Define God

[MrDibble]

[QUOTE=Liberal]
You do reailze that the partakers are knowledge and power, not God1 and God2, right?
[/QUOTE]

Of course, what makes you think I didn’t.

[QUOTE=Liberal]

As I’ve said repeatedly, aesthetics is subjective: one man’s heaven is another man’s hell.

[/QUOTE]

This advances the debate not a whit.

[QUOTE=Liberal]

Even granting you that (for no particular reason), the attributes aren’t possibilities. What you strung together were possibilities.

[/QUOTE]

possibilities of attributes existing, since the point of contention is the possibility of existence. I don’t see how that’s a counterargument.

[QUOTE=Liberal]

Suppose you harmed me in some way. Suppose further that I am a pacifist, and believe that a man who harms me should be forgiven, and so I forgive you. The merciful thing for God to do is forgive you. The just thing for God to do is forgive you. Otherwise, he slights me.

[/QUOTE]

I’d argue that isn’t the just thing. God’s responsibility in your example *isn’t *to you, but to himself, as the judge. This is what that article meant by “exactly the punishment you deserve” when it spoke of Justice. Slighting you is irrelevant to the issue of Justice.

[QUOTE=Liberal]

The argument is called ontological because it deals with the atribute of existence. That’s what the “O” in MOP is for. Existence is the only attribue the argument examines.

[/QUOTE]

Existence of God, who needs a definition. And so we return to where we were.

[QUOTE=Liberal]

Certainly no more than your “you do realize don’t you?” crap.

[/QUOTE]

If my tone is upsetting you, perhaps you are reading too much into it. It’s a way of phrasing things, the same as I’d use in RL conversation, and doesn’t constitute an ad hominem attack anywhere outside your perception.

Certainly not the same as comparing my reasoned, professional cite to a delusional frothing lunatic.

[QUOTE=Liberal]

The article in question is from a professional philosophical journal.But the article in question has nothing to do with ontology. It has to do with allegedly competing attributes other than existence.

Attributes which are central to a definition of God, which is central to the MOP of the existence of God.

I can understand why you want to divorce the actual MOP from its definitional basis (I’d do the same if I were you) but that isn’t going to get a pass here, I’m afraid. The MOP makes assumptions about a shared semantic framework for a definition of God that don’t stand up to scrutiny.

[QUOTE=Liberal]

Philo typically publishes contrary articles. Did Infidels include it?

[/QUOTE]

Do they have to? But it doesn’t look like that Philo had a competing article.

[QUOTE=Liberal]

First of all, I am aware of the weaknesses of the MOP, and competing attributes isn’t one of them.
[/QUOTE]

It seems lots of people don’t agree with you. I’d say it is one of them, because it is an argument philosphers have made.

[QUOTE=Liberal]
Second, Godel’s version is not even valid and isn’t being discussed here.
[/QUOTE]

I also mentioned Plantinga.

[QUOTE=Liberal]

Third, it is ludicrous to objectivize positivity. Light can be the absence of darkness, or darkness can be the absence of light.

[/QUOTE]

How am I objectivising positivity? It’s an adjectival descriptive of an attribute, not the attribute itself. And no, light is a stream of photons.

[QUOTE=Liberal]

Practice what you preach: give an example of any statement from the MOP (modern, not Godel) that addresses any attribute other than existence.
[/QUOTE]

I’ve already said it goes for Plantinga as well. Or what version are you thinking of now?

[MrDibble]

[QUOTE=Liberal]
You do reailze that the partakers are knowledge and power, not God1 and God2, right?
[/QUOTE]

Of course, what makes you think I didn’t.

[QUOTE=Liberal]

As I’ve said repeatedly, aesthetics is subjective: one man’s heaven is another man’s hell.

[/QUOTE]

This advances the debate not a whit.

[QUOTE=Liberal]

Even granting you that (for no particular reason), the attributes aren’t possibilities. What you strung together were possibilities.

[/QUOTE]

possibilities of attributes existing, since the point of contention is the possibility of existence. I don’t see how that’s a counterargument.

[QUOTE=Liberal]

Suppose you harmed me in some way. Suppose further that I am a pacifist, and believe that a man who harms me should be forgiven, and so I forgive you. The merciful thing for God to do is forgive you. The just thing for God to do is forgive you. Otherwise, he slights me.

[/QUOTE]

I’d argue that isn’t the just thing. God’s responsibility in your example *isn’t *to you, but to himself, as the judge. This is what that article meant by “exactly the punishment you deserve” when it spoke of Justice. Slighting you is irrelevant to the issue of Justice.

[QUOTE=Liberal]

The argument is called ontological because it deals with the atribute of existence. That’s what the “O” in MOP is for. Existence is the only attribue the argument examines.

[/QUOTE]

Existence of God, who needs a definition. And so we return to where we were.

[QUOTE=Liberal]

Certainly no more than your “you do realize don’t you?” crap.

[/QUOTE]

If my tone is upsetting you, perhaps you are reading too much into it. It’s a way of phrasing things, the same as I’d use in RL conversation, and doesn’t constitute an ad hominem attack anywhere outside your perception.

Certainly not the same as comparing my reasoned, professional cite to a delusional frothing lunatic.

[QUOTE=Liberal]

But the article in question has nothing to do with ontology. It has to do with allegedly competing attributes other than existence.

[/QUOTE]

Attributes which are central to a definition of God, which is central to the MOP of the existence of God.

I can understand why you want to divorce the actual MOP from its definitional basis (I’d do the same if I were you) but that isn’t going to get a pass here, I’m afraid. The MOP makes assumptions about a shared semantic framework for a definition of God that don’t stand up to scrutiny.

[QUOTE=Liberal]

Philo typically publishes contrary articles. Did Infidels include it?

[/QUOTE]

Do they have to? But it doesn’t look like that Philo had a competing article.

[QUOTE=Liberal]

First of all, I am aware of the weaknesses of the MOP, and competing attributes isn’t one of them.
[/QUOTE]

It seems lots of people don’t agree with you. I’d say it is one of them, because it is an argument philosphers have made.

[QUOTE=Liberal]
Second, Godel’s version is not even valid and isn’t being discussed here.
[/QUOTE]

I also mentioned Plantinga.

[QUOTE=Liberal]

Third, it is ludicrous to objectivize positivity. Light can be the absence of darkness, or darkness can be the absence of light.

[/QUOTE]

How am I objectivising positivity? It’s an adjectival descriptive of an attribute, not the attribute itself. And no, light is a stream of photons.

