Please tell me roughly what its value is in US currency as I am interested in purchasing it and would like to know if I can afford to buy it. — John Gould

You seem to be implying that perfection isn't conceivable. Well, if you're looking for some universal standard then it's obvious you won't find it. We can't even agree on what food to order at a restaurant.

However, we may have our own conception of perfection, in a relative sense. This is possible and also a fact - people have ideals (read perfection) that guide them through life. I'm sure you have your own set of ideals to guide you - it's quite clear from your posts.

So, perfection isn't inconceivable. It is and even universal perfection is, if only we can agree.

You will find Nothing — Vajk

Did you read that somewhere? Is it your personal experience?

Suffering and happiness; barring, of course, exceptions like sadism and masochism. To think of it, even religion resorts to the suffering-happiness paradigm in formulating moral theory. A religion that makes suffering good and happiness bad simply doesn't exist, proving my point.

Predicate logic can't unpack the argument. Anyway I think the argument is flawed in many ways, as can be seen from the posts. Thanks

The truth is, there's more suffering than happiness in the world. So, pessimism seems almost obvious.

An optimist, on the other hand, has to overvalue happiness to suffering to support his position.


So, it's easier to go from optimism to pessimism than the other way round.

I think you're right. The God in premise 1 has to exist to be the greatest being imaginable.

If that's so, premise 4 becomes: If God exists AND God doesn't exist then I can imagine a being greater than God.

Add to that premise 3: I can't imagine a being greater than God

We get (by modus tollens): Either God exists or God does not exist.

Not the conclusion I was hoping for.

Thanks.

This is a perfectly valid argument however we need predicate logic and knowledge about human beings to know that is in fact invalid. Anselm's argument is the same. — Meta

The problem with using predicate logic is

1''Existence'' isn't a predicate.

G = God is the greatest being imaginable, would require g = God, I = is the greatest being imaginable. So G = (Ex)Ix. That would be assuming what we want to prove.

2. There's no way of properly distinguishing, at least as required by the argument, between existence in imagination and existence in the real world.

U = Unicorns are imaginary creatures, would require C = is an imaginary creature. So U = (Ex)Cx and that is saying ''something exists that doesn't exist.

I think I'm getting there.

PB states that, for a given proposition, either P is true OR P is false (but not both). There is no other truth value e.g. ''uncertain'' or ''x% true'' or (P & ~P).

LEM states that, given a proposition P, either P is true OR ~P is true i.e. (P v ~P). ~(P v ~P) is the ''middle'' that's excluded i.e. ~~(P v ~P).

Since ''v'' in (P v ~P) is an inclusive OR, there's the possibility that (P & ~P) and that's why we need the LNC: ~(P & ~P).

In Fuzzy logic, it's PB that's broken. We have the possibility that a proposition P is neither true nor false, as when P is x% true.

For breaking LEM we need uncertain propositons like P = it'll rain tomorrow. In this case, neither P is true nor ~P is true.

Have I got it now? Thanks for your patience.

I accept God, even if only as a concept, has many dimensions. I also agree that they, together, must form a coherent whole. However, just for the moment, I'd like to focus on one specific God attribute - ommipotence - and see if I can prove there can be only one God. That's all. Sorry if you didn't like my responses.

Could you give me a brief description of the perfect button? — John Gould

A perfect button, for me, would have to combine aesthetics, utility, comfort, durability, cost, etc.

So either we don't accept the argument or we accept it, but then we can prove weird things. — Meta

You're right. It can be used to prove weird things. But is weirdness, alone, a good enough refutation? I mean, aside from the weird conclusions we can derive from such reasoning, does the argument also prove God's existence? Is it a sound argument?

If I understand you correctly, there's no difference between

1. God that exists in imagination
And
2. God that exists in imagination AND the real world

Why do you say that?

I can imagine a horse. It may or may not exist in the real world. If it doesn't then it exists only in the imagination. If it exists in the real world, then it exists both in imagination AND the real world. Do the two horses not differ? According to you there's no difference. But there is - one is purely imaginary and the other is real, in the usual sense of the word.

the argument seems to say that if God doesn't exist, he wouldn't be God — noAxioms

Yes, I think that sums it up quite well. Is it true?

The argument seems to be a simple tautology. — noAxioms

Can you please explain how?

Thank you. It's a much better proof than mine.

