"What embitters the world is not excess of criticism, but an absence of self-criticism." - G.K. Chesterton

Monday, July 30, 2007

Omnipotence and the impossible

(Look at that: you wait ages for a post and then two come along at once. I'd only just knocked this one into shape when I noticed that Alex had posted. Mine suffers from a lack of cute pictures though.)

The most common answer from theists to the problem of evil is the ‘Free Will Defence’, which maintains that it’s logically impossible for God to remove evil and provide free will to humans at the same time – therefore the presence of evil is necessary to achieve a greater good.

On the face of it, this is a perfectly good answer – assuming you accept the libertarian concept of free will*. However, I’d argue that serious problems arise when, as many seem to do, you use the FWD alongside claims of God’s omnipotence. A being cannot be all-powerful and yet unable to do something: an omnipotent being would have to be able to create a world in which we had free will yet in which evil did not exist.

Over on his own blog, Revvvvvvvd argued that asking God to do something illogical was to ask a meaningless question: a 4-sided triangle is just as meaningless as tugimahy a hufquest bubaluyte.

But, in order to worthy of the term omnipotent, I’d say that such a being couldn’t be bound by meaning either: I may not be capable of understanding what I’m arguing, but an omnipotent being would have to – I’d ask it to tugimahy a hufquest bubaluyte, it’d tugimahy a hufquest bubaluyte and in that moment I’d understand. In the same way, although I’m incapable of conceiving a 4-sided triangle (for example), or who libertarian free will could co-exist with the complete absence of evil, an omnipotent being would have to be capable of it. To say that X cannot do Y (whatever Y is) is incompatible with X is omnipotent.

Therefore, while the presence of evil is compatible with a loving God, it surely rules out a loving, omnipotent God?

(*I don’t, but that’s another argument)

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43 Comments:

Blogger Alex said...

Hey Matt,
Nice to see we are making up for lost time here.

I really enjoyed listening in on your debate with revvvvvvvd. It was really well thought out. However as you may have guessed I'm a bit flummoxed by your insistence that omnipotence must include being able to do the logically contradictory. I agree with revvvvvvd (and Lewis) when he says that simply constructing a grammatically correct string of words does not guarantee meaning. Or as Lewis says: Nonsense does not cease to be nonsense simply by tacking the words "God should be able to" in front of it. (my paraphrase)

If you really want to, you can have that definition. I won't even ask to borrow it. All I ask is that you don't bring it over when we talk about the Christian God. No one to my knowledge, has ever held such a view of "omnipotence". It reminds me a bit of when Stephen Law tried to attack the Christian God by attempting to use a version of the word "evil" that no Christen would ever assent to. If there is to be an argument against Christianity you must first be willing to use words in the same manor as the Christians do.

At this point I see no reason that the Christian camp should need to revise their definition of Omnipotence from "able to do all that is logically possible", to "able to to all that is logically possible AND all that is not logically impossible". The main reason I say that is because the second definition introduces a incoherent God. Last I checked I haven't heart to many hymns sung to the great incoherence of God. We don't generally praise our father for how he brought incoherence out of nothing.

I guess its an interesting thought, but it really just leads to nonsense.

9:57 AM

 
Blogger Alex said...

Matt,
Sorry if I sounded snotty in that last comment. I just went back and read over it again and I got the impression that I'm kind of a jerk... which is probably true. I'm working on that. My apologies.

11:59 AM

 
Blogger Matt M said...

No worries. I didn't take your comments as snotty at all.

At the risk of it myself though, I'm going to point out that it's not my definition, but that of the Oxford English dictionary, which defines omnipotence as "infinite power", and infinite as "boundless" and "endless".

If a being is bound by what is logically possible then it's not infinitely powerful - if God can't create a 4-sided triangle, or tugimahy a hufquest bubaluyte, then He's not omnipotent in my book. (And my book is a dictionary.) Mind-blowingly powerful perhaps, but not infinitely powerful.

The main reason I say that is because the second definition introduces a incoherent God.

Actually, not if he's infinitely powerful - as such a being would have to be capable of being both coherent AND incoherent at the same time, such is the fun of the infinite.

I don't think that we have the necessary conceptual ability to even begin to understand such a being, so, for me, IF God is omnipotent, then the idea we could ever start to begin to understand Him is impossible, He'd be just too far removed from what we know.

2:53 PM

 
Blogger Matt M said...

No one to my knowledge, has ever held such a view of "omnipotence".

Descartes did.

(At least according to wikipedia)

3:10 PM

 
Blogger Alex said...

Matt,
Whew! Glad you didn't take it that way. I've been kicking myself all day for posting before I had a chance to self edit.

