God a priori

[Chimp]

First, let "God" be initially defined, as the Entity/Being responsible for creating the Universe we perceive. Other definitions that also may apply, must be logically consistent with this definition.


[1.] [God can be proven "to exist"] a priori

[2.] not-[God can be proven "to exist"] a priori

[3.] Let [1.] = A, let [2.] = not-A.

[4.] Assume A is true AND not-A is true

[5.] Both "A and not-A" form a contradiction.

[6.] Therefore A is true or not-A is true but not both.

[7.] If A, then A is necessary

[8.] If not-A then necessarily not-A

[9.] Necessarily A, or necessarily not-A

[10.] A is possible

[11.] Necessarily A

[12.] A

[Godless Wonder]

Originally posted by Chimp
[1.] God can be proven "to exist" a priori

[2.] God can be proven "not to exist" a priori

[3.] Let [1.] = A, let [2.] = not-A.
One problem I see right away: The negation of [1.] is "God can not be proven to exist." and that is not at all the same thing as "God can be proven not to exist."

So [3.] is wrong because [2.] is not "not-A"

But that's the least of your problems. Even if your proof held, it really proves nothing. Your "God" has no properties other than being the cause of the universe, which could be nothing more than a quantum fluctuation.

The whole "necessarily" business looks suspicious as well.

[Chimp]

Originally posted by Godless Wonder
One problem I see right away: The negation of [1.] is "God can not be proven to exist." and that is not at all the same thing as "God can be proven not to exist."

So [3.] is wrong because [2.] is not "not-A"

But that's the least of your problems. Even if your proof held, it really proves nothing. Your "God" has no properties other than being the cause of the universe, which could be nothing more than a quantum fluctuation.

The whole "necessarily" business looks suspicious as well.

[God can be proven to exist] = A

not-[God can be proven to exist] = not-A

"First, let 'God' be initially defined, as the Entity/Being responsible for creating the Universe we perceive. Other definitions that also may apply, must be logically consistent with this definition."

"Entity/Being"

A quantum fluctuation is not "responsible" since it is defined as a random event.

Thanks for the demands for exhaustive clarification though :p

[Scrambles]

[10 a.] not-A is possible
[11 a.] Necessarily not-A
[12 a.] not-A
[13.] not-A and A
[14.] Your system of logic violates the law of contradiction
[15.] Oops!!


Scrambles

[Chimp]

Originally posted by Scrambles
[10 a.] not-A is possible
[11 a.] Necessarily not-A
[12 a.] not-A
[13.] not-A and A
[14.] Your system of logic violates the law of contradiction
[15.] Oops!!


Scrambles

:notworthy :notworthy :notworthy

Yes, ambiguity rears its ugly head once again.


Let U be the collection[universe] of all existing entities. Since U is composite, the reason for its existence is due to factors G, G--->U, "if G then U". The reason for U's existence is G.

More to the point, every existing aspect, A, is either an entity, and thus a component of U, or else a system, such, that all components of A are in U. Ergo, A is a subsystem of U. Thus, G is either a component or a subsystem of U. Such is the case that, G-->G. Thus, G is self-creating and hence noncomposite since no composite can be self-creating. Because G-->U and every aspect, A, is a part of U, then, G is a universal creative factor for every existing aspect, A, itself included.


G is the only self created aspect, since it is the ultimate answer to the question "why does aspect, A, exist. For example, make the supposition that there is another existing self creative entity G2. Then G-->G2 since G is a universal creative factor. But since G2 is self-created it cannot be created by anything outside itself due to its non-composition. Thus, G = G2 and the ultimate nature of G is demonstrated.

For all intents and purposes, G is God.

[Witt]

God a priori
First, let "God" be initially defined, as the Entity/Being responsible for creating the Universe we perceive. Other definitions that also may apply, must be logically consistent with this definition.


[1.] [God can be proven "to exist"] a priori

[2.] not-[God can be proven "to exist"] a priori

[3.] Let [1.] = A, let [2.] = not-A.

[4.] Assume A is true AND not-A is true

[5.] Both "A and not-A" form a contradiction.

[6.] Therefore A is true or not-A is true but not both.

[7.] If A, then A is necessary

[8.] If not-A then necessarily not-A

[9.] Necessarily A, or necessarily not-A

[10.] A is possible

[11.] Necessarily A

[12.] A
-------------------------------------------------------


Where is the logical connection between your claims?

How do you move from [10.] A is possible, to [11.] Necessarily A ?


Your 'proof' is similar to, Hartshorne (1962).