[QUOTE=Liberal]

Practice what you preach: give an example of any statement from the MOP (modern, not Godel) that addresses any attribute other than existence.
[/QUOTE]

“<>G” depends on G, and in defining G you need to assign attributes, or yes, you’re proving the maximal greatness of a slime mould.

[monavis]

[QUOTE=SentientMeat]
I’m not quite sure how we digressed into talking about formulae rather than the objects and processes my definition of the universe specified, but the point I think you’re missing is that physics can also be used to describe (and, in evermore complex networks, explain) systems such as decision-making neural networks. (Note that I said explains rather than predicts – just because physics explains the weather doesn’t mean it can tell you whether it will rain on your birthday). After all, it may well be that we are merely obeying (stochastic) “rules”, and control is an illusion! Even the judgement over what is trivial and what is salient might one day be well understood in terms of outputs from computational “judgement modules” which are every bit as physical as the devices which judge whether a car is speeding or not.
I would personally go as far as to say there are no nontemporal truths, since “truth” itself did not exist for 13.6 billion years – it being, again, the output of a biological computer the like of which simply wasn’t around while galaxies were forming, planets cooling, and molecules self-replicating: Everything is temporary, even physical laws (since all bets are off in the Planck era!), and indeed one can’t be certain about anything (“certainty” itself being merely a … yes, you guessed it!.. output of a blah blahdy blah). In fact, your point about chairs reinforces what I said earlier about the pre-humanity intuition pump. We must all offer an opinion about whether we ourselves, and all our conceiving, statement-making and truth judging, existed for those billions of years, and whether we will exist for billions of years in future. I find the proposition that “I” existed in a universe comprising only hydrogen and helium absurd, and so I seek an explanation of how a conceiving machine might evolve from gas. That is the point of formulating a physicalist philosophy.
Of course – in fact, I apologise for sounding even slightly slighted.
Fair enough, but a word of advice – do endeavour to pinpoint where exactly you disagree with him if you have time. Breaking the Spell and Freedom Evolves are particularly relevant to the points you’ve made in this thread.
[/QUOTE]

Truth has always existed for truth is what is! We may not know the truth but it is there.

Monavis

[Liberal]

[QUOTE=Indistinguishable]
There’s no good reason for us to accept <>G except via the plenitude of “possible worlds” principle: whatsoever is conceivable is possible. If we interpret G as something conceivable, we see that G is possible. But this PoPW principle also commits us to accepting the existence of a “possible world” in which nothing at all exists, and thus forbids us from simultaneously accepting the second premise (that it be logically demanded that if G is true at all, then G can’t be conceived to be false). So, as you say, there’s no good reason to accept both premises here.

[…snip…]

Basically, what the apparent soundness of the argument comes down to, I think, is a sleight of hand, where we find P1 reasonable under one interpretation of necessity/possibility, but not the right one to make the argument go through, but are tricked into conflating the two interpretations. P1 (it is possible that God exists necessarily) seems reasonable on some sort of plenitude-based account: certainly, we could imagine a world W which was part of a multiverse M such that God happened to fall into every “possible world” of M. But if that multiverse M isn’t the full multiverse F of things visible from our actual world (which our commitment to a plenitude-based account of possibility tells us should contain all consistent states of affairs), then God’s necessity in W is entirely dependent upon W being unable to see any worlds outside of M (in particular, W can’t see the conceivable worlds in F where God doesn’t exist). Thus, we are committed to saying that some worlds may be hidden from other worlds if we want to obtain P1 on a plenitude account. Specifically, the manner in which we allow worlds to hide from each other corresponds to something no stronger than an S4 system (worlds can see themselves, and sight is transitive, but sight won’t always be symmetric). The modal argument will go through fine and get us <>G (we can see some world which can only see worlds where God exists), but we won’t be able to move from <>G to G (and thus to G) without the full system S5 (which adds the symmetry condition on sight). So that is the problem with the argument: in order for us to convince ourselves of the truth of the premise <>G, we use a plenitude principle whose validity is based on an understanding of alethic logic as allowing asymmetry in the sight relation between possible worlds; however, to then, later in the argument, move from <>G to G and then G, we must use a logic which demands symmetry on the sight relation.
[/quote]
I envy your gift of clarity. Not surprisingly, your objection to the MOP is exactly properly put together, and is pretty much what everyone from Mackie to Suber has said. But let me share with you one objection to the objection.

To reach the interpretation that there has been a sleight of hand with <>G requires a sleight of hand itself, namely conflating a metaphysical possibility with an epistemic one. The notion of conceiving a world in which nothing at all exists, while epistemically attractive, is metaphysically untenable, especially when that world is held to be accessible to some other world. For one thing, it would need to have, of its own accord, some accessibility description, which it does not because it has nothing. It contains no truth. In fact, even describing it is problematic metaphysically because there is nothing to describe. We cannot even say that it contains nothing because that would assign it to having an attribute. But it has no attributes, including emptiness. It cannot be seen, and it cannot see.

So while there may be such a world for all we know, there cannot be such a world with a metaphysical description, let alone any logical association at any other world. It cannot even be examine by TRIV, because it doesn’t even have an equivalence axiom.

Incidentally, you are now a paid member. I have no idea who did it. (Okay, I’m lying, but play along with me.) I do know, however, how you can repay the person who did it: grace this board with your presence from time to time. Often would be better than seldom.

[Liberal]

[QUOTE=MrDibble]
This advances the debate not a whit.
[/quote]
Then why did you bring it up? You raised the point that I had assigned to morality an aesthetical judgment, but left out that I had described that assignment as subjective, thus countering your assertion that I had described positive as good and negative as bad. Such a description would take the whole thing back to a system of ethics, which is precisely what I was taking it away from. My definition of goodness, and my treatment of morality therefrom, does not even consider any ethical implications.

possibilities of attributes existing, since the point of contention is the possibility of existence. I don’t see how that’s a counterargument.

Well, just to clear that up, if we say that a world is possible, it doesn’t mean that the world contains modal assertions of possibility. It means that the world contains assertions of truth for that world. Thus, if W is possible, and p1, p2, and p3 are true at W, W is comprised not of <>p1, <>p2, and <>p3, but of p1, p2, and p3.

I’d argue that isn’t the just thing. God’s responsibility in your example *isn’t *to you, but to himself, as the judge. This is what that article meant by “exactly the punishment you deserve” when it spoke of Justice. Slighting you is irrelevant to the issue of Justice.