Aaaanyway,
I think I can safely agree with the Oxford English Dictionary without accepting your purposed version of omnipotence. I don't view the traditional definition of omnipotence as a limitation at all. The reason I say that is because logical contradictions are utterly meaningless statements. To say that God cannot produce nonsense is a credit to his reality rather than a limitation upon him.

I can't seem to think of any clever way to change your mind on this one. I'm not exactly sure why you seem drawn to this idea you are advancing. In the past you've always seemed attracted to the more reasoned arguments, but now you want to adopt this very strange view of omnipotence to try and subvert the FWD. I guess if you want it that bad you are free to have it, but just know that when I use the term I will not be using it in the sense you are advocating.

I guess Descartes can have it as well for that matter. I personally see no reason to accept such a position. Anyone else have any thoughts on this? I think I'm pretty much done here.

8:02 PM

 
Blogger Alex said...

One last thing,
If Descartes was attempting to make God prior to the laws of logic with this assertion (as wikipedia seemed to indicate) then my personal view is that his view should go the way of the divine command theorists. In the same way that I view morality to be a refection of God's character, I also view logic to be a glimpse at the mind of God. I see this view as much more satisfying than a God who is amoral and illogical. I also see this view as much more in line with the way he has revealed himself in history.

Okay. I'm done now.

G'night!

8:21 PM

 
Blogger Matt M said...

Alex,

The day blogger adds an edit function for comments there will be dancing the streets!

now you want to adopt this very strange view of omnipotence to try and subvert the FWD.

Actually, I think the FWD falls down on the apparent inability of anyone to give a decent explanation of the libertarian free will (not determined, not random...) idea it stands on.

This post came out of puzzling over the omnipotence paradox - can God create a breakfast so big even He cannot eat it all, etc. after listening to this interview with Andrian Moore over at Philosophy Bites. It's worth a look if you get a spare fifteen minutes.

I have no problem with God being bound by the possible - but that clearly makes Him a finite being: bound by logic and meaning. Trying to insist that He can be both infinite and comprehensible to our limited minds strikes me as a case of trying to have your cake and eat it. A logical being is a finite being.

An infinite being would have to be able to do the impossible - else we can start drawing up a list of things it can't do, which can't be the case with endless power.

5:34 AM

 
Blogger Alex said...

Matt,
Yes indeed an editing feature for comments would be a welcome change if we could all resist the temptation to go back and rework our posts!

I think the FWD falls down on the apparent inability of anyone to give a decent explanation of the libertarian free will (not determined, not random...) idea it stands on.

I have yet to really devote much time to this whole libertarian vs. compatiblist debate. All I know thus far is that I agree with much of what the compatiblist camp has to say, but I don't feel it does justice to the basic gut level way we operate in our day to day lives. However I am also uncomfortable with how many of the libertarians define themselves. I realize this is a very poor footing to base any sort of argument upon, so let's just say it's on my list of things I need to investigate.

Just finished listening to Andrian Moore's interview on infinity. I can't say there was much of anything for me to disagree with in what he said.

Now turning back to this concept of omnipotence. I'd like to offer a bit of a distinction for you to ponder. Traditionally God has been ascribed omnipotence, that is, "infinite power". I would like make a distinction between this concept and what we might call omni-able. Christians have never claimed that God can do anything. For instance: God cannot act contrary to his nature. Nor can he make breakfasts so big he can't eat them.

I don't see this as making God finite. (though for the sort of God you are postulating it shouldn't really matter if he is finite or not as he must be able to be both finite and infinite at the same time. Otherwise he's limited right?)

In the same way that striking out on a moral course that is contrary to God leads to death, the postulation of contradictory logic leads to intellectual death. There's simply nothing there. Both attempts lead to a null set. Since God is, he cannot not be. (that is, be contradictory)

To insist that God must be able to exist and not exist, create one dimensional three dimensional objects, be infinite and finite, all simultaneously only shows that we are capable of forming meaningless statements. I don't believe it says anything about God.

As a Christian I have good theological reasons to believe that God operates in a coherent fashion. If our end goal is a love relationship with God, I would have to believe he created the universe in such a way that we might actually know him. We are told we are made in his image. In light of that it is plain to see that what leads to life and discovery in this world is not incoherence, but rather that which is consistent. We use the law of non-contradition to find truth. Why then would we want to assume that the ultimate truth would be totally foreign to all we have ever experienced? Infinitely more wonderful and inexplicably beyond what we conceive of him in this life, sure. But utterly foreign?

7:52 AM

 
Blogger Matt M said...

I still think you're trying to have your cake and eat it - the God you describe isn't infinite, as you keep imposing limits on what he can and cannot be.

