An argument in support of atheism.

[Witt]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G

I think it was Leibnitz who claimed: that whose possibility ensures its necessity is God.

3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'God does not exist' is logically true

[Silent Dave]

Most atheists, and many theologians, reject premise 2, which is used in many ontological arguments FOR the existence of God.

[Brian Bosse]

Hello Whitt,

Premise 1 in possible world theory means that in at least one possible world God does not exist. Premise 2 says that if God does exist in at least one possible world, then He exists in all possible worlds. Premise 1 and Premise 2 leads to the conclusion that it is necessarily the case that God does not exist. Guess which premise the theist would reject.

Brian

[Witt]

Most atheists, and many theologians, reject premise 2, which is used in many ontological arguments FOR the existence of God.

What theologians reject (<>G -> []G) ?

Since (<>G -> []G) <-> (<>~G -> []~G), I also doubt your claim that most atheists reject (<>~G -> []~G).

[Brian Bosse]

Hello Witt,

I accept premise 2 and reject premise 1. In fact, premise 2 follows directly from the Christian worldview. Theologians who reject premise 2 would not be considered conservative in their theology. Of course, I am thinking stricty in terms of Christian theism.

Sincerely,

Brian

[Witt]

Hello Whitt,

Premise 1 in possible world theory means that in at least one possible world God does not exist. Premise 2 says that if God does exist in at least one possible world, then He exists in all possible worlds. Premise 1 and Premise 2 leads to the conclusion that it is necessarily the case that God does not exist. Guess which premise the theist would reject.

Brian

Hello Brian,

Premise 2. is equivqalent to (<>~G -> []~G), ie. If God does not exist in at least one possible world, then he does not exist in all possible worlds.

Theists argue,
P1. <>G
P2. <>G -> []G
therefore,
3. []G

Atheists argue,
P1. <>~G
P2. <>~G -> []~G
therefore,
3. []~G.

Both arguments are of the same form, and they prove nothing.

Note that, (<>G & <>~G) is a contradiction here.


By the way, on May 12/07 you wrote: Arguments for God’s existence, although perhaps at times expressed formally, are part of informal systems. There is a subset of Christianity that speaks of an axiomatic system. But technically it is not a formal axiomatic system.

I am curious about your claim 'There is a subset of Christianity that speaks of an axiomatic system. But technically it is not a formal system.'

I believe that all deductive systems that use axioms are formal systems.

Could you expand on your point here, an example system would be informative.

[~M~]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G

I think it was Leibnitz who claimed: that whose possibility ensures its necessity is God.

3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'God does not exist' is logically true




Hello,

these signs may help you in the future and it is certainly far more reader friendly:



∃ → ≡ ∀ □ ◊ ⇒


copy and paste.

[Brian Bosse]

Hello Whitt and ~M~,

These signs may help you in the future and it is certainly far more reader friendly: ∃ → ≡ ∀ □ ◊ ⇒ ...copy and paste.

Definitely helpful. Thank you.

Premise 2. is equivqalent to (<>~G -> []~G), ie. If God does not exist in at least one possible world, then he does not exist in all possible worlds.

I agree with you that ◊¬G → □¬G. I deny ◊¬G.

Both arguments are of the same form, and they prove nothing.

They prove their conclusions if they are sound. It just points out that both arguments rest on their respective premise 1's. For the argument to go through each side would have to argue for their premise 1's. That is all. There is nothing inherently wrong with the arguments in and of themselves.

Note that, (<>G & <>~G) is a contradiction here.

Just to be clear: (◊A ∧ ◊¬A) is not a formal contradiction. Let A= "The Germans won WWII." This is true in some possible world and false in another possible world. In this case, (◊A ∧ ◊¬A) is true. However, I grant that if G is defined as ◊G → □G, then (◊G ∧ ◊¬G) is inconsistent.

By the way, on May 12/07 you wrote: Arguments for God’s existence, although perhaps at times expressed formally, are part of informal systems. There is a subset of Christianity that speaks of an axiomatic system. But technically it is not a formal axiomatic system...Could you expand on your point here, an example system would be informative.

There are group of orthodox Christians that subscribe to an epistemological postition called 'Scripturalism'. They claim that their system is axiomatic. However, upon analysis, their system is far from axiomatic, rather turning out to be informal. That was all I meant.

Sincerely,

Brian

[Amedeo]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G

I think it was Leibnitz who claimed: that whose possibility ensures its necessity is God.

3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'God does not exist' is logically true


Your first premise is an unwarranted assumption. You see, your basic mistake is that you do not define "god." You may NOT assume of ANY THING that it is possible for it not to exit; therefore, you may not assume that it is possible for God not to exist.

More fundamentally: We can say that, e.g., it is possible for a dog to exist, because dogs exist. The possibility is inferred from the fact; the possibility is not some quality inherent in the existence of dogs.

By the same token, since dogs exist, it is not possible for dogs not to exist: it is necessary from them to exist -- which does not mean that a dog is ALWAYS existing (eternal). "Necessity" is not some inherent quality of the existence of a dog.

The modalities in question are logical, not ontological modalities... There are no such things [there are no such realities] as a possible being or a necessary being.

_____________
For the unschooled in logic:
Consider the argument --
All men are mortal
Socrates is a man
Hence, it Socrates MUST be mortal
(it is necessary that Socrates be mortal) This means that mortality MUST be predicated of Socrates (since he is a man): We are logically REQUIRED to attribute mortality to Socrates.
The logical necessity holds also for arguments which have a false premise. For example:

All poets write in Greek.
E. A. Poe is a poet.
Therefore, Poe must write in Greek.

... and for arguments about non-existing things:
Geometrical figures are invisible and inaudible.
A square-circle is a geometrical figure.
Therefore, a square-circle must be invisible and inaudible.
(A square-circle is a contradiction in terms and, therefore can not be real. What is real is not self-contradictory.)

[Witt]

Hello Whitt and ~M~,



Definitely helpful. Thank you.



I agree with you that ◊¬G → □¬G. I deny ◊¬G.

They prove their conclusions if they are sound. It just points out that both arguments rest on their respective premise 1's. For the argument to go through each side would have to argue for their premise 1's. That is all. There is nothing inherently wrong with the arguments in and of themselves.

Agreed.

Neither <>G nor <>~G are sound premises of their respective arguments.

Indeed, in virtue of P2 (<>G -> []G), (G <-> <>G) and (G <-> []G) and (<>G <-> []G), that is to say G (God exists) is analytic.

[](G -> []G) <-> [](<>G -> G) <-> (<>G -> []G) <-> (G is analytic).