(1) If God exists, then he necessarily exists.
(2) Either God necessarily exists or he doesn't necessarily exist. (3) If God does not necessarily exist, then necessarily he does not necessarily exist.
(4) Either God necessarily exists or necessarily God does not necessarily exist. (from 2 & 3)
(5) If necessarily God doesn't necessarily exist, then God necessarily does not exist. (from 1 by modus tollens)
(6) Either God necessarily exists or he necessarily does not exist (from 4 & 5)
(7) It is not necessarily the case that God does not exist (it is possible that he does).
(8) Therefore, God necessarily exists. (from 6 & 7)
(9) If God necessarily exists, then god exists.
(10) Therefore, God exists. (from 8 & 9)

[graymouser]

Witt:

The specific logic being referred to is used as a trap to get people to admit that God is possible in normal language, but in modal logic language God it means something different. The transformation is:

PQ <-> ~N~Q

However, modal logic also gives us this beautiful little proof.

1. P~Q (It is possible that God does not exist.)
2. ~NQ (It is not necessary that God exists; from the rule P~Q <-> ~NQ.)
3. Q->NQ (If God exists, then God necessarily exists.)
4. ~Q (God does not exist: modus tollens from 2 and 3.

The point is, in modal logic, P means "exists in some possible world." This is the basis of the relationship between P and N. The modal proof asks us to concede thinking "God is vaguely possible," which is an entirely different ball game.

Almost any argument for God asks you to give the entire argument away at some point; it's just a matter of knowing where to look.

-Wayne

[Clutch]

Wow.

Where do (7) and (8) come from? Necessitation applies only to theorems. Is your thinking that apriority entails necessity? I hope not...

[Goliath]

Originally posted by Chimp
First, let "God" be initially defined, as the Entity/Being responsible
for creating the Universe we perceive.



And why must there be just one such being?



[6.] Therefore A is true or not-A is true but not both.



Correct.



[7.] If A, then A is necessary



I have no idea what you mean by this.



[8.] If not-A then necessarily not-A

[9.] Necessarily A, or necessarily not-A

[10.] A is possible

[11.] Necessarily A

[12.] A



So what?! not-A is possible, too. You haven't proven a thing. By the same idiotic argument, an ethereal block of cheese is floating exactly one foot over your head right now because it's possible for such a block of cheese to be floating over your head.

:rolleyes:

If you've studied any propositional calculus at all, then you know that from a false proposition, any proposition can be derived. Assuming that because A is possible, A must follow is such a proposition.

Sincerely,

Goliath

[pope fiction]

Chimp:
[8.] If not-A then necessarily not-A

[9.] Necessarily A, or necessarily not-A

[10.] A is possible

[11.] Necessarily A

[12.] A
Originally posted by Goliath
So what?! not-A is possible, too. You haven't proven a thing. By the same idiotic argument, an ethereal block of cheese is floating exactly one foot over your head right now because it's possible for such a block of cheese to be floating over your head.

:rolleyes:
I pretty much agree. Although I would've used a different comparison. However, you've got the idea. The quantum leap from [10] to [11] isn't exactly logical.

[Chimp]

Originally posted by Clutch
Wow.

Where do (7) and (8) come from? Necessitation applies only to theorems. Is your thinking that apriority entails necessity? I hope not...


Analytic propositions are necessary truths.

http://en.wikipedia.org/wiki/Analytic_proposition


For example, "All white cats are white" is not only true, but also necessarily true – since a negation of it – "Not all white cats are white" is self-contradictory.

[pope fiction]

I agree with the white cat exaple, however, you can't use that type of logic in the context you used it in.

[graymouser]

Chimp:

You aren't dealing with propositional logic, you're dealing with modal logic. Modal propositions work as follows:

PQ means that Q exists in some possible world.
NQ means that Q exists in all possible worlds.

Some rules:

Q -> PQ (If Q exists, then Q exists in some possible world.)
~PQ <-> N~Q (Q exists in no possible world if and only if it is necessary that Q does not exist.)
~NQ <-> P~Q (It is not necessary that Q exists if and only if Q does not exist in some possible world.)
PQ <-> ~N~Q (Q exists in some possible world if and only if it is not necessary that Q does not exist.)

You make two propositions that you cannot take for granted in modal logic. The first is:

Q->NQ

This requires a whole ton of argumentation that you haven't done, and that Hartshorne failed to do. The other proposition, where your and Hartshorne's arguments fail unequivocally, is:

PQ (or ~N~Q, as they are equivalent)

You see, PQ is a massive assumption, and does not mean what it sounds like in everyday English. It means "Q exists in some possible world," which is entirely unproven. The modal ontological arguments rely on the linguistic trick of getting the second party to agree, erroneously, to PQ or ~N~Q. The argument is a sham.

-Wayne

[The Evil One]

Well said Clutch and greymouser.

Or to put it in non-formal-logical terms:

[7.] If A, then A is necessary

[8.] If not-A then necessarily not-A
There is no reason for supposing these premises to be true. From the mere fact of X being true, we cannot conclude that X is necessarily true. X might just happen to be true, rather than being true through necessity.