I have one objection though. Differences can be perfection-related and non perfection-related. For instance position in space doesn't seem to be related to perfection. A perfect being at position x or y or z...is still perfect. So two perfect beings may share all perfection-related properties such as goodness but may not share the same position in space. Thus making them distinct but not affecting their perfection. Like identical twins. Taking physical attributes as perfection-related and spatial position as not, we can see how two distinct perfect beings may exist. Just saying...Thanks.

What is denied by LEM is that there is a third option, that the apple is neither red nor not red. — Metaphysician Undercover

In logic the expression ''neither...nor...'' has a specific translation:

Apple is red = R
Neither the apple is red nor the apple is not red = Apple is not red AND not apple is not red = the apple is not red AND the apple is red = ~R & R = R & ~R

The ''middle'' that is ''excluded'' is the contradiction R & ~R.

Do you see the difference between LEM and LNC? One says that two opposing statements cannot both be true, the other that two opposing statements cannot both be false. — Metaphysician Undercover

Can you expand on this a bit. Sorry for the trouble.

But this is the same definition of your supposed greater-than-God being, which means it's not greater than God at all, but identical to God. — Michael

1. God is the greatest being imaginable [premise]
4. If God doesn't exist then I can imagine a being greater than God (a greatest being who exists)

Difference between the Gods:

God in 1 exists only in the imagination
God in 4 exists in both imagination and the real world

God in 4 is greater because it exists in the real world.

Yes formalizing in predicate logic is problematic. However, sentential logic formalization is possible; as I've done.

Reality' is presumed by every utterance or proposition. So it cannot not exist. — Wayfarer

I agree every proposition presupposes reality but existence can't be presupposed. Existence/nonexistence need evidence.

Thanks for your comment.

The sentence "God is the greatest being imaginable" when formalized looks something like:
"There exists the greatest being (entity) imaginable and is called God.". In the first premise you assume that God exists, why bother proving its existence? — Meta

No, existence in premise 1 is in imagination. So, no petitio principii fallacy.

I agree to some extent. However premise 1 is God (omniscient, omnipotent, omnibenevolent - OOO) and ''exists'' only in imagination.

In premise 4, the greatest being is the OOO God BUT this time, it exists for real.

LEM literally says "either p or ~p", not "either p or ~p, but not both". — Nagase

For example, if P is the proposition:

Socrates is mortal.

then the law of excluded middle holds that thelogical disjunction:

Either Socrates is mortal, or it is not the case that Socrates is mortal.

is true by virtue of its form alone. That is, the "middle" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (Socrates is mortal) or its negation (it is not the case that Socrates is mortal) must be true. — Wikipedia

Bold emphasis mine.

So it is excluded ''that neither Socrates is mortal nor Socrates is not mortal''

Let P = Socrates is mortal

That means it is excluded that (P & ~P). That's the LNC: ~(P & ~P).

So, LEM isn't the inclusive OR at all.

It does, assuming you mean the argument that God can't be indescribable — BlueBanana

I see. So, it's an assumption. Then I may work with assumption that we can know God. Can we now focus on my argument that there's only 1 God?

No, since disjunction is inclusive. — Nagase

So, if LEM doesn't exclude [P & ~P] what is this ''middle'' that's being ''excluded''?

Actually, the situation is probably the reverse. Assuming classical principles, such as double negation and reductio ad absurdum, it's possible to prove LEM from LNC. — Nagase

Can you give me a short proof from LNC to LEM?
Let me try:

.....................~(P & ~P) > (P v ~P)
1. ~(P & ~P).............assume for conditional proof
2. ~P v ~~P..............1 DeMorgan
3. ~P v P...................2 Double Negation
4. P v ~P...................3 Commutation
5. ~(P & ~P) > (P v ~P).....1 to 4 Conditional proof

Now the other way round:

....................(P v ~P) > ~(P & ~P)
1. P v ~P...........assume for conditional proof
2. ~~P v ~P......1 Double Negation
3. ~(~P & P).....2 DeMorgan
4. ~(P & ~P).....3 Commutation
5. (P v ~P) > ~(P & ~P)....1 to 4 Conditional proof

So (P v ~P) <=> ~(P & ~P)

That is to say LEM and LNC are logically equivalent.

So, what I can't get is what you mean when to my question ''Is ''the apple is red'' AND ''the apple is not red'' also excluded [by LEM]?'' you said ''No, since disjunction is inclusive.''???!!!

Doesn't saying God is a "being" beg the question, since the word "being", implies existence. — Cavacava

That's interesting but ''being'' here seems to a broader term than that which your objection depends on. In the argument ''being'' means both those which exist in reality and those which exist in imagination. So, there's no question begging as the argument flows from the being in imagination to the being in reality.

just that if he was his indescribability would not lead to any contradictions. — BlueBanana

And is that supposed to make my argument unsound? Trying to catch the wind somehow?