[](~G -> []~G) <-> [](<>~G -> ~G) <-> (<>~G -> []~G) <-> (~G is analytic).

God exists cannot be synthetic, there is no empirical condition that alters the truth or falsity of God exists.

(p is analytic) means (<>p -> []p).
(p is synthetic) means (<>p & <>~p).

G is not simpler than []G, they are equivalent.

To believe that 'it is possible that God exists' is to believe that 'it is necessary that God exists'.

Regards,

Witt

[Bobinius]

Witt,

Just an observation: premises are not sound, they are true or false.

Of course, in your argument God is a necessary being, meaning he either exists necessarily or it is impossible for him to exist. It's a good argument, and if you take a closer look, it is exactly the opposite of Plantinga's modal ontological argument for God. I actually used it in order to refute Plantinga's argument. If there is a possible world where God does not exist, he is impossible to exist, ergo he does not exist. Both lines of arguing are equally justified, which shows the futility of any of the lines, including Plantinga's ontological argument.

[wiploc]

premise 1. <>~G
premise 2. <>G -> []G

Could I have the second one in English? I'm struggling with it. Might it need parentheses, or an if/then?

crc

ETA: Never mind, I've got it. The -> implies an if/then. It hurts my head every time someone starts a formal logic thread. :)

[wiploc]

In fact, premise 2 follows directly from the Christian worldview.

That just weirds me out. Can you support it. I'm thinking that there were Christians before there was possible-worlds theory. And there are Christians who don't know about possile-worlds theory. I'm certainly not going to call them unorthodox so long as they believe that god exists in the actual world.

crc

[Brian Bosse]

Hello Wiploc,

Ask yourself what the nature of God would be if Christianity were in fact true. In short, God would be the ground of all being. This translates to God being necessary. Does this help? The point is not that the Bible understands possible world theory, but rather possible world theory can be a template applied to the Bible.

Sincerely,

Brian

[wiploc]

∃ → ≡ ∀ □ ◊ ⇒

∃ ?

→ entails, or if/then

≡ ?

□ is true/ is necessary/ is true in all possible worlds.

◊ is possible/ may be true/ is true in at least one possible world.

What are the first and third symbols?

crc

[Jade]

Hello Wiploc,

Ask yourself what the nature of God would be if Christianity were in fact true. In short, God would be the ground of all being. This translates to God being necessary. Does this help? The point is not that the Bible understands possible world theory, but rather possible world theory can be a template applied to the Bible.

Sincerely,

Brian
Just a quick thought while I prepare for my last exam...

While a Christian modal realist would probably have to agree that God (as the alleged 'ground of being') would be necessary (i.e. existing in all possible worlds), I don't know that this is the same for a Christian with more anti-realist leanings towards possible worlds. For example, lets say you believe a possible world is just (i) a set of propositions (ii) that are mutually consistent with each other and (iii) which together constitute a maximally detailed and complete description of a way the cosmos could be. With such a belief about possible worlds, do you really have to believe that the proposition "God exists" has to be in every single such set if you are a Christian?

[wiploc]

For the unschooled in logic:
Consider the argument --
All men are mortal
Socrates is a man
Hence, it Socrates MUST be mortal
(it is necessary that Socrates be mortal) This means that mortality MUST be predicated of Socrates (since he is a man): We are logically REQUIRED to attribute mortality to Socrates.

I have trouble with this. Often, Christians say that if god exists at all then he does so necessarily. I never understand why they say that.

Brian is an exception. He defines god that way. If Jesus, Jehovah, Heaven, Hell, the crusifixion, and the stuff about sacraments is all true in the actual world, but don't exist in some "possible" fantasy world, then---for Brian---god does not exist.

But for other Christians, the ones for whom god is real even if he doesn't exist in every possible fantasy world, I don't see why they say god must exist if he does exist.

And now you're doing the same thing with Socrates.
- All men happen to be mortal.
- Socrates happens to be a man.
- Therefore Socrates is necessarily a man?
Why isn't the conclusion that Socrates just happens to be a man.

Amedeo, I assume we don't have a real disagreement. I assume you just mean that if the premises are true then it follows that the conclusion is also true. I'm not trying to argue with you. I'm just using your post as a tee-off point to talk about my long-standing confusion on the issue of whether actual things are necessary. It keeps getting said that true things are necessarily true. I keep not getting explanations about why people say that. In Brian's case the answer is clear: actuality implies necessity only in the case of god, and only because that's how he defines god. In other people's cases, I'm still waiting for an answer. So if there's anybody in this thread who thinks actual implies necessary, I'd like an explantion.

And by the way, Brian, I really appreciate your clarity.

crc

[Jade]

∃ ?

→ entails, or if/then

≡ ?

□ is true/ is necessary/ is true in all possible worlds.

◊ is possible/ may be true/ is true in at least one possible world.

What are the first and third symbols?

crc
The backwards 'E' is the existential quantifier (http://en.wikipedia.org/wiki/Existential_quantification). The triple equal-sign is the biconditional (http://en.wikipedia.org/wiki/Logical_biconditional).

[Brian Bosse]

Hello Jade,

It is good to "see" you. I hope you have been well.

Brian

[trendkill]

(p -> q) -> (~q -> ~p)Isn't this the fallacy of denying the antecedent?

[Jade]

Hello Jade,

It is good to "see" you. I hope you have been well.

It's been a little crazy for the past couple of weeks, but it's almost over...

[Jade]

Isn't this the fallacy of denying the antecedent?
No, it's essentially the Modus tollens argument form, compressed into a single statement.

[~M~]

The backwards 'E' is the existential quantifier (http://en.wikipedia.org/wiki/Existential_quantification). The triple equal-sign is the biconditional (http://en.wikipedia.org/wiki/Logical_biconditional).



Thank you.

[~M~]

[QUOTE=Brian Bosse;4453344]Hello Whitt and ~M~,



Definitely helpful. Thank you.



About time i get some appreciation around here. :Cheeky: I got plenty of other symbols ranging from belief logic, ethics, metalogic, etc.

[wiploc]

Originally Posted by Witt
(p -> q) -> (~q -> ~p)

Isn't this the fallacy of denying the antecedent?
No, it looks like it, but that's an optical illusion.
Try it with different letters:

(p -> x) -> (~x -> ~p)

crc

[wiploc]

Hello Wiploc,

Ask yourself what the nature of God would be if Christianity were in fact true. In short, God would be the ground of all being. This translates to God being necessary. Does this help? The point is not that the Bible understands possible world theory, but rather possible world theory can be a template applied to the Bible.

Sincerely,

Brian

Thanks, Brian.