For example: it is true that I am wearing slippers. Is it therefore necessarily true that I am wearing slippers? No. I could quite easily have been wearing shoes or sandals (and in other times and places, I will be/have been). But as it happens, I am wearing slippers.

[Biff the unclean]

Originally posted by Chimp
First, let "God" be initially defined, as the Entity/Being responsible for creating the Universe we perceive.


Since no entity or being (capital letters or not) is responsible for creating the Universe then there is no need for a God

[Chimp]

Originally posted by Biff the unclean
Since no entity or being (capital letters or not) is responsible for creating the Universe then there is no need for a God

Do you have proof of your assertion?

Thanks

[Chimp]

Originally posted by The Evil One
Well said Clutch and greymouser.

Or to put it in non-formal-logical terms:


There is no reason for supposing these premises to be true. From the mere fact of X being true, we cannot conclude that X is necessarily true. X might just happen to be true, rather than being true through necessity.

For example: it is true that I am wearing slippers. Is it therefore necessarily true that I am wearing slippers? No. I could quite easily have been wearing shoes or sandals (and in other times and places, I will be/have been). But as it happens, I am wearing slippers.

A necessary truth is true when its negation creates a self contradiction.

http://en.wikipedia.org/wiki/Analytic_proposition


If God exists, God's existence is necessary.

[The Evil One]

Originally posted by Chimp
A necessary truth is true when its negation creates a self contradiction.

http://en.wikipedia.org/wiki/Analytic_proposition


If God exists, God's existence is necessary.

This is an absurd claim.

First, I will assume (because of the web page you cite) that you are treating "necessary truth" as being the same thing as an "analytic proposition".

Do I understand that you are claiming that the proposition that "God exists" is an analytic proposition?

This is ridiculous and bizarre. As you say, a proposition is analytic when its negation is a self-contradiction.

Could you kindly point out the self-contradiction in either of the two propositions "It is not the case that God exists" or "God does not exist"?

Second of all, even if we were to grant the absurd notion that "God exists" is an analytic proposition, how on earth do you get the idea that this is contingent on it being true?

Essentially what you are saying is If "God exists" is true, then "God does not exist" is self-contradictory. But if it is not the case that "God exists", then "God does not exist" is not self-contradictory.

I hope I do not need to point out that whether or not a proposition is self-contradictory depends solely on the meanings words in the proposition and the syntactic structures used.

Third of all, let's look at your 7 and 8 together:
[7.] If A, then A is necessary

[8.] If not-A then necessarily not-A
What you are saying here is: Of the two propositions, "God exists" and "God does not exist", whichever one is not true is self-contradictory. Again, the same absurdity.

What it boils down to is that your statement If God exists, God's existence is necessary is a) incoherent and b) an unsupported assertion. To fix your argument, you need to put forth a coherent interpretation for that statement and secondly provide some reason for thinking that it is true.

[Chimp]

Originally posted by The Evil One
This is an absurd claim.

First, I will assume (because of the web page you cite) that you are treating "necessary truth" as being the same thing as an "analytic proposition".

Do I understand that you are claiming that the proposition that "God exists" is an analytic proposition?

This is ridiculous and bizarre. As you say, a proposition is analytic when its negation is a self-contradiction.

Essentially what you are saying is If "God exists" is true, then "God does not exist" is self-contradictory. But if it is not the case that "God exists", then "God does not exist" is not self-contradictory.

[...]

What it boils down to is that your statement If God exists, God's existence is necessary is a) incoherent and b) an unsupported assertion. To fix your argument, you need to put forth a coherent interpretation for that statement and secondly provide some reason for thinking that it is true.

It appears that you are saying "the God concept is personally distasteful, therefore God is absurd" ...?


God is by definition, the greatest possible being, possesing the quality of maximal greatness. Necessarily, a being is maximally great iff it has maximal greatness in all possible worlds.

Maximal greatness includes omnipotence, omniscience, and omnipresence.

If God exists, God's existence is necessary.

God's existence is possible in some world.

Therefore God exists.

:eek: :eek: :eek:

[The Evil One]

Originally posted by Chimp
It appears that you are saying "the God concept is personally distasteful, therefore God is absurd" ...?

Umm, nope. I did not say that "God is absurd". I said that your position (that "God exists" is an analytic proposition) is absurd, regardless of whether God exists or not.

However, in your last post you seem to have backed away from defending the position that "God exists" is an analytic proposition, so I must assume that the absurdity of that position is clear to you also.

God is by definition, the greatest possible being, possesing the quality of maximal greatness.

Well, by some definitions. As you mention the three 'O's later on, I will assume that for current purposes, we are to define God as an omniscient, omnipresent, and omnipotent being. Please inform me if this assumption is incorrect.

Necessarily, a being is maximally great iff it has maximal greatness in all possible worlds.

Maximal greatness includes omnipotence, omniscience, and omnipresence.