Simply dismissing the illogical and meaningless as irrelevant is to drag God down to the human level of comprehension. Giving Him such attributes is understandable, but incompatible with the idea of an infinite being. You're committing what a number of your fellow Christians would call the error of Anthropomorphism.

If God is comprehensible He's not infinite. If he's infinite then He's not comprehensible. Trying to reconcile the two is - no pun intended - like trying to square a circle.

8:39 AM

 
Blogger Alex said...

the God you describe isn't infinite, as you keep imposing limits on what he can and cannot be.

I'm not so sure this is the case. Simply because something is infinite does not mean it is without limit in every sense. For instance: If you have an infinite set it cannot, at the same time, be finite. This is a limit, but it does not in any way modify the incomprehensible infinitude of the set in question. The set is still infinite in quantity but is not malleable in it's essence.

I don't have time at the moment to read through the anthropomorphism page you linked to. I'll try and look through it another time. But let it suffice to say that to affirm the coherence of God is a far cry from the heretical sorts of anthropomorphisms that are sometimes heard. (i.e. that God is a man etc...)

If God is comprehensible He's not infinite.

I'm not sure about this as a sweeping sort of statement, but to a degree I think I can go along with what you are hinting at. However, I have not argued that God is comprehensible. To affirm coherence does not necessarily lead to comprehension. For example an infinite progression of increasing whole numbers is perfectly coherent, but none-the-less incomprehensible. Likewise, beginning of time itself is coherent, but equally incomprehensible. I am ready to affirm all manor of paradox and wonderment, but I am simply not willing to affirm that God must be able to exist as a flat contradiction.

9:14 AM

 
Blogger Matt M said...

If you have an infinite set it cannot, at the same time, be finite.

But then you've established a property it doesn't have - rendering it finite.

The problem I have with describing something as infinite is that it gives rise to all manner of paradoxes such as this. The human brain simply isn't equipped to deal with the concept. An infinitely powerful being would have to be capable of both existing and not existing (and much beyond). The moment you begin to establish limits (indeed, as Moore points out, the moment you begin to describe something) it becomes finite.

For example an infinite progression of increasing whole numbers is perfectly coherent

I'm not so sure it is: Take the distance between your face and the computer screen, now halve it, then again, then keep going - at no point will you encounter a number that can't be halved, so you'll never stop. The distance between your face and the computer is clearly finite, but infinite at the same time. If there's an infinite distance between any two numbers - how can any mathematical construct be considered truly coherent?

10:42 AM

 
Blogger revvvvvvvd said...

Oxford's English Dictionary is hardly the appropriate place to begin philosophical discourse.

I have two (maybe more, we'll see) contentions with the omnipotence paradox:

1. It deconstructs the problem of evil. If we do not need an account of how God can guryhugle a tumracky, then we don't need an account of how God can be good and allow evil simultaneously.
2. Abstracting from 1, the assumption that logical rules (e.g., Not 'p' and 'not p'.) apply in discourse about God is fundamental. Without it, our conversation falls to pieces.
3. I will concede that there are some things that appear, prima face, logically incoherent. But we might be wrong. We might lack the conceptual powers to grasp such things. So, God can do all that is objectively, logically possible. He cannot do things that are objectively, logically impossible. But what can we do? We have to assume that the things we perceive of as logically coherent are indeed thus, until proven otherwise. Again, this is a pragmatic, methodological principle!

2:59 PM

 
Blogger Matt M said...

Alex,

Looking back I see that I managed to completely misread your first point! I've been having some technical problems with my computer and was a little distracted at the time - I should've been paying more attention.

For example an infinite progression of increasing whole numbers is perfectly coherent, but none-the-less incomprehensible.

Yes, but there's a crucial difference between something being infinite in extension and infinite in ability - the latter is what we're dealing with, and the latter which I'm arguing is beyond our comprehension.

If God has infinite ability - as many have argued - then He can do anything, and therefore you can't say He's limited by anything. An infinitely powerful God would be beyond rationality and logic - and therefore beyond our framework for understanding in any meaningful way.

3:21 PM

 
Blogger Rev. Dr. Incitatus said...

Revvvvvd said (on his blog),
"Or we could, as a matter of methodology, assume that the sentences that prima facie appear to be nonsensical actually ARE nonsensical, until we have an account of what the sentence might mean. Physicists give an account of parallel lines meeting, and light being both particulate and wave-like. Theologians give an account of how God is triune and how Christ is human and divine."

I think Revvvvvd's on to something here (edit: and in point No. 3 above). Logic is certainly a handy way to navigate our small bit of the cosmos, as Newtonian physics and Euclidian geometry generally are, but how well it holds up to those parts of the universe invisible to our perception (directly at least) isn't very clear.