No, it doesn't help me. I imagine possible world C, in which Christianity is true, and possible world N in which the Norse gods are true. You're asking me to say that if Jehovah created world C, then he also created world N? If that's true, then isn't it also true that Odin or whoever created world C? Isn't it as reasonable to assume that Odin created world C as to assume that Jehovah created world N? (Answer: "Yes.") Are we then to assume that both Jehovah and Odin created this world, the real world, on the grounds that they both exist in other possible worlds? If we do that, doesn't it follow that all creator gods are true in all possible worlds?

And then what about a uncreated possible world? Does that world somehow mean that this world is uncreated?

crc

[Ghostdog]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G

I think it was Leibnitz who claimed: that whose possibility ensures its necessity is God.

3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'God does not exist' is logically true

I'm terribly sorry for this but I must play the role of the arrogant Christian here.

"God created this arguement as another attempt to test the faith of his followers."

Its as simple as that. The will of the Christian is hard to break.

[Amedeo]

I have trouble with this. Often, Christians say that if god exists at all then he does so necessarily. I never understand why they say that.

Brian is an exception. He defines god that way. If Jesus, Jehovah, Heaven, Hell, the crusifixion, and the stuff about sacraments is all true in the actual world, but don't exist in some "possible" fantasy world, then---for Brian---god does not exist.

But for other Christians, the ones for whom god is real even if he doesn't exist in every possible fantasy world, I don't see why they say god must exist if he does exist.

And now you're doing the same thing with Socrates.
- All men happen to be mortal.
- Socrates happens to be a man.
- Therefore Socrates is necessarily a man?
Why isn't the conclusion that Socrates just happens to be a man.

Amedeo, I assume we don't have a real disagreement. I assume you just mean that if the premises are true then it follows that the conclusion is also true. I'm not trying to argue with you. I'm just using your post as a tee-off point to talk about my long-standing confusion on the issue of whether actual things are necessary. It keeps getting said that true things are necessarily true. I keep not getting explanations about why people say that. In Brian's case the answer is clear: actuality implies necessity only in the case of god, and only because that's how he defines god. In other people's cases, I'm still waiting for an answer. So if there's anybody in this thread who thinks actual implies necessary, I'd like an explantion.

And by the way, Brian, I really appreciate your clarity.

crc

There are various reasons why Christian (and others) say that God is a NECESSARY being, but they say so NOT on the basis of any Christian doctrine or any prophetic revelations: Christian thelogians have taken philosophical doctrines and applied them to God. The whole discourse of Parmenides and a few other philosophers -- speakers of Being -- has b een used as a discourse on God. For example, Parmenides and Melissus of Elea said that BEING or WHAT-IS or THAT-WHICH IS ["to ti esti"]... or existence... cannot change. For it to change would be to become non-being. But Non-being neither is nor can be conceived; it is not that into which anything can turn, nor that out of which a being could come. (It is absurd to think that non-being could undergo a change and turn into being). So, Being simply IS, without end, withour being, without alteration.

Being [or God in theology] can be said to be necessary in the sense that it is not possible for it to annihilate or for anything to pop into existence. [This is what is called the law of conservation of matter, in physics. It is a philosophical proposition, though partially evident empirically within the limits of observers' lives. It is also the law of substantial reality, wherefore the occurrences in dreams -- annihilations and pop-ups -- are rejected as imaginary. Children and primitive do not distinguish between dreams and realities.]

Needless to say, the same theologians brush aside or produce fallacious arguments for a fact they admit: the existence of non-God, such as a created world -- something which began to be absolutely and may absolutely end. The Thomas Aquinas solution, that God is the actus purus, the existing of anything that exists, implicitly denies that God is an individual substance, or asserts pantheism... which no Christian really believes in. What I say is that the whole theology which makes use of philosophy was and is a big mistake. The gods of religions are destined to remain pre-philosophical concepts. (There cannot be God/Being and something else.)

I am going to stop here, otherwise I will be writing for a month on all the issues concerning BEING. I will only say in passing that we are obviously acquainted with things that have a beginning and an end. Consider a mule. It had a beginning, but not a created beginning. When God said, "Let there be a beast of burden," it appeared full made, an adult. Real mules begin as REAL specs of matter (from the parents), assimilate nutrients, and grow into mules. Eventually they perish: they do not disappear; they turn into smokes and ashes or what have you. With the birth and death of a mule, the totality of WHAT EXISTS is neither increased nor decreased. What occurs is only alterations of the structures of what exists. The EXISTENT is one, immutable, infinite... (See all the discussions on TIME and on CONSCIOUNESS on the Philosophy Board, for we already in the thick of philosophy.)

As to "logical necessity," it is something that needs not be put in words, as in "Socrates MUST be mortal." It can be called "NON-EMPIRICAL CERTAINTY, as this episode will show:

We are looking into a kitchen through a window. We have only visual experiences: no sound, no heat, no pressure, nor pain, no other experience. We see water in a pot on a stove. We do not know, from touch,whether it is cold, warm, hot or boiling. By we see a big thermometer in it, and we know that "AS THE TEMEPERTURE OF WATER INCREASES, THE MERCURY COLUMN OF THE THERMOMETER GOES HIGHER."

Now we see the mercury rising to 100, to 200, to 212...

So, we are certain that the water is boiling hot, without touching it, without seeing it bubble, and without even seeing vapor.

We made an inference from a general principle and from a given fact. Once we accept the two premises, we are necessitated to make that conclusion.

The water itself cannot be said to be NECESSARILY BOILING, since we had no facts about a fire or something that causes the water to boil. The thermometer events were EFFECTS, not the causes, of the water condition. However, we can male a Backward Inference as say that the themometer's 212th degree PRESUPPOSES that water is boiling, just as smoke presupposes that there is a fire. Even my words "I do not exist" presuppose that I exist.....(Necessity is in the thought processes, not in my existence.)

The syllogism about Socrates that I presented [formally studied by Aristotle] makes the same point I made above:

We do not know whether Socrates, a living man, is mortal or not, but we can assert his mortality with certainty on the basis of the fact that Socrates is a man, and the general principle that any man has a physical and corruptible body. What is corruptible = mortal. So, even though we have not seen Socrates die, we are totally certain that he is subject to death.

On the basis of the Pythagorean theorem and the measuring of a couple of angles and the ground distance between them, you can INFER the distance between the earth and the sun without actually tape-measuring it. (Logically correct thinking = demonstrative argumentation.)

[Witt]

Your first premise is an unwarranted assumption. You see, your basic mistake is that you do not define "god."

It dosen't matter, any definition of God will do. For example God =df that entity whose posssible existence entails its necessary existence, and omni-this and omni-that etc.