Well, that’s just ridiculous. I was the one harmed. Why is the victim irrelevant? You’re describing a system of ethics in which God makes rules and people who break them are punished. The degree to which that resembles anything I’ve proposed is the degree to which it is pertinent to my assertions. And that’s pretty much none at all.

Existence of God, who needs a definition. And so we return to where we were.

No, that’s not right. For the MOP, it is God’s existence that is defined. Now, there can be arguments that demand more, like the argument from cosmology. There, God is a creator being, and thus must have the power and knowledge to create. But to exist, a being need only have bounds that identify him and individuate his existence from the existence of any other being.

If my tone is upsetting you, perhaps you are reading too much into it. It’s a way of phrasing things, the same as I’d use in RL conversation, and doesn’t constitute an ad hominem attack anywhere outside your perception.

Thanks for saying that. The last thing I want is for you and I to fall out again. In fact, I would sooner abandon the argument than allow for that.

Certainly not the same as comparing my reasoned, professional cite to a delusional frothing lunatic.

Well, to their credit, I will say that Infidels has attempted to squash the “can’t prove a negative” business. But it’s hard to unring a bell, and the meme has propogated far beyond the borders of those who consult Infidels.

Attributes which are central to a definition of God, which is central to the MOP of the existence of God.

Such attributes are not only not central to the MOP, they are thoroughly irrelevant with respect to the MOP. And this is not anything unusual in the world of proving things about things. We may prove that an object is a triangle even though the object is also a piece of jewelry. We do not need to know anything about its rubies, gold, or diamonds to formulate a proof that its angles sum to 180 degrees.

I can understand why you want to divorce the actual MOP from its definitional basis (I’d do the same if I were you) but that isn’t going to get a pass here, I’m afraid. The MOP makes assumptions about a shared semantic framework for a definition of God that don’t stand up to scrutiny.

You can convince me simply by showing me. Where, in describing God as necessary existence is there any statement about knowledge, power, or morality — even in the traditional ethics sense of morality?

Do they have to? But it doesn’t look like that Philo had a competing article.

Right. It has a bias, which it even admits. It is dedicated to publishing the viewpoints of materialists. Would you accept a cite from a journal that is primarily associated with a church, and whose mission is to publish primarily the work of church doctrinaires who also happen to be logicians? If so, I can bring in a whole slew of pro-side arguers that I heretofore have left unmentioned.

It seems lots of people don’t agree with you. I’d say it is one of them, because it is an argument philosphers have made.

Somewhere, there is a disconnect. Consider that if A implies B, then it is not necessarily the case that B implies A. The latter is the converse of the former. Why would any logician cite the converse of a statement as implying that the original statement is false? The possibility sentence you gave is the *converse * of the S2 axiom. At best, it is a strawman.

How am I objectivising positivity? It’s an adjectival descriptive of an attribute, not the attribute itself. And no, light is a stream of photons.

Or, light is an electromagnetic wave. Or light is an unaccelerated amplitude of constant speed in a vacuum. Light, like God, may be examined in many different ways, which is a point I made above. But to say that good = positive and bad = negative certainly objectivises positivity, especially if you’re going to hold God as the agent to account. You protested above, saying that God did not have to consider me in His dispensation of justice. Why, if His considerations are not objective?

“<>G” depends on G, and in defining G you need to assign attributes, or yes, you’re proving the maximal greatness of a slime mould.

A slime mold whose being is defined as supreme, making it just a synonym for God — like Allah. I could call a pig a bird. But that wouldn’t make the pig fly. I could call a pig a slime mold, but it will still grunt like a pig. Why use a term (slime mold) that obfuscates when a perfectly good term (God) is already available and universally recognized to mean Supreme Being?

[begbert2]

[QUOTE=Liberal]
To reach the interpretation that there has been a sleight of hand with <>G requires a sleight of hand itself, namely conflating a metaphysical possibility with an epistemic one. The notion of conceiving a world in which nothing at all exists, while epistemically attractive, is metaphysically untenable, especially when that world is held to be accessible to some other world. For one thing, it would need to have, of its own accord, some accessibility description, which it does not because it has nothing. It contains no truth. In fact, even describing it is problematic metaphysically because there is nothing to describe. We cannot even say that it contains nothing because that would assign it to having an attribute. But it has no attributes, including emptiness. It cannot be seen, and it cannot see.

So while there may be such a world for all we know, there cannot be such a world with a metaphysical description, let alone any logical association at any other world. It cannot even be examine by TRIV, because it doesn’t even have an equivalence axiom.

[/QUOTE]
Does one have to postulate a world empty of logical statements in order to postulate one that conceivably could be absent a God? Wouldn’t any old possible world conceived not to have God in it do? How about one in which no object exists, although the various necessary truth statements (which don’t ‘exist’ in the conventional sense anyway) do?
Indistinguishable, I appreciate the confirmation of my disproof of the MOP; I’m sort of feeling my way in the dark here and every confirmation and clarification is useful.

I’m using S5 because, well, it’s the modal logic system under discussion here. Also it’s the only one that makes sense to me so far. How can one speculative universe effect another? They’re all imaginary (excepting the real one), aren’t they? (If this is some sort of Heisenberg uncertainty logic, I’m not certain I want to know about it.)

I guess the most succinct way to say it is that I have not yet grokked ‘accessibility’ (aka ‘sight’). No clue what it means. Is it some kind of grouping mechanism for sets of possible worlds under which a given set of statements is true? Does it say something about the remaining uncertainty implied by any finite set of known facts? Is it something else entirely? How does any of this imply a directional relation? I just don’t get it.

Even so much as a link would be kind of nice, assuming it’s to a nice clear explanation. Be gentle; I’m pretty slow for someone so brilliant.

[Liberal]

I will trust Indistinguishable to inform you that you have not provided a “disproof” of the MOP. What you’ve done is voiced an objection to it. Meanwhile…

@begbert2

Does one have to postulate a world empty of logical statements in order to postulate one that conceivably could be absent a God? Wouldn’t any old possible world conceived not to have God in it do? How about one in which no object exists, although the various necessary truth statements (which don’t ‘exist’ in the conventional sense anyway) do?

I take from that that you agree with my objection to Indistinguishable’s objection since you’re postulating a different objection than a world with nothing, and presenting that different objection to me. Again. I say “again” because it’s the same objection you raised earlier that I already addressed. Let’s say I define Bill as “an unmarried man”. I assert that there must be some sense in which Bill is a bachelor. You scoff, saying that you can conceive a sense in which Bill is married, reasoning that there might be some sense in which a bachelor is defined differently. But since Bill and unmarried man have an equivalence relation, you’re saying that you can conceive a sense in which an unmarried man (substituted for Bill, where unmarried man and Bill are equivalent) is married. You are entitled to hold the position, but I do not envy you for it.