Matt, I think you should change the 4-sided triangle in your analogy to a 2-sided triangle, or else provoke a long and terribly weird discussion about space-time, higher dimensions, and the possibility that what we think is a three-sided triangle may be a tetrahedron as far as God's concerned.

Square might well ask the great omnipotent Sphere to make a di-angled version of a one-angle, but he's liable to suffer a severe, 2-dimensional aneurysm if Sphere tells Square that what he thinks is a one-angle is actually a triangle, and no matter how many dimensions tweak it can't be beaten two angles. I don't think, anyway. Then again...

3:27 PM

 
Blogger Matt M said...

Revvvvvvd,

Oxford's English Dictionary is hardly the appropriate place to begin philosophical discourse.

I'd argue that defining terms is a completely appropriate place to begin such a discussion - it avoids us talking past each other and really focuses the issue.

1. It deconstructs the problem of evil. If we do not need an account of how God can guryhugle a tumracky, then we don't need an account of how God can be good and allow evil simultaneously.

I'd actually agree with this - make God infinitely powerful and any discussion about what He can and can't do becomes pretty meaningless.

2. Abstracting from 1, the assumption that logical rules (e.g., Not 'p' and 'not p'.) apply in discourse about God is fundamental. Without it, our conversation falls to pieces.

Again, I agree. we can only talk (or understand) a being with finite abilities.

This is my argument: An infinitely powerful being (the conventional definition of omnipotent) is beyond the human capacity to understand and discuss.

He cannot do things that are objectively, logically impossible.

Which means He has finite ability.

3:28 PM

 
Blogger Matt M said...

Incitatus,

Matt, I think you should change the 4-sided triangle in your analogy to a 2-sided triangle, or else provoke a long and terribly weird discussion about space-time, higher dimensions, and the possibility that what we think is a three-sided triangle may be a tetrahedron as far as God's concerned.

Um... yeah... I think.

Actually*, that puts me in mind of what I think could be a decent metaphor for what I'm trying to say...

For a finite being to understand an infinite being would be like a person living in a 2D universe trying to understand a 3D concept: impossible.

(*Note to self: buy thesaurus)

3:32 PM

 
Blogger Rev. Dr. Incitatus said...

Wait a minute. Replace all that talk of "angles" with "sides". I was getting confused. A one-angled thingy must have at least two sides &c...

3:45 PM

 
Blogger Timmo said...

As always, the Stanford Encyclopedia of philosophy has a good article on the subject. For the interested/unawares:

Omnipotence

9:58 PM

 
Blogger revvvvvvvd said...

Matt,

I think I see the genius of your argument. You think the inconceivability of an omnipotent constitutes an argument against the existence God. Right? Of course, for this to be so, you need to show that inconceivability entails incoherence. But but but, even if you DON'T show this, you can say that it's pointless talking about God because even if God did exist, we would not be able to conceive of God. So why talk about God at all?

Something like that. Or maybe not. I don't know. *mulls over profundities*

Anyway, I have two other points:
1. I agree that defining terms is important. I reject your (and Oxford's) definition of omnipotence.
2. I disagree that "not being able to perform objectively logically impossible acts" renders God omnipotent? Why? Because " objectively logically impossible acts" are meaningless sentences. They do not refer to any reality.

1:49 AM

 
Blogger Matt M said...

Revvvvvvd,

I think I see the genius of your argument.

Well, it's about time somebody did. :-)

You think the inconceivability of an omnipotent constitutes an argument against the existence God. Right?

I'm afraid not - all I'm arguing is that the ideas that God is infinitely powerful and that God can be understood and meaningfully talked about by us puny little humans are incompatible.

I reject your (and Oxford's) definition of omnipotence.

Every dictionary I've checked defines omnipotence as unlimited power - and given that most dictionaries are based on the most common usage of a word, I think it's fair to say that when the majority of people use the term omnipotence they have the idea of infinite power in mind.

From the Stanford Encyclopedia entry above (thanks Timmo) it seems that a lot of theologians have decided to shift the definition to maximally powerful (which I see as "diet" infinity) - which fits with Lewis's claims and makes the concept perfectly acceptable to me. (Although using a definition different from the commonly accepted one is cheating a little, in my opinion).

If you want to argue that God's power is limited to what's possible, I have no problem with that. My only beef is with the use is with the use of the term infinitely powerful, which cannot (by the commonly accepted definition) be bound by logic or meaning - as these are finite concepts.

4:24 AM

 
Blogger revvvvvvvd said...