You may NOT assume of ANY THING that it is possible for it not to exit; therefore, you may not assume that it is possible for God not to exist.

What? It is clear to me that any described object defined by a contradictory predication cannot exist. It is true that the present king of France does not exist, therefore, It is possible that the present king of France does not exist.. is true.

More fundamentally: We can say that, e.g., it is possible for a dog to exist, because dogs exist. The possibility is inferred from the fact; the possibility is not some quality inherent in the existence of dogs.

By the same token, since dogs exist, it is not possible for dogs not to exist: it is necessary from them to exist --

What? Clearly, it is not the case that dogs exist necessarily.

We cannot say that dogs exist necessarily, but, we can say eg: If dogs bark then dogs exist, my dog barks, therefore, my dog exists.

That is, If dogs bark is true, and my dog barks is true, then, my dog exist is logically true...within classical logic.

The modalities in question are logical, not ontological modalities... There are no such things [there are no such realities] as a possible being or a necessary being.

I said: G = God exists, <>G = It is possible that God exists. []G = It is necessary that God exists.

_____________
For the unschooled in logic:
Consider the argument --
All men are mortal
Socrates is a man
Hence, it Socrates MUST be mortal
(it is necessary that Socrates be mortal) This means that mortality MUST be predicated of Socrates (since he is a man): We are logically REQUIRED to attribute mortality to Socrates.

Nonsense. Threre are no necessary truths for any empirical object.

The argument is necessarily true, not an attribute of the object.

If All men are mortal, and Socrates is a man, then, Socrates is mortal. The whole argument is logically true within classical logic.

But, we cannot say "We are logically REQUIRED to attribute mortality to Socrates".



The logical necessity holds also for arguments which have a false premise. For example:

All poets write in Greek.
E. A. Poe is a poet.
Therefore, Poe must write in Greek.

Unsound arguments necessitate no-thing.

... and for arguments about non-existing things:
Geometrical figures are invisible and inaudible.
A square-circle is a geometrical figure.
Therefore, a square-circle must be invisible and inaudible.
(A square-circle is a contradiction in terms and, therefore can not be real. What is real is not self-contradictory.)

A square-circle is a geometrical figure, is false.

There are no properties of non-existent things at all!

[wiploc]

There are various reasons why Christian (and others) say that God is a NECESSARY being,

Thanks for an interesting and illuminating post.

crc

[Amedeo]

REPLIES after ===>

Quote:
Originally Posted by Amedeo View Post
Your first premise is an unwarranted assumption. You see, your basic mistake is that you do not define "god."

It dosen't matter, any definition of God will do. For example God =df that entity whose posssible existence entails its necessary existence, and omni-this and omni-that etc.

===> It does matter. For example, if you define a god as a spiritual substance, you are defining it by two terms which are mutually contradictory, and IT IS IMPOSSIBLE FOR THERE TO BE such a thing. (There is no such a thing as a dog which is moving and not moving, The law if Identity of reality precludes moving non-moving dogs, squares which have no angles, dehydrated water, and spiritual substance.) In case you do not see mydefinition as being contradictory: What is spiritual = non-physical. What is physical = can change, can initiate an action, can start producing an effect on another physical thing, etc. Spiritual = the negation of all that inheres in the nature of what is physical. Substance, as Plato correctly defines it, = that which can act upon other substances and can be acted upon. Substance is defined by DYNAMIS, as Plato correctly put it. What has no power of acting is an "accident", in the Aristotelian language; e.g. the shape of yoiur body is not a substance. Therefore, that which is spiritual (and cannot act, for acting involves changing) and that which is substantial (and has the capacity of acting and being acted upon) contradict each other: you are saying ZERO or NOTHING when you say "spiritual substance."

That which cannot exist cannot possibly exist. Hence, God, as just defined, is NOT a possible thing.

-----------------------------------------------------
Quote:
You may NOT assume of ANY THING that it is possible for it not to exit; therefore, you may not assume that it is possible for God not to exist.

What? It is clear to me that any described object defined by a contradictory predication cannot exist. It is true that the present king of France does not exist, therefore, It is possible that the present king of France does not exist.. is true.

===>I think the meaning of my statement is obvious from the reply I just gave. However, I could rephrase it thus: You may not assume of ANY THING YOU NAME OR STATE that it is possible for it not to exist. For instance, by naming a king of France, Louis XIV, you do not know ipso fact that it is possible for that king not to exist. Of course, the moment that you state that the King was born at one point of history and died at another point of history, you have added information to the "being king" of a person. Now you can say that it is possible, before anf after the life of the king of France, for there not to be that king of France. The possibility is stated from the fact of the non-existence of the king before and after his life... The "possibility of not being" is NOT attributable to the actual existence of the King. Something named either is or is not; you cannot meaningfully ascribe any possibility or necessity to what is named. (Possibility and necessity are conceptual categories.)

If you name 'being' [(What IS)], you may not assume that it is possible for it not to be. From what exists, you may not infer that it is possible for it not to exist.

---------------------------------------
Quote:
More fundamentally: We can say that, e.g., it is possible for a dog to exist, because dogs exist. The possibility is inferred from the fact; the possibility is not some quality inherent in the existence of dogs.

By the same token, since dogs exist, it is not possible for dogs not to exist: it is necessary from them to exist --

What? Clearly, it is not the case that dogs exist necessarily.

We cannot say that dogs exist necessarily, but, we can say eg: If dogs bark then dogs exist, my dog barks, therefore, my dog exists.

That is, If dogs bark is true, and my dog barks is true, then, my dog exist is logically true...within classical logic.

===> "it is not possible that ... not..." = "it is necessary that...."
If a dog exists, it is not possible for it not to be existing. Again: insofar as a dog exists, it is false that it is not existing.

If the modal language proves to be confusing, I am all for dropping it. In another post, I explained logical necessaity in terms of "certainty" --- which I believe goes a long way to prevent the possible confusion between logical and ontological necessity. (For me, what is simply is, and admits of no speaking of it in terms of possibilities and necessities.)

-------------------------------------
Quote:
The modalities in question are logical, not ontological modalities... There are no such things [there are no such realities] as a possible being or a necessary being.

I said: G = God exists, <>G = It is possible that God exists. []G = It is necessary that God exists.
---------------------------------------

Quote:
For the unschooled in logic:
Consider the argument --
All men are mortal
Socrates is a man
Hence, it Socrates MUST be mortal
(it is necessary that Socrates be mortal) This means that mortality MUST be predicated of Socrates (since he is a man): We are logically REQUIRED to attribute mortality to Socrates.

Nonsense. Threre are no necessary truths for any empirical object.

The argument is necessarily true, not an attribute of the object.

