Witt

Logic provides the essence of truth.

yguy

Prove it.

theophilus

What is the significance of using the term "purported," which is defined as "assumed to be such; supposed" with the conotation of being false? Perhaps there is some technical logical significance of which I'm unaware.

BDS

Witt's proof confuses two different things: human knowledge and reality. Of course if God exists He is necessary. But, if He exists, there is no possibility that He does not exist. So the assumptions on which Witt's proof is based are faulty.

The possibility that God either does or does not exist is a false one. The truth, of course, is that either He exists, or He doesn't exist. The only reason the option which is NOT true is a "possibility" is because human knowledge is imperfect.

Witt's proof says no more than "if it is possible that God does not exist, then God does not exist." Everyone knows that already. If it is possible that George W. Bush is not the President of the United States, then he is not the president. Of course it is "possible" the W isn't president in the linguistic sense (in other words the sentence "W. is not President" is a reasonable sentence, just as "God does not exist" is), but it is not possible in the "real world" sense. Witt's proof mixes these two senses up.

BDS

I just reread my post above, and it's not very clear.

Here's an analogy. Suppose a horse race has already been completed. Someone offers to take your bet on the race. You want to get Seabiscuit at 6:1 odds.

Assuming that neither of you know the outcome of the race, it's perfectly reasonable to make the bet. However, the ACTUAL odds of Seabiscuit winning are not 6:1. They are either 100% or 0 %. The race is already over.

It's the same thing with God. If there's a possibility that God doesn't exist, then he doesn't exist. If there's a possibility that Seabiscuit lost, then he lost.

Bilbo

BDS writes:

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Witt's proof confuses two different things: human knowledge and reality.
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Actually, the proof (as briefly sketched) appears to conflate terms and their denotations. Similiarily with the apparent conflation of assertible sentences, and possible propositions. The existence (or non-existence) of terms or other linguistic entities is certainly not the divide separating those who take up these sorts of theistic arguments.

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Of course if God exists He is necessary. But, if He exists, there is no possibility that He does not exist. So the assumptions on which Witt's proof is based are faulty.
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You're right with the first two statements, but only by accident. (See below)

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The possibility that God either does or does not exist is a false one. The truth, of course, is that either He exists, or He doesn't exist. The only reason the option which is NOT true is a "possibility" is because human knowledge is imperfect.
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If the statement "God exists or it is not the case that God exists" is true, then surely "Possibly, God exists or it is not the case that God exists" is true, since all statements actually true, are possibly true. So there is no problem of "imperfect knowledge" that is relevant here.

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Witt's proof says no more than "if it is possible that God does not exist, then God does not exist." Everyone knows that already. If it is possible that George W. Bush is not the President of the United States, then he is not the president.
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These cases need to be distinguished. A standard Leibnizian interpretation of a standard theistic presentation of these two statements renders the first true, and the second false.

It *is* possible that Bush is not the president (ie there is a world in which Bush is not the president), but that doesn't mean that Bush is not in fact president (in this world).

The case with the existence of God differs significantly from this one.

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Of course it is "possible" the W isn't president in the linguistic sense (in other words the sentence "W. is not President" is a reasonable sentence, just as "God does not exist" is), but it is not possible in the "real world" sense. Witt's proof mixes these two senses up.
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I think the mixup lies elsewhere.


Regards,

Bilbo.

BDS

Bilbo says, "If the statement "God exists or it is not the case that God exists" is true, then surely "Possibly, God exists or it is not the case that God exists" is true, since all statements actually true, are possibly true. So there is no problem of "imperfect knowledge" that is relevant here."

I don't buy it, Mr. Baggins. Of course the statement "God exists or it is not the case that God exists" is true. That's the nature of the word "or". However, this does not imply that "it is possible that God dos not exist" is a true statement.

"1 + 1 = 2 or 1 + 1 = 3" is a true statement. Can we then infer that it is possible that 1 + 1 = 3?

Let me put it another way: there are two kinds of bar bets. One is to bet on future events, like who will win the Super Bowl. Another is to bet on facts, like who won the Academy Award for best movie in 1939. Of course we might say, "There's a good possibility that "Gone With the Wind" won." But all we're saying is, "My memory isn't that great, so I'm not sure if 'Gone With The Wind' won or not." If we had our Almanac with us, we'd know for sure.

In any event, it would be fair (and true) to say (from the perspective of having the Almanac with us), "If there's a possibility that GWTW won, then it won." That's because the event has already taken place, and either happened, or didn't happen. If it didn't happen, then it's impossible that it did. Same with God.

It would be unfair to say, "If there's a possibility that the Green Bay Packers will win the Super Bowl, then they will win." That's because the word "possibility" means two different things in these two different sentences.

Bilbo

BDS wrote:

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Bilbo says, "If the statement "God exists or it is not the case that God exists" is true, then surely "Possibly, God exists or it is not the case that God exists" is true, since all statements actually true, are possibly true. So there is no problem of "imperfect knowledge" that is relevant here."
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I don't buy it, Mr. Baggins. Of course the statement "God exists or it is not the case that God exists" is true. That's the nature of the word "or". However, this does not imply that "it is possible that God dos not exist" is a true statement.
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I never suggested it is. What I said is that if a statement is actually true, then *that* statement is possibly true, not some other statement.