Must've got carried away in my exegesis of your argument. Still, it's a good point; one that most theologians would happily concede. The skeptical (or sceptical) theists would most happily concede. And I generally like sceptical theism, although I worry about some epistemic repercussions the position entails. Another day.

While I see the problem with redefining words to mean slightly different things from their popular meanings, I don't think theologians are to blame in this case. The nature of the God debate makes it such that the definition of words like God and Omnipotence must be up to the theist. Why?

Atheism is, I think, a rejection of theism. It is saying, "God does not exist." But which God? I am an atheist for most gods, as Richard Dawkins would say. (He, and other atheists, just take it one deity further.) The atheist has to talk of God in the theist's terms to say, "This god does not exist."

So...it's not cheating. Theists are within their rights to define words like God and Omnipotence however they like. Atheists can, however, show that a particular kind of omnipotence (say) is inconsistent with other theistic beliefs, or other Christian (say) beliefs.

It's funny: I talk more about methodology than content nowadays. This is a reflection of my current reading. I'm teaching myself epistemology and logic at the moment.

5:53 AM

 
Blogger Alex said...

Hey there everyone!
Glad to see we are all getting such a rise out of this!

Matt,
I'll start with your revision on your first comment.

Yes, but there's a crucial difference between something being infinite in extension and infinite in ability - the latter is what we're dealing with, and the latter which I'm arguing is beyond our comprehension.

First off in a strictly technical sense I would think one could be omni-able even within the bounds of logic. I'm very much in line with what Revvvvvvd said: "objectively logically impossible acts" are meaningless sentences. They do not refer to any reality." If one was to stand before an omni-able agent and demand to see a breakfast so big he couldn't eat it, I'd have to believe the agent would simply shake his head, send you to your room and tell you to think about what you've done.

even so, I am not arguing that God is omni-able. Since I believe logic is a reflection of him and also that he has a specific character that he cannot act in violation of. You might call these things limits, but I feel that has more to do with the poverty of our understanding of perfect love, than any real limit upon God. So again I'm compelled to reemphasize Revvvvvd's remarks when he says: The atheist has to talk of God in the theist's terms to say, "This god does not exist."

If you want to deny the sort of incoherent thing you are describing you are free to do so, but your rejection (or acceptance) of such a being (or thing... seeing as how it would need to be personal/impersonal at the same time) does not in any way impinge upon our usual theme of whether or not the Christian God exists. It's a straw man. Have at'em.

The distance between your face and the computer is clearly finite, but infinite at the same time. If there's an infinite distance between any two numbers - how can any mathematical construct be considered truly coherent?

In this case you are talking about two different things. The distance between my face and the computer screen is not infinite and finite at the same time. The distance, in objective intervals, is finite, but the number of times that distance can be halved may very well be infinite.

The point I was trying to make is that the infinite does not require incoherence. Certainly it passes comprehension, but I do not see the need for (or even the possibility of) incoherence.

6:57 AM

 
Blogger Matt M said...

Revvvvvvd,

Theists are within their rights to define words like God and Omnipotence however they like.

I have no problem with the concept of a God being maximally powerful - but I don't get the impression that it's what most theists mean when they use the term omnipotent.

Alex,

For me, this has nothing to do with whether God exists or not - it's simply about the use of the term infinite. Ascribing a being with infinite power does render it incomprehensible because we can only deal with the finite.

What a lot of theologians seem to have done (and I believe Revvvvvvd and I are on the same page with this now) is shift from infinitely powerful to maximally powerful - which is a very different thing. An infinitely powerful being cannot be bound by meaning and logic, because these are finite terms. A maximally powerful being can. Infinite power is incoherent. Maximal power makes perfect sense (or at least seems to).

The distance, in objective intervals, is finite, but the number of times that distance can be halved may very well be infinite.

You're still left with the paradox of a finite distance being infinitely divisible - i.e. containing an infinite number of points.

7:35 AM

 
Blogger Alex said...

Matt,
Dude. The power just went out here right as I was finishing this post... So this is the second time through. Few things in life fill me with as much rage as this situation. Anyway....

Ascribing a being with infinite power does render it incomprehensible because we can only deal with the finite.

I certainly agree with you here, but I am not rejecting the incomprehensibility of the infinite. I am rejecting the notion that the infinite must include the incoherent. The moment you add "incoherent" as a necessary part of the mix the whole notion of omnipotence becomes self-referenially incoherent. (self-defeating) For to maintain this position you would need to affirm that the omnipotent agent in question is simultaneously omnipotent and utterly lacking in power. If you reject that you introduce a "limitation" that you seem inclined to reject. This would not be a pardox. It's a flat out contradiction. The whole enterprise devolves into utter nonsense.