[Voyager]

[QUOTE=Voyager]
I don’t have time to respond to this right now, though I do understand your point. I’ll get to it tonight.
Originally Posted by Liberal
But I think it is the case. Let’s call omni-knowledge K and omni-power P. The only reason a bi-omni God cannot know K is if it contradicts P, and the only reason He cannot do P is if it contradicts K. But then, the same holds for any other agent because of the relation between K and P. Knowledge is epistemlogical power, and power is metaphysical knowledge.

I know what I know not just because I’ve been exposed to it synthetically, but because I have the power to comprehend it analytically. Likewise, I can do what I can do not just because I am strong enough, but because I know how. An agent who has looked at Godel’s theorems but cannot read is at no advantage over an agent who is blind. And an agent with strong arms who knows nothing about screws and levers has no advantage over the agent with weaker arms who knows how to construct a jack.

And so an agent who knows what will happen but cannot cause it has no advantage over an agent who knows what will happen and can cause it. The latter agent, in fact, is causing the former agent to have knowledge — knowledge the former agent would not have if the latter agent did not have power. There are contradictions between K and P regardless of agency.

The supremacy is in the union of possibilities, where U is the union of elements from sets K and P.

[/quote]

Let’s look at K and P. Let’s define UP be the set of all actions , and UK the set of all knowledge. K and P are subsets of these. Let’s examine the elements of K and P.

First, we can remove the set of logically impossible actions from UP. I don’t think anyone has a problem with that. This gives us say, LP, the let of all logically possible actions. I think that one can remove logically impossible knowledge (like if any Turing machine will halt) but that isn’t important for the discussion.

Now, I see why you wrote union. If K is knowledge, and P is power, the interesection of these things is null, while the union is the set of all known things and possible actions. To correct this, let’s define AP, the set of all actions possible that do not contradict K, and AK, the set of knowledge that does not contradict P. That is not strictly the intersection, but I think it is what you meant.

We have a problem specifying AP and AK. If an action p is known by being in K, ~ap cannot be. ~ap here means a contradictory action, from another choice. If ap is rolling a 2, ~ap is rolling a 1, 3,… Thus, if K includes rolling a 2, then ~ap is not in AP.

Let’s say God can do anything, and decides to roll a 3 instead. The the knowledge of rolling a 3 can be ak, and the knowledge of rolling something else is in ~ak.

There appears to be a problem here, since who can we tell if ak or ap is in AP and AK? Which has primacy?

There is actually an answer, since AP is temporal and AK is atemporal. Assuming that K involves knowledge of the future, and assuming God is eternal, AK is set at the beginning of time, whatever that means. At any time t, God can see AK, and the set AK is unchanging.

Thus, for his actions, AP consists solely of actions in P also seen in AK. Thus, if God sees a 3 being rolled, rolling a 3 is in ap, and rolling a 2 is in ~ap.

Notice I didn’t specify any type of action in AP. If you want to expand P beyond this, K goes to null. If God can change any action, he does not know anything he will do. I think that is a logically consistent defiinition of God, but it is hardly the God you seem to believe in.

So, God is hardly omnipotent, but is he supreme? To examine this, we need to look at another entity. Let’s say this entity has K2 = null. (Not quite true, but assume he cannot see the future and is not close to being omniscient.) In isolation, then, his AP = UP - IP (where IP is the set of impossible actions.) We’re assuming that he can be omnipotent, and looking for problems.

Your’e excellent point is that this entity is also controlled by K - that he also cannot perform actions not in K. Let’s call our omniscient God G1, and our possibly omnipotent God G2.

We know G1’s AP1. I have two problems with calling G1 supreme. First AP2 and AP1 are disjoint. I don’t know how to compare them, and how to consider either superior. Maybe K contains the knowledge that G2 will kick G1’s butt. There is absolutely nothing logically inconsistent in this, but it would be odd for a supreme being losing to a non-supreme one. I also do not know how K and P compare in computing supremacy, which is the partial ordering problem I’ve already mentioned.

Second, while we assume that K is supreme, we have a problem with this. For one entity, we can dial the relative sizes of AK and AP. I didn’t do so, since I don’t know how you’d define supremacy in that way, and AK = K seems simpler. For two entities, I see nothing logically contradictory with AP2 containing actions not in K1. It does contradict the assumption of perfect omniscience, but that just means the premise could be bad. The first problem shows G1 need not be supreme without breaking the premise, so use that if you wish.

Summary. There is no single “intersection” of K and P. If K is UK - IK, the P consists only of the actions of G1 seen within K. We cannot choose one intersection that is “superior.”
If we deal with a different entity, G2, there is nothing impossible about AP2 > AP1. Further, if AP2 = UP2, then AK 1 cannot be UK1, and vice versa. (UKs are universal for all entities, actually.) Since we are not claiming AK2 = UK, there is no internal contradiction with AP2 = UP2. It is true that UK1 is contradictory with UP2, but there is no reason to choose between them. Even worse, we can introduce any number of powerful entities.

In other words, unless you assume supremacy, supremacy is a mess.

[Indistinguishable]

[QUOTE=Liberal]
Incidentally, you are now a paid member. I have no idea who did it. (Okay, I’m lying, but play along with me.) I do know, however, how you can repay the person who did it: grace this board with your presence from time to time. Often would be better than seldom.
[/QUOTE]

I don’t have time to say anything of use for the Great Debate right now, but I just have to say, wow, thanks, I’m just blown away by the generosity. I’ll try my best to live up to it.

[Voyager]

[QUOTE=Liberal]
I will trust Indistinguishable to inform you that you have not provided a “disproof” of the MOP. What you’ve done is voiced an objection to it. Meanwhile…

I take from that that you agree with my objection to Indistinguishable’s objection since you’re postulating a different objection than a world with nothing, and presenting that different objection to me. Again. I say “again” because it’s the same objection you raised earlier that I already addressed. Let’s say I define Bill as “an unmarried man”. I assert that there must be some sense in which Bill is a bachelor. You scoff, saying that you can conceive a sense in which Bill is married, reasoning that there might be some sense in which a bachelor is defined differently. But since Bill and unmarried man have an equivalence relation, you’re saying that you can conceive a sense in which an unmarried man (substituted for Bill, where unmarried man and Bill are equivalent) is married. You are entitled to hold the position, but I do not envy you for it.
[/QUOTE]

In other words, God exists in that world since you’ve defined God to exist in all possible worlds.
If I define a baelgle as a space bird that travels faster than light, then I know it travels faster than light since that’s its definition. Unlike Bill, I need to show the Baegle exists and is possible, just as you need to show that God exists and is possible, and not assume it.