So you saying that, things what you can not see are not determining you arguments? — Vajk

We can't see unicorns but we can make the argument that it doesn't need gasoline.

Any attempt to do so represents nothing more than a foolish, futile word game which very quickly goes "pear-shaped" in the form of semantic problems like the "stone paradox" and so on. — John Gould

So, you don't know if he's omnipotent or not?

According to Wikipedia a trivalent logic has three truth values, true, false, and an indeterminate third value. The third value appears to be best described as "unknown — Metaphysician Undercover

Ok. This is understandable.

The excluded middle is anything other than "is" or "is not". Either the apple is red, or the apple is not red, and the LEM insists that there is no "middle", between being red and being not red. — Metaphysician Undercover

Is ''the apple is red'' AND ''the apple is not red'' also excluded?

1. If it is then why? Also raises another issue viz. why have the law of noncontradiction? It seems to be a corollary of LEM.

2. If it isn't then it leads us to a contradiction and also, why?

The first, and best-known, ontological argument was proposed by St. Anselm of Canterbury in the 11th. century C.E. In his Proslogion, St. Anselm claims to derive the existence of God from the concept of a being than which no greater can be conceived. St. Anselm reasoned that, if such a being fails to exist, then a greater being—namely, a being than which no greater can be conceived, and which exists—can be conceived. But this would be absurd: nothing can be greater than a being than which no greater can be conceived. So a being than which no greater can be conceived—i.e., God—exists — Stanford Encyclopedia of Philosophy

I'm thinking conceive = imagine

Am I wrong still? What's the difference between ''conceive'' and ''imagine''?

Before you properly analyze this argument first imagine a universe in which nothing whatever exists. Would that be preferable to the universe we know? — Wayfarer

That's a good question. I've been thinking is existence greater than nonexistence? It seems to me that the answer won't be a unanimous ''yes'' or ''no''.

For the sake of my argument let's assume it is greater to exist. But how does this impression (existence is greater) cause something to exist? There simply is nothing reasonable that can take me from my preference of x to the existence of x.

His indescribability is a property of human language, not of God. — BlueBanana

How do you know God is indescribable?

I thought science does not answer "Why?"

This is one of the many ''problems'' I'm facing. I'm totally confused on the matter.

I think the question ''why?'' is ambiguous. It has two meanings on a superficial analysis:

1. Asks for reasons - logic
2. Asks for explanations - science

1 clearly leads to an infinite regress. We all know that. However, it's not totally unscientific in the sense that it has application after the laws of nature become established truths. The laws of nature become axioms from which other truths may be proved. Point to note is that the axioms are derived from observations - raw data from instruments.

2 is, I think, is the general objective of science - to provide explanations for phenomena. But these explanations are derived from theories/hypotheses. These too are derived from observations.

So to ask ''why?'' would be essentially asking

A) Why (reason) observations are the way they are?

B) Why (explanation) observations are the way they are?

A doesn't make sense because observations aren't propositions. So, they require explanations, not reasons.

B is problematic, similar to the problem of induction, because all we have access to are observations themselves. Any answer to B would require us to go beyond the observations and that isn't allowed in science. Perhaps it's a question for philosophy.

I still don't get it. Let me ask you 2 questions:

1. I more or less understand that PB allows either true or false. What would a TRIvalent system look like?

2. In LEM what is the ''middle'' that is ''excluded''?

Thanks for the clarification. I think I have some grasp of the idea now.

Can you have a look at the above questions. Thanks.

I got it from God who (mercifully) gave this knowledge to me Himself through — John Gould

What of all the other people who claim knowledge of God? Are they bogus?

Invisible? :) — Vajk

You may have a point but it's irrelevant to my argument.

the fact that human language totally lacks any capacity to even begin to attempt a description of ANY aspect of the true nature of God — John Gould

And the irony is you use words to describe what, according to you, is indescribable. How do you get this kind of privileged knowledge?

And your point is?

9 All Greek to me. Anyway(Y)

A leg is not a chair. — Metaphysician Undercover

:D Where in the world did I say that or anything that could be interpreted as that. I think your materialistic interpretation is a category error.

If I understand the Wikipedia article correctly, exception to PB is a claim of exception to the law of non-contradiction, instead of claiming exception to the law of excluded middle. So to violate PB is to claim "both P and ~P", whereas an exception to the law of excluded middle would claim "neither P nor ~P". — Metaphysician Undercover

It's exactly the opposite. Violating PB is admitting a multivalued logic that I described. Violating LEM is a contradiction.