Now you see, this is where you're losing me again. Let us pretend, for the time being, that there are only two possible worlds: one were God exists (World X) and one where God doesn't exist (World Y). In World X, God is maximally great (according to your definition). In World Y, there is no maximally great being, so we can say that God does not exist in World Y (since God is defined as being maximally great).

Now you seem to be saying that God, in World X, cannot be maximally great unless he is also maximally great in World Y. But I don't buy that. I don't see any reason to suppose that that is true. Let us not forget, of all the possible worlds, only one is the actual world (disregarding for now the many-worlds interpretation of Quantum Mechanics). Therefore, if there is a possible world in which God does not exist, that does not reduce the greatness of God in any possible world in which God does exist (since at most one of those two possible worlds can be the actual world).

And after all that, you jump again to :

If God exists, God's existence is necessary.

But you haven't shown this. Or explained it. You're just asserting it again. By necessary do you mean it's an anlytic proposition? Or some other form of necessity? How is this necessity contingent on God's existence? Why can God's existence not be a matter of happenstance, rather than a matter of necessity?

God's existence is possible in some world.

Therefore God exists.
I will happily agree with you, for the sake of argument, that there are one or more possible worlds where God exists. But you have still not demonstrated the key point, that if God exists he exists necessarily. This is needed to demonstrate what you are trying to demonstrate, that the actual world is one of those possible worlds where God exists.

[Chimp]

Evil One wrote:

However, in your last post you seem to have backed away from defending the position that "God exists" is an analytic proposition, so I must assume that the absurdity of that position is clear to you also.

Yes, it is not exactly a necessary[tautological?] definition such as:

"All glorks are glorks"

Let Total Existence = X

aspect of existence = x

X--->x

and

not-X--->x

creates a contradiction.

therefore X--->x is a necessary truth.


X = God?

The question mark means that ambiguity still remains. So a true "argument" must begin with a genuinely true statement, of the form X = X.





God is by definition, the greatest possible being, possessing the quality of maximal greatness.



Well, by some definitions. As you mention the three 'O's later on, I will assume that for current purposes, we are to define God as an omniscient, omnipresent, and omnipotent being. Please inform me if this assumption is incorrect.



The greatest possible entity/being would possess those properties, it seems.




Necessarily, a being is maximally great iff it has maximal greatness in all possible worlds.

Maximal greatness includes omnipotence, omniscience, and omnipresence.



Now you see, this is where you're losing me again. Let us pretend, for the time being, that there are only two possible worlds: one were God exists (World X) and one where God doesn't exist (World Y). In World X, God is maximally great (according to your definition). In World Y, there is no maximally great being, so we can say that God does not exist in World Y (since God is defined as being maximally great).

Now you seem to be saying that God, in World X, cannot be maximally great unless he is also maximally great in World Y. But I don't buy that. I don't see any reason to suppose that that is true. Let us not forget, of all the possible worlds, only one is the actual world (disregarding for now the many-worlds interpretation of Quantum Mechanics). Therefore, if there is a possible world in which God does not exist, that does not reduce the greatness of God in any possible world in which God does exist (since at most one of those two possible worlds can be the actual world).


By definition "maximal greatness" and the three "O's" must mean for all possible worlds, if God is defined as that which is greater than can be conceived. It must also mean for all imaginary worlds, possible worlds, and actual worlds. How can the maximal greatness hold for the actual world, if it is also not maximally great for the other possible world? unless, "all possible worlds" mean that more than one God is possible, but then there would be competing "gods" some greater than others, and the argument falls apart.

If God is maximally great, God, "G", is maximally great in all worlds X, Y, ...Z, etc...If
G were not maximally great in all possible worlds, then God would be less than maximally great. Omniscience means that G is aware of all possible worlds.

G >= All possible worlds

and

G >=< G creates a contradiction.

Therefore

G is maximally great in all possible worlds.




Evil One:
And after all that, you jump again to :



If God exists, God's existence is necessary.


Evil One wrote:

But you haven't shown this. Or explained it. You're just asserting it again. By necessary do you mean it's an anlytic proposition? Or some other form of necessity? How is this necessity contingent on God's existence? Why can God's existence not be a matter of happenstance, rather than a matter of necessity?


If G is understood/defined to be the "creator" of that which is created, G's existence is necessary. Of course, then the greatest possible entity/being is G creates x, where x is the aspect(s) of existence.

But you are correct, in that ambiguity does exist, so it is not the same type of necessary truth as the statement: "all dogs are dogs".



God's existence is possible in some world.

Therefore God exists.


I will happily agree with you, for the sake of argument, that there are one or more possible worlds where God exists. But you have still not demonstrated the key point, that if God exists he exists necessarily. This is needed to demonstrate what you are trying to demonstrate, that the actual world is one of those possible worlds where God exists.




God is defined as the greatest of all things; all-powerful, all-knowing, all-present. Such an entity, by definition, cannot be reliant, on any other form of existence. By its definition, God, is not created by anything else, hence it is not dependent upon anything else; yet it is a necessary entity/being for everything else TO exist.