In light of that, I see no need to shift from "infinitely powerful" to "maximally powerful" as I see the infinite as necessarily being confined to the logically possible.

You're still left with the paradox of a finite distance being infinitely divisible - i.e. containing an infinite number of points.

Sure. I have no problem with that, but this is a far cry from incoherence.

Well, my dear friend, as much as I'd like to continue beating this around, I really must get to my papers. It's been a quality couple of days. It's been a while since we've had this sort of highly "engaged" conversation. Good stuff! ...I think.

8:12 AM

 
Blogger Matt M said...

Alex,

Strangely enough, I can deal with losing posts. It's computer's slowing down that gets to me - if I'm halfway through a comment and the computer just stops for a while, or slows to a crawl with letters appearing at the rate of 2 or 3 every minute (thank you Norton Antivirus and your need for 80% of my CPU to update!) it completely throws me. It's truly frustrating.

I am rejecting the notion that the infinite must include the incoherent.

Then you have to reject the accepted definition of "infinite" and come up with one of your own: the infinite is boundless... endless... without limitation in any way... that's it's most important property - so you can't say it's bound by anything, including meaning or logic. The moment you begin to describe a being as this or that you move firmly into the realm of the finite.

The whole enterprise devolves into utter nonsense.

That's the consequence of a finite being trying to comprehend the infinite - it is nonsensical, in that it's outside reason. A being of infinite - unending - power would have to be capable of making itself coherent, incoherent and neither all at the same time.

I see the infinite as necessarily being confined to the logically possible.

The infinite cannot be confined by its very definition - it is the unconfined. Anything that is confined is finite.

Sure. I have no problem with that, but this is a far cry from incoherence.

There is both a finite and infinite number of points in any measurement - and you don't regard that as incoherent?

It seems we may have reached an impasse. As long as you keep insisting that the infinite can't be infinite we've got nowhere to go. All I can do is repeat the definition of the word over and over again.

10:19 AM

 
Blogger Timmo said...

Hey guys,

I noticed at various points in this discussion people have said that contradictions are meaningless. A meaningless sentence does not express any proposition at all: it just a series of signs. For example, "Colorless green ideas sleep furiously" is a grammatical sentence, but, prima facie does not mean anything. A contradiction, such as "Bond is a spy and Bond is not a spy", is not similarly meaningless. Contradictions are false, and as a result are not meaningless. It is false that Bond is a spy and Bond is not a spy. Moreover, contradictions are not empty in content, like people sometimes say. In classical logic, a contradiction entails every other proposition. Thus, at least in classical logic, contradictions have as much content as a proposition can have!

Also, it does not help to characterize omnipotence as *infinite* power. I suppose the idea is something like this: x is omnipotent if and only if the set of possible actions x is capable of performing is infinite. However, under this definition, you and I are omnipotent! We can each utter any one of the infinite number of grammatical English sentences, and this means there are infinitely many things we are capable of doing.

In general, I am of the mind that before importing the notion of infinity into a discussion, it should be well-defined, otherwise it only obfuscates the main issue. Infinity is a well-defined mathematical notion: a set S is (Dedekind) infinite exactly if there exists a proper subset P of S such that there exists a bijection between S and P. The set of natural numbers is Dedekind infinite since there exists a bijection between the set of natural numbers and the set of even natural numbers (one of its proper subsets).

10:44 AM

 
Blogger Tom Freeman said...

“Let me through, I got here late!”(H. Simpson)

Although there’s really not much left for me to say. Any of these statements seems perfectly reasonable:

Matt: If you want to argue that God's power is limited to what's possible, I have no problem with that. My only beef is with the use is with the use of the term infinitely powerful, which cannot (by the commonly accepted definition) be bound by logic or meaning

Revvvvvd: ”objectively logically impossible acts" are meaningless sentences. They do not refer to any reality

Alex: I see no need to shift from "infinitely powerful" to "maximally powerful" as I see the infinite as necessarily being confined to the logically possible.

I’m not really concerned to fight over definitions, although I’d probably lean to the view that ‘infinite power’ means ‘able to perform any action’, and that logically impossible descriptions don’t actually denote actions, so no great loss. In fact, no loss at all.

‘Create a 4-sided triangle’ is incoherent not because of the intellectual limits of our minds. The abstract concepts ‘4’, ‘side’ and ‘triangle’ are not complicated and we know enough about them to see that they simply don’t and couldn’t cohere. A triangle is something that by definition has exactly three sides. Three is by definition not four.

‘tugimahy a hufquest bubaluyte’ is incoherent because (take your pick here) either three of the words don’t have meanings or three of the letter-strings aren’t words. Either way, no action is being described.