You are not talking about the chair, you are talking about a specific part of the chair. — Metaphysician Undercover

Ok. Where's the contradiction?

No, LEM explicitly states that there is not any other possibility. It states that of any subject we can predicate either P or ~P, and there is no other possibility. If you insist that there is another possibility of truth value, you break LEM. — Metaphysician Undercover

I think the PB and LEM are poorly worded - they sound very similar. I'm confused too - that's why the post.

As far as I understand...

PB restricts truth value possibilities to 2 viz. true or false. A proposition can be either true or false. Nothing else. As an example take an electric light switch. It is either on or off and the light is either on or off respectively. No other possibility exists.

Then there are light intensity modulators (M). If it's a dial you turn it and the intensity of light progresses from dark to moderately bright to full brightness. Here M can have 3 states and the bulb can have three states (dark, moderate, bright).

LEM states that either it's true that the light is in one state (dark, moderate, bright) or it's true that the light is NOT in that particular state (dark, moderate, bright). So, either the light is dark or not dark (moderate/bright). Either the light is moderate or not moderate (dark/bright). Either the light is bright or not bright (dark/moderate).

This is how I understand PB and LEM. Does it make sense?

Can you please have a look at my post above. Am I right?

I provided an argument showing U is actually incoherent when you analyze it. Modal facts about logical possibility are facts. The statement "it is logically possible that it will rain tomorrow" can be true or false. "Unicorns are logically possible" can be true or false.

"U is logically possible" can be true or false. If this statement is false, then it is no threat to omniscience. If it is true, my argument shows it self-contradicts, as I know facts about U. — Chany

Thanks again for your valuable criticism. I offer you two options:

1. Let's change the definition of U as something about which something can't be known. If U is defined this way then O can't exist because either U exists or U does not. If U exists then there's something which O can't know. And O can never know that U doesn't exist because there are an infinite number of universes to check.

2. Let's stick to the original definition of U i.e. U = something about which nothing can be known. The only thing we know about U is that it is possible. I'll agree with you in that we do know that U is possible. So, it is a fact which is true. However I have a small problem with this counting as knowledge of U. Take for example the case of unicorns. Unicorns are logically possible. This is a fact and I admit we know it. However, in the general sense of the term "knowledge" it doesn't pass muster. From the fact that you know unicorns are possible can you describe any of its real properties? Take another example: We know angels are possible.. Does this count as knowledge of angels?

In essence, I'm drawing a distinction between knowledge of possibility and knowledge of existence. The former is meta-knowledge, if you will and the latter is what we actually refer to when we say knowledge is true justified belief.

No, they weren't all powerful, but, eitherway, I'm not sure how this is relevant. — Πετροκότσυφας

Ok. They (USA & USSR) were most powerful on Earth. That's the point. They couldn't make themselves all powerful because they put a check on each other's influence.

Thanks for your post. Interesting POV. However, didn't God create the universe? Even if we interpret omnipotence qualitatively there's no avoiding the quantitative aspect of God's omnipotence. So the matter isn't resolved; at least not as you expected it.

If there is one, then there is a way to make an other one. — Vajk

Imagine 2 omnipotent beings x and y. Either x can limit y's power or not. If it can then y isn't omnipotent. If it can't then x isn't omnipotent.

I think this works just fine because 0 is a number and this reasoning can be applied to any number of gods. — Sir2u

I thought of that. It does seem, prima facie, that even one omnipotent God can't exist (stone paradox). But in the case of one omnipotent being it can choose not to create such a stone and there's no contradiction.

You and I can do all of them, we are both all-powerful. I'm not sure where balance of power came from or what does it even mean in this context. — Πετροκότσυφας

Think of USA and the erstwhile USSR. Did they not limit each other's influence. It was a deadlock. In our small world both were all-powerful. Yet they undermined each other.

You don't read replies, do you? — Chany

Sorry. Perhaps I misunderstood but...

1) Your claim that U is self-contradictory is false.

2) Infinity doesn't have an end. So I don't know what you mean by ''

The being just knows it all already — Chany

Can you clarify.

Also thanks for your criticism. I think it would be better to define U as something about which something can't be known instead of U = something about which nothing can be known. If you like we can go with definition viz. U2 = something about which something can't be known.