IOW, you need a better response than defining away possible worlds without god, something I predicted you would do way back a bunch of pages ago. (Not out of any dishonesty, just because it is the only think you can do to make your “proof” work.

[begbert2]

[QUOTE=Liberal]
I will trust Indistinguishable to inform you that you have not provided a “disproof” of the MOP. What you’ve done is voiced an objection to it. Meanwhile…

I take from that that you agree with my objection to Indistinguishable’s objection since you’re postulating a different objection than a world with nothing, and presenting that different objection to me. Again. I say “again” because it’s the same objection you raised earlier that I already addressed. Let’s say I define Bill as “an unmarried man”. I assert that there must be some sense in which Bill is a bachelor. You scoff, saying that you can conceive a sense in which Bill is married, reasoning that there might be some sense in which a bachelor is defined differently. But since Bill and unmarried man have an equivalence relation, you’re saying that you can conceive a sense in which an unmarried man (substituted for Bill, where unmarried man and Bill are equivalent) is married. You are entitled to hold the position, but I do not envy you for it.
[/QUOTE]
Again (and I say ‘again’ because I already addressed this in Point 3 of my monolithic post):

There’s two ways to interpret ‘Let’s say I define Bill as “an unmarried man”’.

1. Bill means “an unmarried man” in the manner of straight equivalence. By this definition, “Bill” is a property of other entities and not an entity itself. The use of this would be “Bob is a Bill”, if Bob is an object that has the property of being an unmarried man.

2. “Bill” is a specific object, that has the property “an unmarried man”. By this definition, Bill is an object, which might possibly exist. If it exists, then it has that property. Any object that does not have this property is definitely not Bill.

Pick a definition and stick with it. If case 1 is true, then Bill cannot exist, since existing is not something a property does. If case 2 is true, then Bill does not have an equivalence relationship with “an unmarried man” since one is an object, the other a property.

You say I can attempt to postulate a sense in which Bill “is married”. This phrasing requires Bill to be an object, since it has a property: that’s case 1. Citing the two phrases’ equivalence, which is critical to your post here, that requires case 2. Logically speaking, it can’t be both. Again, pick a definition and stick to it.

Incidentally, the MOP uses case 2 of the definition. Explicitly. It’s formulated into premise 2. This is why the premise becomes a tautology if you define case 2 again as part of G; it basically becomes “If god exists as defined, then god exists as defined.” Incidentally.

[begbert2]

[QUOTE=Liberal]
I take from that that you agree with my objection to Indistinguishable’s objection since you’re postulating a different objection than a world with nothing, and presenting that different objection to me.
[/QUOTE]
Sorry to double-post, but I forgot to respond to this. I do not disagree with Indistinguishable’s objection; I believe that you misunderstood it, and thus misrepresented it, and therefore took a potshot at a strawman.

I don’t think that Indistinguishable posited a world in which no logical statements exist; that would probably be impossible anyway by the Necessitation Rule. (Not that I understand what that rule means, but I presume it necessitates at least the axioms of modal logic we’ve decided to use). I think that Indistinguishable was positing a world in which various statements have truth values, including the statement “Nothing exists”.

If I’m wrong about his meaning (which is hardly impossible), he can correct me at his leisure.

[MrDibble]

[QUOTE=Liberal]
Then why did you bring it up? You raised the point that I had assigned to morality an aesthetical judgment, but left out that I had described that assignment as subjective, thus countering your assertion that I had described positive as good and negative as bad.

[/QUOTE]

I brought it up to show you that asking me “how is positive defined” was a useless endeavour if we don’t agree on a semantic frame for our discussion.
I didn’t say what you imply I said in the bolded bit, I said that was what I understood them to mean, subjectively.

[QUOTE=Liberal]

Well, just to clear that up, if we say that a world is possible, it doesn’t mean that the world contains modal assertions of possibility. It means that the world contains assertions of truth for that world. Thus, if W is possible, and p1, p2, and p3 are true at W, W is comprised not of <>p1, <>p2, and <>p3, but of p1, p2, and p3.

[/QUOTE]

I’m aware of this - but we are not referring to a world, but an entity in that world, one that’s defined in most formulations of the MOP I’ve seen as a sum of some set of positive attributes.

[QUOTE=Liberal]

Well, that’s just ridiculous. I was the one harmed. Why is the victim irrelevant?

[/QUOTE]

Because Justice (at least, the way I understand it) is an abstract ideal. What you’re describing is indeed Mercy, and it’s you who are conflating the two

[QUOTE=Liberal]
You’re describing a system of ethics in which God makes rules and people who break them are punished. The degree to which that resembles anything I’ve proposed is the degree to which it is pertinent to my assertions. And that’s pretty much none at all.
[/QUOTE]

I disagree that you get to redefine words like Justice and Mercy to suit your argument.

[QUOTE=Liberal]

No, that’s not right. For the MOP, it is God’s existence that is defined. Now, there can be arguments that demand more, like the argument from cosmology. There, God is a creator being, and thus must have the power and knowledge to create. But to exist, a being need only have bounds that identify him and individuate his existence from the existence of any other being.

[/QUOTE]

How are you going to individuate him without defining him?

[QUOTE=Liberal]

Thanks for saying that. The last thing I want is for you and I to fall out again. In fact, I would sooner abandon the argument than allow for that.

[/QUOTE]

I’m totally with you on this - in fact, see the end of my post.

[QUOTE=Liberal]

Well, to their credit, I will say that Infidels has attempted to squash the “can’t prove a negative” business. But it’s hard to unring a bell, and the meme has propogated far beyond the borders of those who consult Infidels.

[/QUOTE]

Then I’d suggest continuing to hold it against them is not right.

[QUOTE=Liberal]

Such attributes are not only not central to the MOP, they are thoroughly irrelevant with respect to the MOP.

[/QUOTE]

I disagree that anything that’s needed to define God is irrelevant to the MOP

[QUOTE=Liberal]

You can convince me simply by showing me. Where, in describing God as necessary existence is there any statement about knowledge, power, or morality — even in the traditional ethics sense of morality?

[/QUOTE]

I’m going by every argument about the MOP that I’ve seen so far. It comes into it every time. If God were just necessary existence without any other attributes, all you’ve shown is that necessary existence exists (if you buy the premises), which is hardly an argument. You have to attach other attributes to the necessarily existing entity to get God out at the end.