[1.] The concept of a maximally great being is logically self-consistent.

[2.] If God exists, God's existence is necessary.

[3.] God's existence is possible.

[4.] Therefore, there is at least one logically possible world in which a maximally great being, God, exists.

[5.] If an entity of maximal greatness, God, exists in one logically possible world, it exists in every logically possible world.

[6.] Therefore, an entity of maximal greatness ," God" exists in every logically possible world.

[Philosoft]

Chimp, how does it follow that a "maximally great" being must be omni-everything? Maximal greatness in actuality is not equivalent to maximal conceptual greatness, is it?

[Chimp]

Chimp, how does it follow that a "maximally great" being must be omni-everything? Maximal greatness in actuality is not equivalent to maximal conceptual greatness, is it?

The "ontological argument" appears to fail due to its ambiguity?

If the premise is ambiguous then the conclusion is ambiguous. If the conclusion is ambiguous then the proof is not a ..."proof", since proof entails nonambiguity...

:confused: :eek: :boohoo:

[Goliath]

God is defined as the greatest of all things;



This goes back to my first question: What do you mean by "greatest"? What ordering are you using?!

And why do you continue to refuse to answer my straightforward questions?

Sincerely,

Goliath

[xorbie]

The "ontological argument" appears to fail due to its ambiguity?

If the premise is ambiguous then the conclusion is ambiguous. If the conclusion is ambiguous then the proof is not a ..."proof", since proof entails nonambiguity...

:confused: :eek: :boohoo:

This is not a respons to the argument, just an off topic tangent that barely qualifies as an argument, followed by some smilies. In the future, posts like this will be edited.

xorbie
EoG Mod

[Goliath]

{removed}

Sincerely,

Goliath

[Chimp]

This is not a respons to the argument, just an off topic tangent that barely qualifies as an argument, followed by some smilies. In the future, posts like this will be edited.

xorbie
EoG Mod

Incorrect. It is a response with a bit of humor[smilies]. The ontological argument hinges on the initial premise that basically "God is the greatest possible being" or "God is a perfect being".

These definitions contain ambiguity.

If the premise contains ambiguity the conclusion contains ambiguity.

Do you disagree?

[Goliath]

"God is the greatest possible being"

Why have you refused to tell me what you mean by this in a straightforward manner?

Sincerely,

Goliath

[Tyler Durden]

Previously Posted Elsewhere...
**************************
The conception of God as a priori involves the effort of moving from the idea of necessity to the existence of necessity. Why is this so?

1- The very notion of a necessary being entails a contradiction, because that presupposes the total awareness of perfection and identification of that perfection.
2- Since we are unable to move from the logical to the ontological (ontological argument of God) there is an incommensurable divide between the concepts of necessary and contingence.

This is a direct allusion to Leibniz's effort to reason that the idea of a necessary being entails its existence. A necessary being, in its possibility and description as necessary, must absolutely exist. Yet Jean-Paul Sartre formulated an objection that restricted the level of understanding to the level of knowledge. In other words, possibility as an ideal is not the possibility of being. Ontological or real possibility exists only to the extent being maintains the possibilities in existence. Possibility follows existence, not vice versa.

Well, apparently Sartre's atheism is specifically addressed to a particular theism, that we can have a clear and distinct concept about the a priori possibility of God. In order to conceive of the impossibility of God is to assert to have a clear concept of the nature of God. Similar to the conception that a circle-triangle is impossible because we have a clear idea of a triangle and a circle.

However, it is quite possible to construct an ontological argument against the existence of anything in particular. I consider the philosophical terms 'necessary' and 'demonstrable' both interchangeable. This leads me to the assertion that phrases such as 'necessary existence' or 'demonstrable existence' are meaningless.

Premise1- No assertion is necessary unless its negation is contradictory.
P2- No negation of a fact is contradictory.
P3- All assertions about the existence of things are matters of fact.
Conclusion 1- Therefore, no negation of an assertion that some thing exists is contradictory.
C2- Hence there is nothing whose existence is necessary.

The possibility that at least one exceptional being whose existence is necessary is broken down in different ways:

Existential propositions in mathematics are necessarily true. If my 'empirical epistemology' can except these, could a case be made for the necessary existence of the Supreme being? The existence of mathematical entities is hardly similar to a supreme being. Math depends upon human stipulation while God is 'absolutely independent and self-subsistent.' The existence of mathematical entity is no more similar to the existence of a Supreme Being than a brick could be like the raging inferno of a solar flare.

A second way would discuss the 'eternal' existence of a Supreme being- as the great theistic religions have claimed - whether God exists, He has always existed and will never go out of existence. However, the word 'necessary' or 'demonstrable' does not entail 'always existed and will never go out of existence.' The word 'necessary' or 'demonstrable' is misleading- it is an elucidation, not an a priori demonstration. In the immortal words of David Hume: "Whatever we can conceive as existent, we can also conceive as nonexistent," because it remains an open question whether God does in fact exist.