If All men are mortal, and Socrates is a man, then, Socrates is mortal. The whole argument is logically true within classical logic.

But, we cannot say "We are logically REQUIRED to attribute mortality to Socrates".

===> It is obvious to me now that you have no conception of LOGICAL neccessity, even though you use the concept of IMPLICATION in your argumentation.

What I said is not something that holds for classical logic, as if it were a primitive or a faulty logic. Do yourself a favor: study the logic works of Ariostotle and of the Stoics, and stop get confused by the modern symbolism which allows you to think mechanically or automatically. A computer can do an excellent thinking with symbololic logic, and it or you do not have to understand one iota of what you are thinking.

The conclusion from premises is an IMPLICATION; it does not ascribe any necessity to anything. So, do yourself a favor: get it rid of Modal logic, and you will not be making the fallacy in question: confusing the logical with the ontological (and imagining that I or other were attributing to beings what belong to a reasoning process.).
----------------------------
Quote:
The logical necessity holds also for arguments which have a false premise. For example:

All poets write in Greek.
E. A. Poe is a poet.
Therefore, Poe must write in Greek.

Unsound arguments necessitate no-thing.

===> I have said enough already. You do not even recognize VALID arguments. But do you know what the term "validity" means?
----------------------------------

Quote:
... and for arguments about non-existing things:
Geometrical figures are invisible and inaudible.
A square-circle is a geometrical figure.
Therefore, a square-circle must be invisible and inaudible.
(A square-circle is a contradiction in terms and, therefore can not be real. What is real is not self-contradictory.)

A square-circle is a geometrical figure, is false.

There are no properties of non-existent things at all!

===> I am glad you recognize, now, that a square circle is a nothing. (Proceed a little further and you will recognize that "god" is another nothing, whefore you cannot say that it is, or that it is possible, or that it is necessary).

Now, if I had said, "Let SC be a geometrical figure," and I had added that geometrical figures are spiritual things [invisible; unperceptible... for the physical is perceptible in principle], surely you would agree with the conclusion that SC is a spiritual thing. I am sure you could transpose my categorical syllogisms into the logic of classes... -- or could you? The logic or predicates and the logic of classes are functionally the same, but if you stick with the logic of classes, you exposes your mind to innumerable fallacies, including the important one, " secundum quid ... et simpliciter," which has a longer name, and I am too tired to explain. ((Get thee a book of Fallacies, which are not exactly the same as the invalidities of reasoning processes.))

[Amedeo]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G [see comments below]

I think it was Leibnitz who claimed: that whose possibility ensures its necessity is God.

3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'God does not exist' is logically true

As I have discussed your Premise 1, Now I turn to your Premise 2:

It says that if it is possible for something [God] to exist, then it is necessary for it to exist.

In other circumstances, such as the demonstrating of a theorem about triangles, the premises are of different kinds, such as a Definition of a right-angle triangle; Axioms [stated or unstated] which deal with established properties of triangles; and a given triangle (whose sides are AB, etc.); and (stated or unstated) logic postulates (such as the law of transitivity, etc.)

Your second premise is actually a logic postulate. Like any other logic postulate, it may not be arbitrary. The subject of the argumentation is at once own discretion [a triangle, a god, a planet, or the tooth-fairy]; the laws of logic are not arbirary -- though at the moment I will not discuss the difference between arbitrary and objective laws of any kind.

The postulate, "If it is possible that x exists, then it is necessary for x to exist," is false. It can be refuted by innumerable facts. For example, it is possible for an apple to grow on a tree (since it has the bud, the likes of which grow into apples), but it is possible for the bud to be destroyed: what is possible is not necessarily realized.

Furthermore, your two premises are inconsistent: they imply a mutual contradiction:

If it is possible that God does not exist (or that a bottle of wine does not exist in my kitchen), then it is possible that there is not, there was not, and that there will never be a bottle of wine in my kitchen. Hence it is not necessary for the bottle to ever be there.

Now, there is also the possibility that there is a bottle there: I said the possibility, not the fact, of its being there. The possibility does not imply that the bottle must be there. But let us suppose it does. (Let's admit Premise 2 as being true, for a moment.) Well then, the necessity of the bottle being being there contradicts Premise 1, namely the idea that it is possible for the bottle not to be there.

In brief, from the premises we can infer that

IT IS NECESSARY THAT GOD EXISTS implies IT IS POSSIBLE THAT GOD DOES NOT EXIST. (This is an example of plain ABSURDITY.)

[Amedeo]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G

I think it was Leibnitz who claimed: that whose possibility ensures its necessity is God.

3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'God does not exist' is logically true


Finally, I will look at some steps in your argument.

For the sake of argument, I assume that there are no problems of any kind with your two premises.

Step # 3 is a valid inference.

Step # 4 has a big problem. You did NOT quote # 3, which is a simple implication; you stated,
~[]G <-> <>~G This is a mutual implication or EQUIVALENCE or tautology. It certainly does NOT follow from # 3 or from anything else; you just made it up.

This vitiates the rest of your argument. Whatever conclusion you made cannot be valid.

[Brian Bosse]

Hello Amedeo,

Witt and I are usually in opposite corners, but on this one we are in agreement. I think your formal analysis on this misses the mark, although understandably so.

The postulate, "If it is possible that x exists, then it is necessary for x to exist," is false. It can be refuted by innumerable facts. For example, it is possible for an apple to grow on a tree (since it has the bud, the likes of which grow into apples), but it is possible for the bud to be destroyed: what is possible is not necessarily realized.

Two points regarding this: (1) "If it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist," is not a proposition that can be true or false. In this sentence ‘x’ is what is called a free variable. Only once you identify the ‘x’ through quantification or specification does it take on the status of a proposition that can be rightly said to be true or false. Consider the proposition, “For all ‘x’, if it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist.” This is clearly false. However, consider this proposition, “There exists some ‘x’ such that if it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist.” This is true for any ‘x’ that is necessary.

(2) Witt is using the terms ‘possible’ and ‘necessary’ within the context of possible world semantics. These terms are technically defined and are univocal. Your use of the terms above is in accordance with common parlance and is not how Witt is using them.

Furthermore, your two premises are inconsistent: they imply a mutual contradiction…

The two premises are as follows: P1 ◊¬G, and P2 ◊G → □G. If they were contradictory, then it would follow that ¬(◊¬G ∧ (◊G → □G)) is a tautology. Yet, this is not the case. If these two premises are true, then by force of logic we are lead to the conclusion □¬G. There is no inconsistency.

