Witt

BDS:
However, I stand by my critique of Witt's initial proof, and my statement "If it is possible that GWTW won the academy award, then GWTW won the award." It all depends on what we mean by "possible". Of course it is "logcially possible" that GWTW did not win, but it is historically true that GWTW DID win. So, if we accept this historical fact, I don't see how this statement is fallacious. The fact that there is one winner, and only one winner means that it is impossible that any other movie won, and that the ONLY possible correct answer is the ONE correct answer.


Hi BDS,

If either possible or necessary are taken primitive the other is defined in terms of it.

That is: nec(p) defined ~pos(~p), or, pos(p) defined ~nec(~p).
Logical possibility and Logical necessity, is what is intended.
True in all possible domains or true in all possible worlds, are common interpretations.

BDS:
I can see that, given certain definitions of "possible", your (2b) can be a fallacy. However, here I'll plug my syllogism into the (2b) format:
Syllogism 2b: "If GWTW won the 1939 Academy Award, then it is not possible that GWTW did not win."

"[2b] If p, then its not possible that not-p" is invalid.

This is not valid because of the above definitions of possible and necessary.
p -> nec(p), is invalid.

p -> pos(p), and, ~p -> pos(~p), are valid.

GWTW won the 1939 Academy Award, is true.
But, ~pos(GWTW did not win the 1939 Academy Award), is false.

~pos(GWTW did not win the 1939 Academy Award), means, nec(GWTW did win the 1939 Academy Award).

It is not actual that, GWTW did not win the 1939 Academy Award, is true. ..but it is possible!

Actual truths are not considered necessary truths.
Necessary truths are: tautologies, analytically true, apriori, deductively true.

Factual truths and factual falsities are indeed possible but they are not necessary.
Nor are necessary truths factual.

Witt

Witt

Witt:
If God is described or defined by a contradictory predication, then, that God does not exist.
Therefore, it is possible that God does not exist ..can be asserted.

Hi metacristi,

metacristi:
Can be asserted indeed but not necessarilly from the noncontradiction law.

It's possible that God does not exist, and, God does exist ..is contradictory.
It's possible that God does not exist, and, It's possible that God does exist, ..is contradictory.
It's possible that God does not exist, and, it's necessary that God exists, ..is contradictory.

metacristi:
Even if we accepted that reality should 'obey' the rules of logic [we must nor forget that logic is only a feature of human reasoning there is no necessity to believe that reality should follow it's rules] the conclusion do not follow from the premises given by the noncontradiction law for all concepts of God as you asserted.

I disagree with "logic is only a feature of human reasoning there is no necessity to believe that reality should follow it's rules".

Logic exhausts the possibilities of truth, it must include all of reality.

I did not assert that every definition of God is contradictory for all concepts of God.

I did say "Therefore, it is possible that God does not exist ..can be asserted".

metacristi:
The interesting fact is that even if we had sound arguments logically proving/disproving a certain concept of God since logic is a feature of human reasoning and from this does not result with necessity that 'reality' should obey the rules of logic we are still entitled to doubt the conclusions [in the absence of experimental confirmations beyond all reasonable doubt].Sure a disbelief in the conclusions is made nonrational but skepticism [that the conclusion represent true knowledge in absolute as opposed to 'fallible truth'] is still rational in the absence of experimental arguments 'confirming' the conclusions beyond all reasonable doubt.

Each of: God exists, possibly God exists, and necessarily God exists, are true in virtue of necessity not by experimental propbabilities.
They are tautologous or contradictory, like 1+1=2 or, p v ~p.

There is no amout of empirical evidence that can provide proof of their truth.

God's existence must occur prior to its creation of time-space-mass-energy. ???

How do we get time before time??

The very process of creating time, entails a prior time.
No event can occur without time.

Surely there are no timeless things, are there?

Witt

metacristi

Witt,

Leibnitz' variant of the ontological argument (whose conclusion is D1) referes at our world too and is based on the fact that a perfect being (a noncontradictory concept) must possess also the attribute of existence.The argumentation is not sound,besides even many theists accept that this variant of the ontological argument is not compelling enough.
Let accept however that D1 is valid,TRUE.'God exists is not necessary implies God exists is not possible' is logically valid but since the sentence 'God exists is possible implies God exists is necessary' is TRUE results that it is impossible for God to not exist because he is necessary.

If God is not defined as the perfect being then the argument totally falls apart because there is virtually no base to argue that he must possess the attribute of existence as it was possible (though totally unconvincing) in the previous case.But let's assume that D1 is valid even for this case.
'God exists is possible implies God exists is necessary' means that every valid logically concept of God must be necessary in a certain reality (not necessary ours).The same argument as above is still valid: because they are necessary in their reality it follows that the sentence 'God exists is not necessary implies God exists is not possible' though logically valid has no importance at all,it is impossible for every such God to not exist in his own reality.

BDS

Witt:

OK. But then the error in your proof becomes clear.

I admit that all the mathematical symbols confuse me, because I forget exactly what they mean. However, it seems to me that your proof fails because:

"If God exists, then God is necessary"

already contradicts the conclusion

"God does not exist is possible".