I think pretty much everyone who discusses these things (except, apparently, Descartes) shrugs off rock-type paradoxes with a gentle refinement of what ‘omnipotent’ means.

“There’s nothing you can do that can’t be done.” (The Beatles)

10:50 AM

 
Blogger Tom Freeman said...

Just seen Timmo's comment:

x is omnipotent if and only if the set of possible actions x is capable of performing is infinite. However, under this definition, you and I are omnipotent! We can each utter any one of the infinite number of grammatical English sentences

What about: x is omnipotent if and only if the set of possible actions x is incapable of performing is empty.

Also, Matt: the infinite can be bounded and limited. The set of integers is infinite, but doesn't include 3.1 or 9.8 (or curry, or Peru...) Talking about 'infinite power' brings a category (actions) just as does talking about integers.

(Drat! I did get into a fight about definitions!)

10:57 AM

 
Blogger Matt M said...

Ultimately, this seems to come down to whether the infinite is (or should be) limited to the possible - I say no, others say yes.

11:00 AM

 
Blogger Matt M said...

Tom,

Matt: the infinite can be bounded and limited. The set of integers is infinite, but doesn't include 3.1 or 9.8 (or curry, or Peru...) Talking about 'infinite power' brings a category (actions) just as does talking about integers.

Then, according to the dictionary definition, the set of integers must be infinite and finite - unlimited and limited.

I'm arguing against the term "infinite" precisely because it gives rise to these kind of paradoxes.

11:21 AM

 
Blogger Rev. Dr. Incitatus said...

- God makes all the rules

- Therefore, God is omnipotent if we define an omnipotent being as one for whom there is no rule that cannot be created, altered or destroyed (essentially Tom's definition).

- If God is omnipotent, he cannot do anything 'illogical' because the rules of logic are his own and set by his whim. (If he were to act outside of an initial set of created rules, it would simply be due to his creating/changing or deleting a rule.)

So I would argue that an omnipotent being cannot do the impossible (with respect to its world view, I mean); not because there is a limitation, but precisely because there are no limitations.

It just seems that inevitable that evil - or even simply the absence of good - is either a byproduct of God's manipulation of the rules (if he is omnipotent), or something independent of God (in which case he isn't omnipotent and we're back to spiritual dualism).

The best answer to the, "Why did God allow evil/absence of good into the world", is for the theist to say, "Because that is his will", and leave it at that. Any response to that on the basis of human logic can then be countered by appealing to the possibility that God's rules preclude us from understanding all of God's rules. I think any attempt to deal with this issue in terms of our own logic is just not going to give the theists the answer they are looking for.

12:02 PM

 
Blogger Timmo said...

Tom,

Taken together with some of your other comments, the definition of omnipotence you offer is interesting. You write,

What about: x is omnipotent if and only if the set of possible actions x is incapable of performing is empty.

Your idea seems to be that an agent x is omnipotent just when {A | It is not the case that possibly, x performs A} is empty. Then, you can say that God is omnipotent because He can perform every action. The description 'the act of moving an immovable rock' fails to denote -- there is no such action. We can say, then, that God can not perform the action of moving an immovable rock (since there is no such action to perform) while at the same time say that the set of actions God can not perform is empty. One is tempted to say that the act of moving an immovable rock is in the set of actions God can not perform, but, since there is no such act, it is not the case that the act of moving an immovable rock is in the set of actions God can not perform!

(A quick proviso: I mean to talk about act types here, not act tokens.)

Taking this suggestion the distance would be difficult, I think. We need some criteria for telling us when actions exist -- and I shirk from thinking those up!

12:51 PM

 
Blogger Tom Freeman said...

Matt,
Then, according to the dictionary definition, the set of integers must be infinite and finite - unlimited and limited.
I'm arguing against the term "infinite" precisely because it gives rise to these kind of paradoxes.


It may well be an unhelpful term, but in this case I don't think it's paradoxical as there are two different senses of the word being applied.

The set of integers is infinite in number but limited in scope. 'Infinite' needn't mean 'all-encompassing'.

Also on the matter of the distance between the face and the computer screen, which is "clearly finite, but infinite at the same time". The 'infinite' aspect of this is not because of anything mysterious about this 40cm or so - it's that this distance can theoretically be cut into infinite divisions, which can only be infinite in number at the cost of being infinitesimal in size.

(Zeno's paradox about the arrow that can never travel a finite distance because it has an infinite number of sub-distances to get through dissolves when it's pointed out that the amount of time being allowed is also being divided into infinitesimal chunks that fly by as surely as the arrow itself.)

