. By substituting terms you are saying they are equivalent. But "lie" and "not truth" are not equivalent.

They are not equivalent until you place them in sentence. Then you cannot "define" them without a reference to the other. Why is it necessary for me to provide definitions, but not you? Why can your sentences and logic exist outside the language rules, but not mine? You are picking choosing to make your point. Either omnipotence is a logical possibility without ontological completion, or all bets are off for every logical possibility and therefore we cannot know anything. 4,000 years of philosophy agrees with me.

Stamen

 

[stamenflicker]

Beyond the above, let me take a different tack, since we are clearly missing each other in our posts. Let's try something else for fun.

1. Omnipotent is the ability to exert all power in every possible universe.

2. Unbreakableness is the ability to resist all power in every possible universe.

3. If omnipotence exists, then there is no such thing as the ability of unbreakableness. If unbreakableness exists there can be no such thing as the ability of omnipotence, by definition.

4. If omnipotence and unbreakableness occur within the same universe, that universe is said to be not possible.

Are we on the same page here or not? If so, then basically we are saying one of the following which is fine with me:

1. Omnipotence does not exist in any possible universe.

2. Unbreakableness does not exist in any possible universe.

3. Both omnipotence and unbreakableness do not exist in any possible universe.

4. Omnipotence and unbreakableness both exist, but not in the same possible universe.

Now your statement: "Can God say, I create this and it will never be broken."

1. The said god is omnipotent, then there is nothing the said god can create that he himself cannot break, by definition and logical possibility. To do so, God creates an impossible universe, which I suppose God can do, but then we really can't talk about it can we?

2. All-trustworthy is the ability to say something that will never be proven false.

3. The said god can says, "I create this item, it will never be broken because I will never break it."

4. The said god is all-trustworthy.

5. The item can never be broken and is hence unbreakable.


Implications:

At first glance, it would seem that the said omnipotent god cannot speak a trustworthy phrase, sense if he is omnipotent then he should be able to create a trustworthy phrase that he himself cannot prove to be false. But by definition we are back up to the top of this thread and in the realm of possible logical universes.

However if the said god is both omnipotent (statement 1) and trustworthy (statement 3), there can be no possible world in which what he says can be proven false, not that it isn't possible for it to be false, again by definition. And if there is no possible world where things can be unbreakable, then it is his trustworthiness, not his power which is ultimately the referent of the "omni" adjective.

In fact, if we take this tack, then we are instantly debating two different "types" or "classes" of adjectives. The grammar of the argument makes all the difference, logically speaking. And your grammar is illogical and incomplete.

Neverthess, given the above maxiums, it is possible for God to remain omnipotent in the same possible universe as an unbreakable kingdom.

Stamen

 

[ReFLeX]

1. Omnipotent is the ability to exert all power in every possible universe.

...

4. Omnipotence and unbreakableness both exist, but not in the same possible universe.

These two statements are incompatible.

...God creates an impossible universe...

I thought the OP implied that God could NOT do this.

...but then we really can't talk about it can we?

So why is this whole first statement there?

2. All-trustworthy is the ability to say something that will never be proven false.

I don't think many people would agree with this. Personally, I prefer my omnipotent beings honest... But seriously, how can I consider someone trustworthy by relying on fallacy of ignorance?

Neverthess, given the above maxiums, it is possible for God to remain omnipotent in the same possible universe as an unbreakable kingdom.

...what?!
I appreciated your attempt to simplify things at the beginning of the post, but I had trouble understanding how your sets of statements were logically connected, and I absolutely didn't see your conclusion supported anywhere. I don't know what the addition of "possible universes" brought to the discussion, either.
Incomplete grammar? Why didn't you show us that, instead?

 

[Robin]

Originally posted by stamenflicker
However if the said god is both omnipotent (statement 1) and trustworthy (statement 3), there can be no possible world in which what he says can be proven false, not that it isn't possible for it to be false, again by definition. And if there is no possible world where things can be unbreakable, then it is his trustworthiness, not his power which is ultimately the referent of the "omni" adjective.