Step # 4 has a big problem. You did NOT quote # 3, which is a simple implication; you stated, ~[]G <-> <>~G This is a mutual implication or EQUIVALENCE or tautology. It certainly does NOT follow from # 3 or from anything else; you just made it up.

Step #4 is valid even though Witt did not properly present the argument. Step 4 says: ◊¬G → □¬G. Given premise 2, it follows by force of logic. Rather than using formal modal logic to prove this (you seem to have an aversion to it), allow me to explain informally. In possible world semantics, when we say ‘x’ is possible this means that ‘x’ is true in at least one possible world. In possible world semantics, when we say ‘x’ is necessary this means that ‘x’ is true in all possible worlds. Using this to translate premise 2 we get: “If ‘x’ is true in at least one possible world, then ‘x’ is true in all possible worlds.”

At this point, premise 2 is a given. Given premise 2 as true, we are asking ourselves what is the logical consequences of this if we assume ¬G is true in at least one possible world? Can it be the case that G is true in some other possible world in this senario? The answer is “no” because we would end up in a contradiction. The only way to avoid this contradiction is for ¬G true in all possible worlds (that is, ¬G be necessary). Here is why: Given 2, if G is true in any world, then it is true in all worlds. But if we assume ¬G is true in at least one possible world, then G cannot be true in all worlds. This means G cannot be true in any world because if it were true in some world, then it would be true in all worlds given 2. Therefore, if we assume ¬G is true in at least one possible world, then we are forced to conclude that ¬G is true in all possible worlds given 2. This is the same thing as saying: ◊¬G → □¬G, which is Witt’s step 4. He can conclude this because he is using step 2 as his given. I know this can be a little confusing, and that is why I say these misunderstandings are understandable.

All in all, Witt’s argument, though not spelled out in exactness is valid.

Sincerely,

Brian

[Amedeo]

........


Two points regarding this: (1) "If it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist," is not a proposition that can be true or false. In this sentence ‘x’ is what is called a free variable. Only once you identify the ‘x’ through quantification or specification does it take on the status of a proposition that can be rightly said to be true or false. Consider the proposition, “For all ‘x’, if it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist.” This is clearly false. However, consider this proposition, “There exists some ‘x’ such that if it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist.” This is true for any ‘x’ that is necessary.
.......

Brian
No way! the particular quantification is not a magical act. You can SAY, "there exists an x such that it is possible", but this X is a concept, not an existing thing. To avoid equivocation, just use the old word "some" and no trick occurs: "some x is possible."

You MAY say that certain things are possible ON THE BASIS OF THE FACT THAT THEY EXIST OR HAVE EXISTED. So, this is correct:

If an x exists, then x is possible, NOT THE OTHER WAS AROUND.

Also: if an x exists, then IT CANNOT NOT EXIST; that is, it necessarily exists (by the principle of non-contradiction)

What is merely conceived as possible implies the possibility that it is never actual and, therefore, NOT NECESSARY. In casting 2 dies, we can think of the possibility of a 3 and a 3, but there is no law of nature that this combination must ever be realized. The theory of probability tells us that, in the long run, a 3&3 will occur one-sixth of the times for each die, an so forth. Flip a coin. Is it heads half of the times in the long run? Bunk! What could happen has no reason or basis that it should ever happen. If the dies are cast in the same manner and under the same conditions, one result will be repeated forever and the others will never occur. The same for the coin. Now we are talking about a law of nature, which is ultimately based in the ontological law of IDENTITY. (Natural occurrences are "intelligent," not chance-events. Water is formed ALWAYS by the combination of two specific elements, not by any random mixing of elements.)

[Brian Bosse]

Dear Amedeo,

You can SAY, "there exists an x such that it is possible", but this X is a concept, not an existing thing.

You need to read more carefully. I was pointing out to you how “If it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist,” is not a proposition that can be true or false. I then gave you two examples that are propositions that can be true or false. One of those examples was…

“There exists some ‘x’ such that if it is possible that ‘x’ exists, then it is necessary for ‘x’ to exist.”

This statement is either true or false. I said that anything necessary when substituted in for ‘x’ makes the statement true.

If an x exists, then x is possible, NOT THE OTHER WAS AROUND.

It is becoming clear that you are not reading posts for understanding. Witt’s and my use of the terms ‘possibility’ and ‘necessity’ are technical terms in possible world semantics. I gave you these definitions in my lst post. You either did not understand this, or you ignored it.

Also: if an x exists, then IT CANNOT NOT EXIST; that is, it necessarily exists (by the principle of non-contradiction)

Again, you are missing or ignoring the context of this discussion. For example, in possible world semantics, there exists a world where Germany won WWII and there exists a world where Germany did not win WWII. If you are not going to engage Witt’s arguments within the context of possible world semantics, then you are arguing against air. At least show the courtesy of engaging an argument on its own terms.

Brian

[Amedeo]

G means Germany exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G


3. ~[]G -> ~<>G
By: premise 2, and (p -> q) -> (~q -> ~p).

4. <>~G -> []~G
By: 3, ~[]G <-> <>~G, and []~G <-> ~<>G.

5. []~G
By: premise 1, 4, and modus ponens.
That is, ((<>~G & (<>~G -> []~G)) -> []~G, is tautologous for any G.

6. []~G -> ~G
By the modal axiom []p -> p.

7. ~G
By: 5, 6, and modus ponens.

That is to say: if premise 1 and premise 2 are true then 'Germany does not exist' is logically true

ADDITION: A fact:
8. ~ (~G)

9. Conclusion, by the Modus Tollens:
Premise 1 and premise 2 are false.

[Brian Bosse]

Hello Amedeo,

Try and understand what is being said in this post before you respond. I will lay it out in numbered propositions to make it clearer for you.

--------------------------------------------------------------

1. Witt’s argument, made within the context of possible world semantics, is as follows:

If one is given the following propositions (that is to say, they are assumed to be true):

P(1): It is possible that it is not the case that God exists.
P(2): If it is possible that it is the case that God does exist, then it is necessary that it is the case God does exist.

then we are led to the conclusion:

C: It is necessary that it is not the case that God exists.

--------------------------------------------------------------

2. Another way to say this is as follows: If P(1) and P(2), then C.

--------------------------------------------------------------

3. Witt’s conclusion is sound.

--------------------------------------------------------------

OK. It is laid out for you. You seem to object to this. Which of the 3 points do you think is wrong?

Brian

[Amedeo]

Hello Amedeo,

Try and understand what is being said in this post before you respond. I will lay it out in numbered propositions to make it clearer for you.