My rejection of 'necessary existence' is a referral to logical necessity. The existence of God is factually necessary, not logically necessary. All factual necessity accounts are appeals to notions like 'uncaused,' 'independent,' or 'eternal.' It remains to be seen whether in fact, there exists anything that is factually necessary and whether that is identified with God.

The statement 'God exists' is not a tautology. There are tautologous existential statements, such as 'Fictitious objects do not exist.' This statement is an analytic proposition, which entails the non-existence of the subject-class. It is as straightforward as saying 'nonexistent invisible purple Godzilla do not exist.' However, the analyticity of the statement 'God exists' is an open question, one that depends on whether His existence is true, since the meaning of the word 'exists' does not analytically repeat the meaning of the word God. One can assert that god doesn't exist and be wrong, but it is no self-contradiction.

[The Evil One]

Let Total Existence = X
aspect of existence = x
X--->x
and
not-X--->x
creates a contradiction.

therefore X--->x is a necessary truth.

OK, problems with this: What do you mean by "Total existence"? What do you mean by "aspect of existence"? What do you mean by "--->"?

Also, to say [A and not A] is indeed a contradiction, but this is not enough to show that A is an analytical proposition, as I understand it (and please, if any readers know more formal logic than I do, let me know if I'm understanding it correctly!). Not-A must be a self-contradiction in and of itself for A to be an analytical proposition.


How can the maximal greatness hold for the actual world, if it is also not maximally great for the other possible world?

Very easily. You are losing sight of the fact that the other possible worlds aren't real places. So it is not a contradiction to say "God is maximally powerful everywhere" and then to say "there is a possible world which does not have a maximally powerful God".

unless, "all possible worlds" mean that more than one God is possible, but then there would be competing "gods" some greater than others, and the argument falls apart.

Why? There are all kinds fo possible worlds, and they may or may not each contain a God or Gods. You seem to be assuming that God, if he exists, exists in all possible worlds simultaneously, as the same being. This strikes me as missing the point of the way possible worlds work.


If God is maximally great, God, "G", is maximally great in all worlds X, Y, ...Z, etc...If
G were not maximally great in all possible worlds, then God would be less than maximally great.

No he's not, because (assuming that God exists) the places (possible worlds) where he is not maximally great don't exist. Therefore there is no place where God is not maximally great. Therefore God is (if he exists) not less than maximally great.

G >= All possible worlds

and

G >=< G creates a contradiction.



Are you trying to use mathematical symbols??????

If G is understood/defined to be the "creator" of that which is created, G's existence is necessary.

Why? In what sense of the word "necessary"?

Of course, then the greatest possible entity/being is G creates x, where x is the aspect(s) of existence.

But you are correct, in that ambiguity does exist, so it is not the same type of necessary truth as the statement: "all dogs are dogs".

I just don't understand this. Sorry.

God is defined as the greatest of all things; all-powerful, all-knowing, all-present. Such an entity, by definition, cannot be reliant, on any other form of existence. By its definition, God, is not created by anything else, hence it is not dependent upon anything else; yet it is a necessary entity/being for everything else TO exist.

Again, how are you defining "necessary"? I must say I suspect you of equivocating this term, so you need to define it very carefully.



[1.] The concept of a maximally great being is logically self-consistent.

[2.] If God exists, God's existence is necessary.

[3.] God's existence is possible.

[4.] Therefore, there is at least one logically possible world in which a maximally great being, God, exists.

[5.] If an entity of maximal greatness, God, exists in one logically possible world, it exists in every logically possible world.

[6.] Therefore, an entity of maximal greatness ," God" exists in every logically possible world.
I will grant [1] for the sake of argument. I will also grant [3] and [4] for the sake of argument, despite the incoherence of making the necessity of a proposition dependent on its truth. But [2] (and [5], which is the same thing said differently) does not appear to me to be supported - and until you define exactly what you mean by "necessary" it will remain so.

Edit to add: oops I bungled here. The "making the necessity of a proposition dependent on its truth" incoherence occurs in point [2], not point [3]. My bad.

[Goliath]

(to Chimp)
Are you trying to use mathematical symbols??????


Yes. He's vomiting up mathematical symbols and terminology and expecting us to be fooled into thinking that he has the slightest clue as to what he's talking about. <comment removed - ex-xian>
Sincerely,

Goliath

[Goliath]

Chimp,



[1.] The concept of a maximally great being is logically self-consistent.



We've been over this. Such an assertion is ABSOLUTELY WORTHLESS until you tell me what ordering you're using!

You've already conceded the fact that you have no such ordering. Why do you persist, when you've been soundly trounced?