[QUOTE=Liberal]

Right. It has a bias, which it even admits. It is dedicated to publishing the viewpoints of materialists. Would you accept a cite from a journal that is primarily associated with a church, and whose mission is to publish primarily the work of church doctrinaires who also happen to be logicians? If so, I can bring in a whole slew of pro-side arguers that I heretofore have left unmentioned.

[/QUOTE]

Do they also publish counter-arguments? It’s a fallacy that just because *Philo *didn’t have a counterarticle for that one article, that they don’t publish pro-theology article. A glance at their website shows this. There is a mission, and a bias, but you’ve not shown that they are not a professional philosophical journal.

[QUOTE=Liberal]

Somewhere, there is a disconnect. Consider that if A implies B, then it is not necessarily the case that B implies A. The latter is the converse of the former. Why would any logician cite the converse of a statement as implying that the original statement is false? The possibility sentence you gave is the *converse * of the S2 axiom. At best, it is a strawman.

[/QUOTE]

But it’s not cited to counter S2, it’s cited to show that a definition of both Godel and Plantiga’s formulations of the MOP are not coherent. I don’t know why you keep bringing up the relation to S2, it’s not relevant. What’s relevant is what you’ve already agreed, that it is not a true statement.

[QUOTE=Liberal]

Or, light is an electromagnetic wave.
[/QUOTE]

This is the same statement as what I said.

[QUOTE=Liberal]
Light, like God, may be examined in many different ways, which is a point I made above. But to say that good = positive and bad = negative certainly objectivises positivity, especially if you’re going to hold God as the agent to account.
[/QUOTE]

I don’t agree - like I said, they are attributes not things. I fail to see how that objectifies them.

[QUOTE=Liberal]
You protested above, saying that God did not have to consider me in His dispensation of justice. Why, if His considerations are not objective?

[/QUOTE]

But they are objective, if you assign the quality of All-Just to God. That’s supposed to be the point of Ultimate Justice.

[QUOTE=Liberal]

A slime mold whose being is defined as supreme, making it just a synonym for God — like Allah. I could call a pig a bird. But that wouldn’t make the pig fly. I could call a pig a slime mold, but it will still grunt like a pig. Why use a term (slime mold) that obfuscates when a perfectly good term (God) is already available and universally recognized to mean Supreme Being?
[/QUOTE]

Because I’m trying to see where, if the only property exhibited is “supreme existence”, it makes any difference.

Let me ask this straight out, and I’d like a straight answer: Are you saying that God need have no other attributes at all except existance? That that would fulfill the criteria for something to be God to you? It wasn’t enough for Godel or Plantinga. Both their MOP variants speak of properties attached to God.

Or are you saying that from necessary existance, other attributes of God naturally follow? Because I’m not seeing where you showed that.

Now, to my last point - I don’t think I’m ever going to buy into the MOP, because I don’t agree with the idea that perfection is possible, in any possible world. I think the onus is on the ones invoking it to show that it is. Consider this a denial of the metaphysical, if you will. I’m happy with this, and I’m cool with just watching the debate from now on. I’ll set up my chair here, right next to SentientMeat. I’ve agreed with every pixel he’s put forth so far (well, except I have to track down the books he’s referenced).

[Liberal]

[QUOTE=Voyager]
Let’s look at K and P. Let’s define UP be the set of all actions , and UK the set of all knowledge. K and P are subsets of these. Let’s examine the elements of K and P.

First, we can remove the set of logically impossible actions from UP. I don’t think anyone has a problem with that. This gives us say, LP, the let of all logically possible actions. I think that one can remove logically impossible knowledge (like if any Turing machine will halt) but that isn’t important for the discussion.

Now, I see why you wrote union. If K is knowledge, and P is power, the intersection of these things is null, while the union is the set of all known things and possible actions. To correct this, let’s define AP, the set of all actions possible that do not contradict K, and AK, the set of knowledge that does not contradict P. That is not strictly the intersection, but I think it is what you meant.
[/quote]
Okay, I’m squarely with you all the way through here. It would seem that whether it is a union or an intersection would depend on how you distribute the elements. But just so we understand one another, that’s the important thing. By the way, your post was an enjoyable read. I read it several times, not because it was unclear, but because it was meaty. You made it easy for me to see whether we split off.

We have a problem specifying AP and AK. If an action p is known by being in K, ~ap cannot be. ~ap here means a contradictory action, from another choice. If ap is rolling a 2, ~ap is rolling a 1, 3,… Thus, if K includes rolling a 2, then ~ap is not in AP.

I think part of the problem with setting all this up has to do with whether we separate an alethic element from a deontic element. I think what we must ask ourselves (or else, what we assume without asking) is whether just because God can do something, He must do it. In other words, what if it’s the case that there is no Op in P and no Ok in K, where O is a deontic element? Suppose instead that all P are Ap and all K are Ak, where A is an alethic element. And I think it really makes more sense, considering the way in which we’re framing P and K, to consider what is possible rather than what is obligated. Note, incidentally that p-proper cannot be in P and k-proper cannot be in K because that would mean that they are things already done in P and already known in K.

Let me spell this out to make it more clear:

Let p be an action, and let k be something known. Then if p1, p2… pn comprise P, P is the set of all things actually acted out; otherwise, they wouldn’t be actions, they’d be either potential actions or obligated actions not yet done. And if we’re going to describe the set as “omnipotent”, it makes more sense in my opinion to populate the set with things that can be done, rather than with things that must be done because if they must be done, then the so-called omnipotent being’s hands are tied. That sounds more omni-impotent than omnipotent. And so I think it’s reasonable to call all p AP — things that God is capable of doing, but under no obligation to do. So…

P{p1, p2… pn} is the set of all actions already done.

P{Op1, Op2… Opn} is the set of actions that must be done.

P{Ap1, Ap2… Apn} is the set of actions that are possible to do.

Just to cover our bases, though, we should dispense with whether we ought not to examine P completely deontically; i.e., whether things are required, permitted, or prohibited. But permission differs fundamentally from possibility in that permission relies on agency (an agent to give the permission) and possibility relies on accessibility (a relation between one world and another). But again, it seems inappropriate to deem that an omnipotent being must seek permission from some agent before acting. I’d be inclined to think that the power to give permission must belong to the omniscient one Itself.

And so, what we end up with is that P is the union of P{p1, p2… pn} and P{Ap1, Ap2… Apn}. Thewe are the things that God has already done plus the things that God is capable of doing. But there is no thing that God is obligated to do. Which we would expect from an agent to which we will eventually assign moral perfection and free will. We would expect of our God that P contains no act of evil (no e) and no obligation to do evil (no Oe), but a capability of doing evil (an Ap) if our God so chose.