--------------------------------------------------------------

1. Witt’s argument, made within the context of possible world semantics, is as follows:

If one is given the following propositions (that is to say, they are assumed to be true):

P(1): It is possible that it is not the case that God exists.
P(2): If it is possible that it is the case that God does exist, then it is necessary that it is the case God does exist.

then we are led to the conclusion:

C: It is necessary that it is not the case that God exists.

--------------------------------------------------------------

2. Another way to say this is as follows: If P(1) and P(2), then C.

--------------------------------------------------------------

3. Witt’s conclusion is sound.

--------------------------------------------------------------

OK. It is laid out for you. You seem to object to this. Which of the 3 points do you think is wrong?

Brian

IN POST # 37
I ACCEPTED THE WHOLE ARGUMENT [for the sake of argument].
I SIMPLY USED "GERMANY" INSTEAD OF "GOD".

THEN I CONTINUED THE ARGUMENT
BY SAYING THAT
GERMANY EXISTS (it is not the case that Germany does not exist)

AND I DREW THE STATED LOGICAL CONCLUSION.

DO YOU FIND ANYTHING LOGICALLY wrong WITH
MY LOGICAL CONCLUSION?

Or is, by any change, the original argument an AD HOC ARGUMENT -- valid only when G is God?

[Brian Bosse]

Hello Amedeo,

No reason to yell at me. The interesting thing about Witt's argument is that it is sound no matter what 'G' stands for. So, if you let 'G' stand for "Germany Exists," then given premises 1 and 2, the conclusion that "it is necessary that it is not the case that Germany does exist" follows by force of logic.

You did not answer the only question I asked you in my last post. I'll ask again. Which of the 3 points in my last post do you think is wrong?

Brian

[ughaibu]

In short, a pathological result.

[Amedeo]

Hello Amedeo,

No reason to yell at me. The interesting thing about Witt's argument is that it is sound no matter what 'G' stands for. So, if you let 'G' stand for "Germany Exists," then given premises 1 and 2, the conclusion that "it is necessary that it is not the case that Germany does exist" follows by force of logic.

You did not answer the only question I asked you in my last post. I'll ask again. Which of the 3 points in my last post do you think is wrong?

Brian

We are speaking different languages...

I just finished saying that I accepted the original argument.

I repeat: There is nothing wrong with the original argument.

I was not screaming at you. I wanted to draw your attention to what I added to the original argument.

You have not answered my question yet.

[Brian Bosse]

Hello Amedeo,

Miscommunication happens in a medium like this. No biggy.

I just finished saying that I accepted the original argument.

Not quite. You stated, "IN POST # 37 I ACCEPTED THE WHOLE ARGUMENT [for the sake of argument]." The "for the sake of the argument" is a qualifier. It does not necessarily mean you truly accept the argument.

You have not answered my question yet.

I apologize. Your argument really amounts to adding a third premise, namely that Germany does exist. This addition is inconsistent with the conjunction of premises 1 and 2. You conclude from this that both premises 1 and 2 are false. This not the case. In possible world sematics, the existence of Germany is not logically necessary, but is possible. Therefore, premise 1 is true. It is premise 2 that is false. Of course, this is only the case if someone gives more epistemic weight to your added premise than to the other premises. By the way, I think it is reasonable to do so.

Are you now saying that Witt's argument is sound? If not, then which of the 3 propositons in my previous post is false?

Brian

[Gundulf]

I'm jumping in here, and it has been a while since I took my undergrad logic classes, so correct me if I'm way off here... But the whole question seems inherently contradictory: "If God exists, he exists necessarily."

"IF GOD EXISTS" - implies mere possibility, right? That his existence is possible, but not necessary. (hence, premise #1 - possible that God does not exist.)

So, rewording the question, you have:

If a thing (which does not necessarily exist) exists, then that thing necessarily exists.

So if this thing exists, it both necessarily exists and does not necessarily exist?


In other words, if the argument is sound (seems like it to me), it seems that it proves nothing more than that nothing can be both not necessary and necessary.

'There needs no ghost come from the grave, my Lord, to tell us this...'



In fairness, it does well demonstrated that the phrase, "If [fill in the blank] exists, it exists necessarily" is logically absurd. So you can clean the clocks of any Christians who try to use that argument, but I don't think you can do better than that.

[Brian Bosse]

Hello Gundulf,

Witt's argument is made within the context of possible world semantics. That means he is using terms like 'possible' and 'necessary' in a technical manner. This technical usage does not necessarily correspond to comon parlance. I italicized 'necessarily' because the way I used it in the last sentence was not in its technical usage. So, if your objections are not based within the context of possible world theory, then your objections miss their mark. You would be arguing against a straw man. Here are the technical definitions:

Possible (◊): 'G' is possible (◊G) if and only if 'G' is true in at least one possible world.
Necessary (□): 'G' is neceessary (□G) if and only if 'G' is true in all possible worlds.

"IF GOD EXISTS" - implies mere possibility, right? That his existence is possible, but not necessary. (hence, premise #1 - possible that God does not exist.)

Right away you are confusing the technical usage of 'possible' with your informal understanding of a conditional. Conditionals do not predicate 'possibility'. Also, you are not representing Witt's argument correctly. His premise two is this:◊G → □G. This reads, "If it is possibly the case that God exists, then it is necessarily the case that God exists." Using the definitions above this can be further teased out to mean, "If God exists in at least one possible world, then God exists in all possible worlds." So, the antecedent in this conditional is not "God exists", but rather "it is possible that God exists."

If a thing (which does not necessarily exist) exists, then that thing necessarily exists. So if this thing exists, it both necessarily exists and does not necessarily exist?

No. When we say that 'G' is possible it is fallicious to conclude that 'G' is therefore not necessary. In fact, all necessary things are possible things.

In fairness, it does well demonstrated that the phrase, "If [fill in the blank] exists, it exists necessarily" is logically absurd.

Again, this is mistaken. If there is anything that is necessary, then the following is true: If [fill in the necessary thing here] is possible, then [fill in the necessary thing here] is necessary. Witt's argument is sound.

Don't you guys find it ironic I am (a theist) is defending Witt's argument?

Brian :Cheeky:
P.S. Witt, where are you in all of this? I seem to remember you disparaging my logical abilities in another thread. ;)

[Amedeo]

Hello Amedeo,

Miscommunication happens in a medium like this. No biggy.



Not quite. You stated, "IN POST # 37 I ACCEPTED THE WHOLE ARGUMENT [for the sake of argument]." The "for the sake of the argument" is a qualifier. It does not necessarily mean you truly accept the argument.