Suppose that you are right think about it. Was it me who put "all-trustworthiness" into the "omnipotence" basket? No, I just took my definition from the standard theological definition stated by St Thomas of Aquinas.

So according to this definition God's inability to break a promise is one of the intrinsic impossibilities with respect to omnipotence. So according to this definition it would be, by definition, intrinsically impossible for God to break his promise, and in consequence intrinsically impossible for the object to be broken.

The fact that the statement will never be proven false is thus an inconsequential by-product of the fact that the statement is absolutely true!


You see one thing we must accept is that God has the power to back up his promise. Not only that, if God ever broke the object then God would know this when he made the promise and would not make a false statement.

In fact, if we take this tack, then we are instantly debating two different "types" or "classes" of adjectives. The grammar of the argument makes all the difference, logically speaking. And your grammar is illogical and incomplete.

It is pointless to use set-theoretic concepts like this in the absense of some set-theoretic notation. In any case, although it is a long time since I studied DM, I am pretty sure that "types" are an obsolete terminology and that it is not possible to represent an adjective with a class. The appropriate plain language analogy to a class would be a noun and adjectives might be represented using predicates. When Russell speaks of "grammar" he is referring to the rules of composition for the PM axiomatisation.

In fact my grammar is fine and my logic is consistent with respect to the definitions I am using.

 

[ceo_esq]

I've come across a 1983 article by the philosophers Thomas Flint and Alfred Freddoso that, although new to me, has apparently been hugely influential on contemporary philosophical work relating to omnipotence.

The authors put forward a complex philosophical definition of omnipotence that, while obviously influenced by classic figures such as Aquinas and Anselm, possesses several advantages over certain previous formulations. The first is that it has not been "corrupted", in the authors' words, by religious considerations. That is, it is entirely neutral as to what other properties (particularly, theologically significant ones) besides omnipotence that an omnipotent agent might have (e.g. benevolence, moral perfection, omniscience ...). Second, it appears rather neatly to evade certain traditional "paradoxes of omnipotence" (unliftable rocks and so forth).

Here it is:

S is omnipotent at t in W if and only if for any state of affairs p and world-type-for-S Ls such that p is not a member of Ls, if there is a world W* such that

(i) Ls is true in both W and W*, and
(ii) W* shares the same history with W at t, and
(iii) at t in W* someone actualizes p,

then S has the power at t in W to actualize p.

In the formulation above,

S = an agent (the being under consideration)

t = a given time

p = a hypothetical state of affairs (i.e. a proposition) expressed linguistically by the nominalization of a complete declarative phrase. The authors argue that the problems with trying to characterize maximal power in terms of an agent's ability to perform tasks (expressed linguistically by the nominalization of a verb phrase) are well known to philosophers, and that for this reason it is widely accepted in philosophy that an analysis of maximal power should be stated in terms of an agent's power to actualize, or bring about, states of affairs.

W = a given possible world

W* = any other possible world

Ls = a given "world-type-for-S". This is a somewhat complex concept developed to reflect the fact that in a world containing free beings, any given being is going to be confronted with a set of counterfactuals of freedom which it is logically impossible for him to control, regardless of how powerful he is. (A counterfactual of freedom, let us recall, is a counterfactual in which the consequent is a statement about a free action, of the form If person X were in circumstances C and left free with respect to action A, X would freely choose to do A.) So for any given world, its world-type is a set of all counterfactuals of freedom for that world. Such world-type is true if and only if every proposition that is a member of it is true. The idea here, again, is that it is logically impossible for any being to bring about a state of affairs which is inconsistent with the truth of that being's world-type.

You can broadly see how the formula has been tailored to defeat certain problems or objections. The inability to actualize necessarily unrealizable states of affairs is recognized in (ii). Logical objections to changing the past (such that events both occurred and did not occur) are handled by (ii) and (iii) together. The inability to completely causally determine how another being will freely act is dealt with by the concept of a world-type-for-S. Objections of the sort "But that makes us all omnipotent!" are prevented in (iii), by ensuring that to count as omnipotent a being - regardless of its nature - must possess the maximal amount of power consistent with the other logical conditions.