Timmo,
We need some criteria for telling us when actions exist -- and I shirk from thinking those up!

And I stand shoulder to shoulder with you in shirking that!

Sometimes, like with making the 4-sided triangle, we can deduce pretty easily whether that could denote and action. With other things (time travel?), understanding whether they're logically possible may be beyond our ken.

It's not a properly actionable definition, but I thought that couching omnipotence negatively, in terms of lack of inability, might be worth a pop.

1:48 PM

 
Blogger Crushed by Ingsoc said...

No, it rules out an authotitarian God, not a God who trusts so much in love, that he granted everything the free will to reject him.

5:16 PM

 
Blogger revvvvvvvd said...

I think I'll contend against talking about logical rules that God made up.

It'll not so much that God made up some logical rules within which God must then work, but that some syntactically and grammatically sound sentences do not correspond to any reality.

Am I making sense?

I think I will also contend against any theists who want to talk about God being infinitely powerful, in the strong sense. If theologians have moved from speaking of infinite power to maximal power, it is only because they have erroneously moved TO speaking of infinite power to begin with.

I was about to talk about biblical theology, but then I wonder if there is such a thing, and if there is I wonder if the "God of the Bible" is what we really want.

Tidbit: There's a 8th (?) century BCE vase, depicting two anthropomorphic bovine-ish things, with the inscription: "...YHWH and Asherah, his wife." Or something like that. It was my desktop picture for a while but my Christian friends frowned upon it.

8:06 PM

 
Blogger revvvvvvvd said...

Oh yea, I've been meaning to ask for some help on something. This has nothing to do with God. Not directly anyway:

How do monists (I presume we're all broadly monists here) solve the hard problem of consciousness?

I seem to remember Dennett saying something terribly insightful here, but I forget. Does he show that the ghost-in-the-machine idea leads to infinite regress?

8:09 PM

 
Blogger Timmo said...

Revvvvvvvd,

How do monists (I presume we're all broadly monists here) solve the hard problem of consciousness?

That's a big question, and I would love to be of help. Maybe you could write a longer comment, or a post somewhere, and flesh out just what you mean to ask. What do you mean by 'monist' and why do you think consciousness is an especially hard problem for monism?

9:59 PM

 
Blogger Matt M said...

Tom,

The set of integers is infinite in number but limited in scope. 'Infinite' needn't mean 'all-encompassing'.

According to the dictionary definition, it does.

If the infinite is endless and boundless then it's nonsense to talk about an "infinite set" - it cannot be boundless and have a boundary at the same time. If we had an infinite amount of curry, it would be impossible to talk about it co-existing with, say, an amount of rice - as the sum total of all this would have to be more than infinite, which doesn't make much sense.

Surely it makes more sense to talk about the maximal amount of curry - the most curry that there could possibly be. Be removing the terms endless and boundless (i.e infinite) we render the concept meaningful.

4:26 AM

 
Blogger Rev. Dr. Incitatus said...

Matt,
You mean like covering a sphere with vindaloo. That would yield a maximum, but finite (and unbounded in 2D at least) amount of curry. But where would the lager go?

A similar argument used for God though will still aply limitations to Him that probably would seem unacceptable to a theist.

6:55 AM

 
Blogger Tom Freeman said...

Revvvvvvvd,
I seem to remember Dennett saying something terribly insightful here, but I forget. Does he show that the ghost-in-the-machine idea leads to infinite regress?

This used to be my thing! Dennett did nicely lampoon the idea of a homunculus looking at experiences in the ‘Cartesian theatre’, but the idea that that’s an infinite regress has been around for longer, I think.

He also tellingly discussed how a zombie (supposedly a non-conscious being physically and behaviourally like us) would have to be just as convinced as us that it was conscious. Although personally, I was actually only convinced by this argument when I read David Chalmers’s attempt to refute it (I’m a bit contrary like that).

I’ve decided to stick my neck out and post some of my nine-year-old writing on this…

(i.e. it was nine years ago, not written by a nine-year-old)

10:21 AM

 
Blogger revvvvvvvd said...

Tom, could I be so bold as to ask for a copy of your dissertation? A pdf perhaps?

4:53 PM

 
Blogger Tom Freeman said...

As a quick indicator of how very, very clever I undoubtedly am, I completely failed to include this link in that last comment, thus rendering it utterly pointless.

The chunks I've posted run to about 2000 words and the whole thing is 15000! If you like I can send you the original - to the Gmail listed on your profile page?

5:28 PM

 
Blogger revvvvvvvd said...

Yes, the Gmail account will do. You DID put a link there, I think. I followed one at the bottom of this page. Or did you not do that?

6:13 AM

 

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