So, P1{e, Ap} is a subset of P, but P2{Op} is not a subset of P.

I’m sorry to have been so longwinded about all this, but it leads to the next question and, I think, helps illustrate why it is necessary: namely, should we examine K in the same way we examine P? At first blush, the answer seems to be “no”. You sort of hooked into this by saying that P is temporal, and then proceeded to reconcile your P with your K. But I say that it isn’t a matter of P being temporal since a combination of God’s eternity and His metaphysicality suggest a being unbounded by time. Time is a physical thing, just like space. In fact, it can be argued that spacetime is not even separable into space plus time, that they both describe one thing just like electricity and magnetism do. But in any event, time is contingent on the physical universe.

That is to say that there are or ought to be things that God could have done and/or will have done outside the universe with its time constraint. Otherwise, if He is as contingent on the universe as time is, then He isn’t the sort of God we use in our cosmological arguments. (Or, for that matter, the sort of God that some people seem to want to assign to the God we use in our ontological arguments.)

Therefore, I’d say that P should not be examined base on time for each p, but on actuality for each p. Thus, the p1, p2… pn of P{} aren’t there because the time when they were done is past, but because their done-ness is actual. They have indeed been done or else will certainly be done. And it’s important to note that those “will certainly be done” things won’t be done because God is obligated to do them, but because from His perspective, He can see that they already have been done in actually. Being unbounded by time, He sees beginning, middle, and end all simultaneously, just as a 3D creature sees both the inside and outside of a circle simultaneously, being unbounded by rising above the plain.

Now, with your take that P is temporal, we have to examine K differently. But with my take that P is not temporal, we can examine K the same way we examine P; that is we can shoot straight to this:

K{k1, k2… kn} is the set of all things already known.

K{Ok1, Ok2… Okn} is the set of things that must be known.

K{Ak1, Ak2… Akn} is the set of things that are possible to know.

And I think it’s okay to assign to God the union of K{k1, k2… kn} and K{Ak1, Ak2… Akn}, all for pretty much the same reasons given for P. There is no reason that God should be required to know something since a knowledge agent does not know what he cannot know — just as a power agent does not do what he cannot do. But notice that we would not say that the converses of those are true: that is, we would not say that a power agent cannot do what it does not do, nor that it cannot know what it does not know because since what is not actual is not obligated, what is not actual is possible (p U Ap) and (k U Ak).

Of course, this introduces something new that might cause us to recoil at first. But once the though sinks in, it makes perfect sense. What’s new is that there are things that God is capable of knowing but has not actually known. This makes Him no less omniscient since the possibility of knowing Ak is contingent on k being revealed, just as the possibility of doing Ap is contingent on p being done. In other words, there are certain things that metaphysically cannot be known until other things are already known. It is not the case that the k elements are contingent on the p elements, but that the k elements are contingent on the <>k elements. Wherever a p would contradict a k, there is simply no <>p and no <>k.

So in that sense, God’s power and knowledge is indeed the union of P and K.

[Liberal]

[QUOTE=MrDibble]
Consider this a denial of the metaphysical, if you will. I’m happy with this, and I’m cool with just watching the debate from now on. I’ll set up my chair here, right next to SentientMeat. I’ve agreed with every pixel he’s put forth so far (well, except I have to track down the books he’s referenced).
[/QUOTE]
Fair enough. You couldn’t have picked a better place to sit.

[Liberal]

[QUOTE=Indistinguishable]
I don’t have time to say anything of use for the Great Debate right now, but I just have to say, wow, thanks, I’m just blown away by the generosity. I’ll try my best to live up to it.
[/QUOTE]
You are thoughtful to have acknowledged the deed, and I’d love to crow about how magnanimous I am, but sponsorship is a tradition at the SDMB. Lots of people sponsor others for different reasons, from helping with economic hardship to bringing in a like-minded person. But for me, what I value most is being challenged. My experiences have led me to make examinations, and God deserves no less than the best. I would have sponsored many of the people involved in this discussion for the same reason I sponsored you. That said, your mastery of logic (obviously by formal training) combined with your ability to express it with such remarkable coherence is unique among us all, and worth far more than the paltry price of 15 bucks.

[SentientMeat]

@Lib

And I don’t see how something real can emerge from something that isn’t real.

Apologies for quoting only this sentence from your entire post, but this (and I assure you I’m not just induging in melodrama to pep up a fly-by!) might just be the most important question in all of philosophy: How can X emerge from NOT X?

Stars from gas. Life from non-life. Computers from rocks. Consciousness and self from atoms. “Real” from “not real” (whatever they mean – in fact, I’ve generally stopped using the word since it’s so unhelpful). Even spacetime itself from a supercooled Higgs field!
These gradual transitions are the bane of the logician who yearns for Venn diagrams with razor-edged set boundaries, with which he can divide up the cake-mix of the world into neat little scones (substitute N. American equivalent here). This is what old Dickie Dawkins calls the tyranny of the discontinuous mind, and crikey, what a pall it casts.

In fact, I’m tempted to start a new thread, largely just for the two of us (so far as that’s possible - interlopers welcome!), which explores this based on your “Everything that’s conceivable plus everything that isn’t” strapline (which I hope I might convince you to change). I could probably only return to it every few days so it would be rather like playing postal chess, but would you be interested? If nothing else, it might provide an example of polite yet cutting debate and I could show myself to be far more clumsy, partisan and … well … human than the pedestalled scholar you’ve kindly but inaccurately portrayed in this thread.

[Liberal]

Clarification for Voyager:

“Note, incidentally that p-proper cannot be in P and k-proper cannot be in K because that would mean that they are things already done in P and already known in K.”

Obviously, that is based on there being no further analysis of actual elements versus modal elements. Just wanted to be sure that was clear.

[Mapache]

So, Lib, are you ever going to reply to my post #400? If you aren’t, or can’t, I would appreciate it if you would just have the common courtesy to say “No, I’m not going to answer.” Or even, “No, I can’t answer your objections”. Thank you.

[Voyager]

As an introduction, the problem I have with your analysis is that it does not let us test superiority against other entities. If the possibility of Ap is contingent on p being done, some other entity might do more ps, or superior ps, and thus their set AP would be larger.

Now the details.