The foregoing is a drastic simplification, so please refer to the article itself, which fortunately is available online (see below). It's reasonably tough reading. I'd be interested, in particular, to know Robin's and Stamen's reactions.

A. Freddoso & T. Flint, "Maximal Power", in Alfred J. Freddoso, ed., The Existence and Nature of God (Notre Dame, IN: U. of Notre Dame Press, 1983)

 

[Robin]

This is an interesting paper, it will take me a while to digest it. Initial reaction is that it is technical, but quite clear reading - a refreshing thing in modern philosophy. I like the idea that '...maximal power should be stated in terms of an agent's power to actualize or bring about states of affairs.', this fits to my own approach that an object be unbreakable, not because it resists power to break, but that it cannot be broken in any circumstances for whatever reason.

It seems that my scenario where there can be a stone that S cannot move and that S is nevertheless essentially omnipotent would still be valid. The writers appear to be operating under a prior assumption that an inability to move the stone would contradict essential omnipotence:

(10) Its being the case that there will be a stone which Sam, though he exists, cannot move?
The answer depends upon what further properties Sam has. If Sam is essentially omnipotent, then he cannot at t actualize (10). But (D) does not require that he have this power, since in that case (10) is a logically impossible state of affairs and thus not possibly such that anyone actualizes it. On the other hand, if Sam is only contingently omnipotent, then (D) might well require that he have the power at t to actualize (10). But there is no paradox here. By actualizing (10) Sam would merely bring it about that at some future time he will be nonomnipotent.

Note that they say either (i) S cannot actualise (10) or (ii) (10) is logically impossible or (iii) S can actualise t but is only contingently omnipotent. But I still think that I have shown that S can actualise (10) and be essentially omnipotent (and this is unproblematical since a rock does not have free will).

It also occurs that if there is maximal power then there would also be an optimal W containing all the states that S will actualise (perhaps S performs a hill climbing algorithm on the set of all possible W's), similar to Leibniz best of all possible words. This seems to have some interesting implications.

Also I have to run the 'world-for-type-S' concept past O1 and O2 to see what they make of it.

 

[Beerina]

Ossai, the statement above is true because the statement X can do anything except what X can't do is necessarily true for all X.

It's more like saying X can do anything except what Y cannot do, for all y.

The set X only contains omnipotent beings. Furthermore, it would necessarily be a set of either 1 or 0. If it were 2 or more, the beings could interfere with one another, and thus would not be omnipotent, at least with respect to each other.


It all really boils down to "can God do what cannot be done?" Things like round squares (truly round ones, not semantic games with oddball dimensional landscapes) are easy: Can't be done, no impact to omnipotence as they are a contradiction.

Harder, though, are things like the rock so heavy even God cannot lift it. To that I would only suggest He could not lift it until he wished to lift it.


Sunday School Teacher: ...and so you see, God is infinite.

Stan: But can God make a rock so heavy even He cannot lift it?

Teacher: Ummm, I guess he could if he wanted to.

Cartman: Can God make a gay man so sexy that even God cannot resist hot manlove?

[Teacher looks stunned, gets up, sound of running off screen, car door slams, screeching tires]

[Stan & Kenny laughing]

Stan: Cartman, you suck 99% of the time, but it's that 1% why we keep you around.

Cartman: Thanks, guys!


Anyway, it's all pointless argument based on misunderstandings of the infinite. Since there is no largest transfinite number, there is no largest "bag of infinite abilities", and hence, no "most infinite" god. Any god you can imagine, I can imagine another one. Specifically, one that can beat him up.

And even God can't get around that logic.



Stan: Oh yeah? My god is infinite!

Cartman: My god is stronger than yours!

Stan: Can't be! He's infinite! He has every power!

Cartman: My god has all the powers of yours, plus the additional power that he can beat the crap out of your god.

Stan: Shut the F[beep] up, fatass!