Sincerely,

Goliath

[Chimp]

Again, how are you defining "necessary"? I must say I suspect you of equivocating this term, so you need to define it very carefully.


I will grant [1] for the sake of argument. I will also grant [3] and [4] for the sake of argument, despite the incoherence of making the necessity of a proposition dependent on its truth. But [2] (and [5], which is the same thing said differently) does not appear to me to be supported - and until you define exactly what you mean by "necessary" it will remain so.

http://en.wikipedia.org/wiki/Modal_logic


The basic modal operators are usually given to be possibility, actuality, necessity, and contingency. A sentence is said to be actual if it is true; it is said to be possible if it might be true (whether it is actually true or actually false). A necessary statement is one which could not possibly be false; by contrast, a contingent statement is one that might be true and also might be false. (This is not the same, of course, as saying that it is a statement which might be both true and false; there are no statements of that sort.)






http://en.wikipedia.org/wiki/Necessary_and_sufficient_conditions#Necessary_conditions


If A is a necessary condition for B, then the logical relation between them is expressed as "If B then A" or "B only if A" or "B → A".

[Goliath]

Chimp,

Again, please either define your ordering or concede.

Sincerely,

Goliath

[Chimp]

Chimp,

Again, please either define your ordering or concede.

Sincerely,

Goliath

Give me the precise, mathematically exact, definition of "ordering" and I will try to comply.

[The Evil One]

All right, Chimp. I'll take you at your word.

A necessary statement is one which could not possibly be false

Now let's look at this.

If G is understood/defined to be the "creator" of that which is created, G's existence is necessary.

Why? Why does being defined as a "creator" mean that the proposition that "God exists" cannot possibly be false?

[2.] If God exists, God's existence is necessary.

which I now translate as

[2a] If God exists, "God exists" cannot possibly be false.

Hmm. Not sure whether that's a vacuous tautology or a wild unsupported assertion.

What you are basically doing, Chimp, is building in as an assumption the idea that "God exists" is a necessary statement. This is a classic begging the question. If one of your premises is that "God exists" is a necessary statement, then OF COURSE your conclusion will be that God exists.

What you have to do - and what you have still not done - is give us some reason to believe that the statement that "God exists" cannot possibly be false.

Your other argument:

Let Total Existence = X
aspect of existence = x
X--->x
and
not-X--->x
creates a contradiction.

therefore X--->x is a necessary truth.

I now translate as


An aspect of existence is a necessary condition for Total existence
and
An aspect of existence is a necessary condition for not-Total existence
creates a contradiction.

therefore "An aspect of existence is a necessary condition for Total existence" is a necessary truth.
Which is, to be quite frank, insane and incoherent.

[Chimp]

You appear to misunderstand the logic.

X--->x

X

therefore x

Is the correct statement


This statement:

X--->x

x

therefore X

is a logical fallacy

[Goliath]

Give me the precise, mathematically exact, definition of "ordering" and I will try to comply.

A relation ~ on a set A is a subset of AxA (where "x" denotes the cartesian product).

A relation <= is called a partial ordering on A if it is a relation on A and:

1. <= is reflexive (that is, for all x in A, x<=x).

2. <= is antisymmetric (that is, for all x,y in A, if x<=y and y<=x, then y=x).

and 3. <= is transitive (that is, for all x,y,z in A, if x<=y and y<=z, then x<=z).

A relation <= is called a quasi-ordering if <= is reflexive and transitive.

A relation <= on A is called a linear ordering if it is a partial ordering and for all x,y in A, either x<=y or y<=x.

A relation <= on A is called a well-ordering if it is a linear ordering and if each subset of A has a least element under <=.

Sincerely,

Goliath

[The Evil One]

You appear to misunderstand the logic.

Nope, I don't. What you put in your recent post is the valid form of inference, which I am quite capable of recognising. It is not, however, the same as your original argument

X--->x
and
not-X--->x
creates a contradiction.

therefore X--->x is a necessary truth.

which doesn't seem to mean anything at all (once X and x are translated).

[Chimp]

A relation ~ on a set A is a subset of AxA (where "x" denotes the cartesian product).

A relation <= is called a partial ordering on A if it is a relation on A and:

1. <= is reflexive (that is, for all x in A, x<=x).

2. <= is antisymmetric (that is, for all x,y in A, if x<=y and y<=x, then y=x).

and 3. <= is transitive (that is, for all x,y,z in A, if x<=y and y<=z, then x<=z).

A relation <= is called a quasi-ordering if <= is reflexive and transitive.

A relation <= on A is called a linear ordering if it is a partial ordering and for all x,y in A, either x<=y or y<=x.

A relation <= on A is called a well-ordering if it is a linear ordering and if each subset of A has a least element under <=.