Here's an easier example than fuzzy logic. Suppose some statements are true (T), some statements are false (F), and some statements are both true and false (B, also called a truth-value glut)---so bivalence does not work — Nagase

Is this a bad example?:s

The point I made above is that we must state what we are referring to either the whole, or the parts, because it is contradictory to refer to the whole as parts. — Metaphysician Undercover

Indeed contradiction is dependent on sameness of a given truth. P & ~P is only a contradiction when the two P's refer to the same thing. What I don't see it's contradictory to talk of the whole as parts? Take a chair. I may talk of its seat, its back or its legs without any contradiction. If you're referring to logical entities such as truth and falsity it's clear that truth/falsity can't be divided into parts.

If there is another possibility, like this, then you deny the LEM — Metaphysician Undercover

No, another possibility of truth value doesn't brrak the LEM. LEM simply puts a restriction on a specific combination of truth values viz. P & ~P.

U is self-contradictory. — Chany

U isn't self-contradictory. That's why you accepted it as a possibility. About possibility consider this: ''It'll rain tomorrow'' is a possibility but it isn't true. We're merely entertaining possibilities here. Truth comes later. Truth needs to be established with evidence.

However, U contradicts O. And O being the weaker assumption compared to U it becomes necessary to abandon O. Why is O weaker? Because the mere possibility of U is enough to contradict O. The converse isn't true because U can't check infinite universes.

The being just knows it all already. — Chany

Infinity can't be known like the number 2 or 3,000. It simply extends without end. Asking O to give us the largest natural number will elicit the response that no such number exists. So, there are limits to knowledge but that, in my opinion, doesn't devalue omniscience. It's simply the nature of infinity.

Also, you didn't address my point. I know something about U- that U is logically possible. — Chany

Just because you know something is possible doesn't mean you know it in the general sense of the word ''knowledge''. Knowledge is a justified true belief. As you can see U isn't known to be true (it's only possible) and so doesn't count as knowledge or something known.

What's self-contradcictory about O? — Chany

O can't check all universes, which I've shown is infinite, for the existence of U. So, O is NOT omniscient. If U exists then O is not omniscient.

U is the assumption. O is a real possibility. We can both play this game — Michael

This can't be done because the possibility of U derives no contradiction. However the existence of O results in one.

Please read my OP.

Situation A
Only 1 omnipotent being A
Creating the unstoppable spear (Sp) AND the impenetrable shield (Sh) is a contradiction.

But A can create either Sp OR Sh. A can also destroy the Sp and create the Sh or vice versa. No contradiction.

Situation B
There are two omnipotent beings A and B
To maintain a balance of power A has to modify its actions on B's actions and vice versa. This constraint makes both non-omnipotent.

Do you guys understand the difference between PB and LEM? If you do kindly explain it to me.

My understanding is this:

PB seems to limit the truth value of propositions to true or false. It doesn't permit another interepretation re truth. This is all good when we have clear-cut divisions as in math e.g. x = 2 is either false or true. However, there are lot of areas in which this clarity is missing e.g. heights and weights of people as relates to concepts such as tall and fat respectively. A person may be neither fat nor thin and neither tall nor short. Basically, PB fails to capture the fuzzy cases and thus, I guess, fuzzy logic.

LEM on the other hand doesn't restrict possible truth values. Rather it simply states: for a given propsition P, either P is true or ~P is true. From here my comprehension is an indirect one. From the law of noncontradiction (LNC) we can see that for any given proposition P it is impossible that P & ~P. In other words ~(P & ~P). Using DeMorgan's rule ~(P & ~P) is logically equivalent to P v ~P which is LEM. Basically the ''middle'' that is ''excluded'' in LEM is the contradiction P & ~P.

In fuzzy logic we saw that PB is false and LEM is true. In paraconsistent logic (I'm guessing here) PB is true but LEM is false.

What do you think?

It's impossible by definition, unless you think it's meaningful to say there can be an impenetrable shield and an unstoppable spear at the same time (who made them is irrelevant as long as they're supposed to exist in the same world). — Πετροκότσυφας

Yes I though of that objection. Even if there's only 1 omnipotent being there is only the possibility of the contradiction unstoppable spear vs impenetrable shield. It never actualizes because the omnipotent being can choose not to do so. It can either make the unstoppable spear or the impenetrable shield but not both.

In the case of multiple omnipotent beings the situation is different. The only way the contradiction isn't actualized is through some kind of pact between omnipotent beings and this will preclude the creation of both the unstoppable spear and the impenetrable shield since their creation would undermine the power of one of the omnipotent beings.