That is, the second clause ("God is necessary") is contingent on the first clause ("God exists").

Let's plug it into my analogy:

GWTW winning the academy award is possible implies that GWTW winning is necessary (given the fact that it has already happened and given a more "real world" definition of "possible".

GWTW NOT winning is possible (given your definition)

Therefore: GWTW winning is NOT possible.

It seems to me that your proof for the non-existance of God is conflating the two different definitions of "possible" in precisely the same way as my proof that GWTW did not win the 1939 Academy Award.

I recognize that you dispute my first statement, but shouldn't you equally dispute the initial statement about God in your proof?

Also, couldn't you conclude from your proof that "God exists, but He is not necessary"?

In other words, your D1 ("D1. Its (God's) possible existence implies its necessary existence") is precisely the logical error you claim I'm making about GWTW. So, given your own statement that this is a logical fallacy, even though it is hidden in your proof as a "definition" instead of postulates, it brings the whole proof crashing down.

BDS

Metcristi and I cross posted, but we appear to be making the same basic point.

Witt

BDS,
Metcristi and I cross posted, but we appear to be making the same basic point.

I am not so sure.
Both of you seem to present different objections.

I will try to deal with your point of view first.

Witt

Witt

BDS:

OK. But then the error in your proof becomes clear.

I admit that all the mathematical symbols confuse me, because I forget exactly what they mean. However, it seems to me that your proof fails because:

"If God exists, then God is necessary"

already contradicts the conclusion

"God does not exist is possible".

That is, the second clause ("God is necessary") is contingent on the first clause ("God exists").

Let's plug it into my analogy:

GWTW winning the academy award is possible implies that GWTW winning is necessary (given the fact that it has already happened and given a more "real world" definition of "possible".

Witt:
No factual truths are necessarily true.
No necessary truths are factually true.

GWTW NOT winning is possible (given your definition)

Therefore: GWTW winning is NOT possible.

It seems to me that your proof for the non-existance of God is conflating the two different definitions of "possible" in precisely the same way as my proof that GWTW did not win the 1939 Academy Award.

I recognize that you dispute my first statement, but shouldn't you equally dispute the initial statement about God in your proof?

Also, couldn't you conclude from your proof that "God exists, but He is not necessary"?

In other words, your D1 ("D1. Its (God's) possible existence implies its necessary existence") is precisely the logical error you claim I'm making about GWTW. So, given your own statement that this is a logical fallacy, even though it is hidden in your proof as a "definition" instead of postulates, it brings the whole proof crashing down.
---------------------------------------


If GWTW exists is true, then,
GWTW exists is possible, is true.
GWTW exists is necessary, is false.

GWTW exists is true, then, GWTW exists is necessary ..is false.
GWTW exists is possible, then, GWTW exists is necessary ..is false.

GWTW exists, is factually true or it is factually false.
God exists, is necessarily true or it is necessarily false.

If God exists is true, then,
God exists is possible, is true.
God exists is necessary, is true.


If God exists is true, then, God exists is necessary ..is true.
If God exists is possible, then, God exists is true ..is true.

(both follow from D1.)



~<>E!(God)

Proof:

premise 1. <>E!(God) -> []E!(God).

premise 2. <>~E!(God).

If God is defined by a contradictory predication, then,
it is possible that God does not exist, is true.
That is to say, It is possible to define God such that it does not exist.

If God is not defined by a contradictory predication, then, God exists, is possible ..is true.

3. ~[]E!(God) -> ~<>E!(God).
By, premise 1 and (p ->q) <-> (~q -> ~p).

4. <>~E!(God) -> ~<>E!(God).
By, 3 and ~[]p <-> <>~p

5. ~<>E!(God). by, premise 2 and 4 and modus ponens.

Where did I go wrong here?

Witt

BDS

Sorry, Witt. You're losing me. I did look up "necessary" and "contingent" and "sufficient" in a philosophical dictionary, so I understand that I was using "necessary" differently from how it's used in philosophic logic. Obviously, now that I know this specialized meaning of "necessary" it becomes clear that it was not "necessary" that GWTW won the Academy award, given the specialized meaning of the word (although it is using the dictionary definition).

I'll try to respond later.

Witt

Sorry, Witt. You're losing me. I did look up "necessary" and "contingent" and "sufficient" in a philosophical dictionary, so I understand that I was using "necessary" differently from how it's used in philosophic logic. Obviously, now that I know this specialized meaning of "necessary" it becomes clear that it was not "necessary" that GWTW won the Academy award, given the specialized meaning of the word (although it is using the dictionary definition).

I'll try to respond later
-----------------------------

Thank you for your honesty. It is often difficult to expess a view that is contrary to another view without leading to insults and flames. Your civility is appreciated.
The distinction between philosophical logic as opposed to mathematical logic is not, often, made clear.

My attention, recently, is to try and discern the subtleties (please excuse my bad spelling) concerning logical necessity and empirical necessity. I will e-mail you about these things if you are interested. It seems to me that It's anybody's ball game, when it comes to this kind of philosophy .. what do you think about this stuff?

Regards,

Witt