[QUOTE=Liberal]
Okay, I’m squarely with you all the way through here. It would seem that whether it is a union or an intersection would depend on how you distribute the elements. But just so we understand one another, that’s the important thing. By the way, your post was an enjoyable read. I read it several times, not because it was unclear, but because it was meaty. You made it easy for me to see whether we split off.

I think part of the problem with setting all this up has to do with whether we separate an alethic element from a deontic element. I think what we must ask ourselves (or else, what we assume without asking) is whether just because God can do something, He must do it. In other words, what if it’s the case that there is no Op in P and no Ok in K, where O is a deontic element? Suppose instead that all P are Ap and all K are Ak, where A is an alethic element. And I think it really makes more sense, considering the way in which we’re framing P and K, to consider what is possible rather than what is obligated. Note, incidentally that p-proper cannot be in P and k-proper cannot be in K because that would mean that they are things already done in P and already known in K.

[/quote]

I think I agree with most of this. If there were no K - our non-omniscient entity - we certainly should consider what is possible, not what is actual or obligated. That this entity chooses to roll a 2 does not mean he cannot also roll a 3.
As for obligation, you might think about the impact of your requirement for goodness. Does this reduce the possibilities? Would an amoral entity be superior to God in your definition, in the sense of AP, at least? Since my working definition doesn’t include goodness, it is not a factor in my analysis, but it does introduce another item to the partial ordering.

P{p1, p2… pn} is the set of all actions already done.

P{Op1, Op2… Opn} is the set of actions that must be done.

P{Ap1, Ap2… Apn} is the set of actions that are possible to do.

I’d say P{p1,…} is a subset of P{Ap1,… } I think that you say they are equivalent below. Now, to jump ahead, if K includes preknowledge of P, and if the entity is truly omniscient, then all three sets are identical. Anything preseen must be done, anything not pre-seen is impossible to do, and in the atemporal sense, it has already been done if an entity with perfect knowledge has seen it being done in the “future.” The must here is a logical must, not an obligation in the moral sense or a duty to any agency.

I’m sorry to have been so longwinded about all this, but it leads to the next question and, I think, helps illustrate why it is necessary: namely, should we examine K in the same way we examine P? At first blush, the answer seems to be “no”. You sort of hooked into this by saying that P is temporal, and then proceeded to reconcile your P with your K. But I say that it isn’t a matter of P being temporal since a combination of God’s eternity and His metaphysicality suggest a being unbounded by time. Time is a physical thing, just like space. In fact, it can be argued that spacetime is not even separable into space plus time, that they both describe one thing just like electricity and magnetism do. But in any event, time is contingent on the physical universe.

The difference is that an action is connected to a time, even given that God is not bound by time. Knowledge is not. While I agree that God would be unbounded, in having no beginning and no ending, he would be unable to undo actions done in the “past” because of the very familiar time travel paradoxes that arise. Since you agree that logical impossibilities are not in AP, he can’t order and enable Abraham to go back in time and kill his grandfather either!

I didn’t really reconcile P with K - I showed the range of possibilities. The whole point is that I don’t think there is one way of doing it.

That is to say that there are or ought to be things that God could have done and/or will have done outside the universe with its time constraint. Otherwise, if He is as contingent on the universe as time is, then He isn’t the sort of God we use in our cosmological arguments. (Or, for that matter, the sort of God that some people seem to want to assign to the God we use in our ontological arguments.)

True, but irrelevant for this discussion. I’m not sure what the situation would be for actions and knowledge outside of time. Perhaps God can exist only outside of a temporal universe, which would support the deists, not the Christians.

Therefore, I’d say that P should not be examined base on time for each p, but on actuality for each p. Thus, the p1, p2… pn of P{} aren’t there because the time when they were done is past, but because their done-ness is actual. They have indeed been done or else will certainly be done. And it’s important to note that those “will certainly be done” things won’t be done because God is obligated to do them, but because from His perspective, He can see that they already have been done in actually. Being unbounded by time, He sees beginning, middle, and end all simultaneously, just as a 3D creature sees both the inside and outside of a circle simultaneously, being unbounded by rising above the plain.

Now, with your take that P is temporal, we have to examine K differently. But with my take that P is not temporal, we can examine K the same way we examine P; that is we can shoot straight to this:

K{k1, k2… kn} is the set of all things already known.

K{Ok1, Ok2… Okn} is the set of things that must be known.

K{Ak1, Ak2… Akn} is the set of things that are possible to know.

And I think it’s okay to assign to God the union of K{k1, k2… kn} and K{Ak1, Ak2… Akn}, all for pretty much the same reasons given for P. There is no reason that God should be required to know something since a knowledge agent does not know what he cannot know — just as a power agent does not do what he cannot do. But notice that we would not say that the converses of those are true: that is, we would not say that a power agent cannot do what it does not do, nor that it cannot know what it does not know because since what is not actual is not obligated, what is not actual is possible (p U Ap) and (k U Ak).

The difference here is that K{k1,…} always includes all actual ps. The list of actions already done changes with time, but not knowledge. Now, if God knows he will roll a 2, is it possible for him to know he will roll a 3? I’m not sure, but I think the first set is the only one that is important. Similar to the last argument, the second and first may be identical, since he must know all the things that he can know.

Of course, this introduces something new that might cause us to recoil at first. But once the though sinks in, it makes perfect sense. What’s new is that there are things that God is capable of knowing but has not actually known. This makes Him no less omniscient since the possibility of knowing Ak is contingent on k being revealed, just as the possibility of doing Ap is contingent on p being done.

But k is revealed in a way unbounded with time, just as god is unbounded. Do you contend that God learns things? I reject the contention that God not knowing something he will not do makes him less omniscient. Omniscience involves knowing only true things, after all. The reduction in omniscience I am talking about is if an action by God, done in free will and temporal, is shrouded from K in order to increase P. If God is atemporal in actions, there can be no such action, since there is not time for him to change his mind in. However, if he has complete power to change his mind, he can know nothing - if he knows everything, he has no power to change an action. If the answer is somewhere in between, which spot on the continuum is superior?

In other words, there are certain things that metaphysically cannot be known until other things are already known. It is not the case that the k elements are contingent on the p elements, but that the k elements are contingent on the <>k elements. Wherever a p would contradict a k, there is simply no <>p and no <>k.

So in that sense, God’s power and knowledge is indeed the union of P and K.

True, but superiority rests on the fact that no entity can do more. And, I don’t agree that knowledge is contingent necessarily - not omniscient knowledge. Is the set of k and <>k elements set somehow? Do n entities vying for superiority need the same set? If a set of P1 contradicting K for entity 1 be less than the set P2 for entity 2 necessarily? Which was my question.