I apologize. Your argument really amounts to adding a third premise, namely that Germany does exist. This addition is inconsistent with the conjunction of premises 1 and 2. You conclude from this that both premises 1 and 2 are false. This not the case. In possible world sematics, the existence of Germany is not logically necessary, but is possible. Therefore, premise 1 is true. It is premise 2 that is false. Of course, this is only the case if someone gives more epistemic weight to your added premise than to the other premises. By the way, I think it is reasonable to do so.

Are you now saying that Witt's argument is sound? If not, then which of the 3 propositons in my previous post is false?

Brian

I misunderstood the whole thing and I withdraw from the conversation!!!
I agree with you that IN possible WORLD SEMANTICS, God does not exist.

I hope that that you do not imagine that you have refuted the existence of God in the real world.

Farewell,
-- Amedeo the Atheologian

[Gundulf]

Hello Gundulf,

Witt's argument is made within the context of possible world semantics. That means he is using terms like 'possible' and 'necessary' in a technical manner. This technical usage does not necessarily correspond to comon parlance. I italicized 'necessarily' because the way I used it in the last sentence was not in its technical usage. So, if your objections are not based within the context of possible world theory, then your objections miss their mark. You would be arguing against a straw man. Here are the technical definitions:

Possible (◊): 'G' is possible (◊G) if and only if 'G' is true in at least one possible world.
Necessary (□): 'G' is neceessary (□G) if and only if 'G' is true in all possible worlds.



Right away you are confusing the technical usage of 'possible' with your informal understanding of a conditional. Conditionals do not predicate 'possibility'. Also, you are not representing Witt's argument correctly. His premise two is this:◊G → □G. This reads, "If it is possibly the case that God exists, then it is necessarily the case that God exists." Using the definitions above this can be further teased out to mean, "If God exists in at least one possible world, then God exists in all possible worlds." So, the antecedent in this conditional is not "God exists", but rather "it is possible that God exists."



No. When we say that 'G' is possible it is fallicious to conclude that 'G' is therefore not necessary. In fact, all necessary things are possible things.





Don't you guys find it ironic I am (a theist) is defending Witt's argument?

Brian :Cheeky:
P.S. Witt, where are you in all of this? I seem to remember you disparaging my logical abilities in another thread. ;)

Thanks for the clarifications. I do remember the possible world stuff, but my question still stands - premise #1 is that "it is possible that God does not exist." This is merely assumed. Yet, as I read the initial question, it is rightly assumed by the phrasing of the question, "if God exists..." To start a question by stating IF X exists, implies a possible world where that thing does not exist, hence, it implies that X is not necessary....


In other words, is it proper, in possible world language, to say, "If a necessary thing exists...."? I don't recall this being proper, since it is absurd to ask 'if' a necessary thing exists - the necessary thing, by definition, must exist - no "ifs" about it. Hence, to ask "IF something exists," implies that this thing is NOT necessary. Or have I missed something here?

So it still seems to boil down into, "If X is both necessary and not necessary...."




Again, this is mistaken. If there is anything that is necessary, then the following is true: If [fill in the necessary thing here] is possible, then [fill in the necessary thing here] is necessary. Witt's argument is sound.



Not sure I totally agree with you here (but I stand to be corrected, like I said, this has been a while). After all, it looks like it was demonstrated well that ANYTHING you substitute for G comes out as not possible. Nonetheless, the equation in question is not STARTING with the assumption that G is necessary, and then saying "if G is possible, then G is necessary."

It is STARTING with the assumption that G is NOT necessary (i.e., P1, <>~G).

But since <>~G is a rephraising of ~[]G (Do I have that right?), you have...

1. ~[]G
2. If <>G, then []G.

Since you already have premise #1 on the table, just to phrase it to see the conflict, you might as well be able to say...

3. If <>G, then []G and ~[]G. But this would be a obvious contradiction. So... because
4. ~ ( []G and ~[]G),

Therefore, ~ <>G.

ANYTHING you plug into that will come out with 'therefore, G is impossble.' Which, again, proves little more than that nothing can be both 'not necessary' (premise 1) and necessary (premise 2)???

[Brian Bosse]

Hello Gundulf,

Hence, to ask "IF something exists," implies that this thing is NOT necessary. Or have I missed something here?

I believe you are mistaken here. Implications (“if…then…” statements) make no assertions about their antecedents (everything after the ‘if’ but everything before the ‘then’). For instance, “If I go outside, then I will get wet.” This statement makes no assertion as to whether or not I go outside – or even if I can or cannot go outside. Applying this to the original argument we have…

“If it is possible that God exists, then it is necessary that God exists.”

This statement makes no assertions as to whether or not it is possible for God to exist. It only asserts a consequence if it is possible that God exists.

But since <>~G is a rephrasing of ~[]G (Do I have that right?), you have...

1. ~[]G
2. If <>G, then []G.

This is very good. By the way, there is a logical law called Modus Tollens. It goes something like this: If one premise says “If ‘X’, then ‘Y’” and another premise says ‘~Y’, then you can conclude ‘~X’. Applying this to the two premises above we can conclude ~<>G. You do not need your step 3 and 4.

ANYTHING you plug into that will come out with 'therefore, G is impossble.' Which, again, proves little more than that nothing can be both 'not necessary' (premise 1) and necessary (premise 2)???

Not quite, but close. This shows that anything that is (1) not possible and is such that (2) if it is possible, then it is necessary ends up being impossible.

Sincerely,

Brian

[Matt_Matt_]

The conclusion does follow from the premises. However, the premises are pretty messed up. I have no problem with <>~G, but the other one...<>G->[]G, that doesn't come from anywhere. The second one necessarilly entails that either god exists in all possible worlds, or god exists in no possible world. From the tautology (<>G or ~<>G) and the second premise we get ([]G or ~<>G), which means the same as ([]G or~[]G). It's this assumption, ([]G or[]~G), which is logically equvalent to the second premise. That just seems to come from right out of the blue to me. Where does it come from?

[spamandham]

G means God exists.
<> means it is possible that.
[] means it is necessary that.

premise 1. <>~G
premise 2. <>G -> []G...

Isn't this just the classical modal ontological argument with "it is possible god exists" changed to "it is possible god does not exist"? Just as the original argument does not prove the existence of anything meaningful, neither does this disprove the existence of anything meaningful.

'existence' is a property of ideas, not things, so if an idea can be described only as 'it exists', this is no different from an idea that can only be described by 'it doesn't exist', which is why you get two that outcomes that appear exclusive from the proof depending on whether you start with "it's possible god exists" vs "it's possible god doesn't exist". I think it was Russell who showed there is no difference between these outcomes because 'existence' is not a property of things. That which can only be described as necessarily existing, has not been described at all, and so the proof doesn't prove the actual existence or nonexistence of anything. It's a very subtle and clever equivocation.