Sincerely,

Goliath

http://www.linuxguruz.com/foldoc/foldoc.php?Boolean+algebra



If a and b are elements of a Boolean algebra, we define a <= b to mean that a ^ b = a, or equivalently a V b = b. Thus, for example, if ^, V and - denote set intersection, union and complement then <= is the inclusive subset relation. The relation <= is a partial ordering, though it is not necessarily a linear ordering since some Boolean algebras contain incomparable values.

Note that these laws only refer explicitly to the two distinguished constants 1 and 0 , and in two-valued logic there are no others, but according to the more general mathematical definition, in some systems variables a, b and c may take on other values as well.

[Goliath]

Chimp,

STOP DIGGING UP LINKS! Tell me what ordering you are using for your particular god argument!

Sincerely,

Goliath

[Chimp]

Nope, I don't. What you put in your recent post is the valid form of inference, which I am quite capable of recognising. It is not, however, the same as your original argument


X--->x
and
not-X--->x
creates a contradiction.

therefore X--->x is a necessary truth.


which doesn't seem to mean anything at all (once X and x are translated).

X = X is an analytic proposition, a "necessary truth" because X = ~X is a contradiction.


Since ambiguity exists in the definition of "God", you are correct. Thanks for the help.

[The Evil One]

X = X is an analytic proposition, a "necessary truth" because X = ~X is a contradiction.

Since ambiguity exists in the definition of "God", you are correct. Thanks for the help.

Well, I'm glad you think I'm correect, but puzzled that you seem to think that what I've been saying has anything to do with ambiguity in the definition of "God". Ah! ---- never mind, whatever makes sense to you.

[Chimp]

Chimp,

STOP DIGGING UP LINKS! Tell me what ordering you are using for your particular god argument!

Sincerely,

Goliath

A Boolean algebra is not always a linear ordering, my irate friend

[Goliath]

All right, I've almost had it with you. First of all, you are *NOT* my friend. Are we absolutely, positively clear on that?

Look, I'll make it easy for you. Fill in the following blanks:

"In the god argument that I'm presenting, I'm using the following set: ________. The ordering on this set is defined by: _________."

Either fill in both of those blanks, or please concede.

Sincerely,

Goliath

[Goliath]

A Boolean algebra is not always a linear ordering

Also, this is nonsensical, since an algebra is not an ordering!

Sincerely,

Goliath

PS Please check your PM box.

[Chimp]

All right, I've almost had it with you. First of all, you are *NOT* my friend. Are we absolutely, positively clear on that?

Look, I'll make it easy for you. Fill in the following blanks:

"In the god argument that I'm presenting, I'm using the following set: ________. The ordering on this set is defined by: _________."

Either fill in both of those blanks, or please concede.

Sincerely,

Goliath

Universal Set

linear ordering, partial ordering

[Goliath]

Universal Set

There is no such thing, whence your arugment fails.

linear ordering, partial ordering

WHICH LINEAR ORDERING? WHICH PARTIAL ORDERING?

Sincerely,

Goliath

[Chimp]

There is no such thing, whence your arugment fails.



WHICH LINEAR ORDERING? WHICH PARTIAL ORDERING?

Sincerely,

Goliath

Goliath just sent this PM:


Private Message: Why?
Today, 11:17 AM
Goliath
Veteran User


Join Date: March 2001
Location: Fargo, ND, USA
Posts: 1,743 Why?


Why are you doing this? Why won't you just admit that you haven't the slightest clue as to what you're talking about? You're only making an ass out of yourself in front of everyone at the IIDB.

Sincerely,

Goliath




Let me be the first to say that I don't have the slightest clue as to what I am talking about and that I am not an authority on any subject. My apologies to anyone who may have been offended.

With that out of the way I respectfully ask "Goliath" to stop harrassing me.

Theists have told me I will "burn" in hell and atheists have told me I am an idiotic ass.

Trying to Prove the existence of a supreme being must really tick people off eh?

[Goliath]

Goliath just sent this PM:

Ummm..there is a reason why PMs are PMs...it's unbelievably bad form to post a PM or private e-mail in a public board.



Let me be the first to say that I don't have the slightest clue as to what I am talking about and that I am not an authority on any subject.



Thank you. At least you're starting down the path to honesty now.



My apologies to anyone who may have been offended.



Apology accepted.



With that out of the way I respectfully ask "Goliath" to stop harrassing me.



It was not my intention to harass you, rather to try to understand why you continued to blather on about things on which you were transparently ignorant.

Sincerely,

Goliath

[Chimp]

Ummm..there is a reason why PMs are PMs...it's unbelievably bad form to post a PM or private e-mail in a public board.



Thank you. At least you're starting down the path to honesty now.



Apology accepted.



It was not my intention to harass you, rather to try to understand why you continued to blather on about things on which you were transparently ignorant.

Sincerely,

Goliath

Yes, I am an ignoramus, now will you let me blather in peace?

[Goliath]

now will you let me blather in peace?

As long as you blather honestly, yes.

Sincerely,

Goliath