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"1 + 1 = 2 or 1 + 1 = 3" is a true statement. Can we then infer that it is possible that 1 + 1 = 3?
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Of course not. From the truth of a (non-trivial) disjunction we can't infer the truth of any of its atomic disjuncts. In fact, from a true disjunction we can't infer the *possibility* of any of its atomic disjuncts. But from a true disjunction we *do* validly infer the possibility of the disjunction. There are some important distinctions here that need to be recognized.

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Let me put it another way: there are two kinds of bar bets. One is to bet on future events, like who will win the Super Bowl. Another is to bet on facts, like who won the Academy Award for best movie in 1939. Of course we might say, "There's a good possibility that "Gone With the Wind" won." But all we're saying is, "My memory isn't that great, so I'm not sure if 'Gone With The Wind' won or not." If we had our Almanac with us, we'd know for sure.
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The term "possibility" has various senses, most of which are context dependent. The two senses you allude to here are typically characterized as broad logical possibility, and epistemic possibility, respectively.

When we speculate about future contingents; like the winner of next year's superbowl, we usually have in mind broad logical possibility, or one of its derivatives. When we speculate (in ignorance) about the winner of the '39 Oscar for Best Picture (in this world), we have something different in mind; namely epistemic possibility. But in philosophical contexts, its important to identify the appropriate sense when analyzing relations between statements containing those terms. Failure to do so generates unimpressive results.

When philosophers talk about God and necessity, they almost invariably have *broad logical possibility* in mind.

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In any event, it would be fair (and true) to say (from the perspective of having the Almanac with us), "If there's a possibility that GWTW won, then it won."
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But why would you think this? The statement: "If its possible that GWTW won the Oscar, then GWTW won the Oscar" is false on either interpretation. We can make both senses explicit as follows:

[1a] If it is concievable (so far as I know) that GWTW won the Oscar, then GWTW (in fact) won the Oscar.

and

[1b] If it is logically possible (in some possible world) that GWTW won the Oscar, then (in *this* world) GWTW won the Oscar.

Given the proviso that winning the Oscar is a contingent achievement of anything that succeeds at it, it follows that both [1a] and [1b] are false.

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That's because the event has already taken place, and either happened, or didn't happen. If it didn't happen, then it's impossible that it did. Same with God.
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You seem to be confusing *necessity of the consequence*, with *necessity of the consequent*; a well known fallacy that attends conditionals of this sort.

From colloquial expressions like: "If 'p' is true, then 'not-p' can't be true" its important to get the sense of "can't" right. The above statement admits of many interpretations, the most relevant being:

[2a] If p, then its not the case that not-p
[2b] If p, then its not possible that not-p
[2c] Necessarily, (If p, then its not the case that not-p)

Your statement above appears to mirror the fallacious [2b], rather than the other two; both of which are acceptable.

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The possibility that God either does or does not exist is a false one.
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This is incorrect. From what you've said so far, I don't think you understand the meaning of that statement, or the implications it generates.

Regards,

Bilbo.

BDS

Dear Barrel Rider,

You appear to be more formally educated than I am in philosophic logic. However, with a few exceptions, I still think I'm right.

I admit that I misstated your initial syllogism. I did so on purpose, because (although I knew the syllogism was correct as stated) I thought you were implying that the syllogism IMPLIED something that it did not. If I was wrong (as is evidently the case), I retract.

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.

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."

This is the sentence that you call fallacious. I don't see why, though. Because the event has already happened, and because we can look up the answer, the statement seems to me to be perfectly reasonable, and absolutely true. The reason, of course, is that for events that have already happened, the "possibilities" are exhausted. Until we invent time travel, your (2a) and (2b) are identical, in this particular case. If it is not the case that Wizard of Oz won, then it is not possible that Wizard of Oz won.

Of course there may be some special meaning of "possible" in a logical, philosophical, or mathematical sense of which I am unaware. I'm just using the common-sense meanings of words. If you can point out to me how MY 2b is fallacious, I'll gladly abandon my critique of Witt's proof.

By the way, I understand that your [1a] and [1b] are false. The way I'm using the word, "possible" means neither "conceivable" nor "logically possible (in some possible world)" It means "possible in this world".

metacristi

Witt


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

Indeed if the attributes assigned to a type of God are internally coherent then this type of God represents a logical possibility.Because this concept of God represents a logical possibility it follows that we do not have the right to assign to the statement 'God [coherent internally] exist' a truth value of 0 [without making reference to experimental data].That is we cannot say that the above sentence is logically false.Results from here that from logic alone we cannot make a clear difference between God existence and God nonexistence and therefore we can affirm that 'it is possible that God does not exist' is true logically [as I've said without making reference to experimental data for the moment].Now if we cannot assign a truth value of 0 [making reference to experimental data this time] for this concept of God then it is empirically possible.But if the probability is not 1 then the sentence 'it is possible that God does not exist' is still true.

Your conclusion do not necessarilly follow from the law of noncontradiction then.


Only if we cannot assign a truth value of '1' for the sentence 'God exists' [that is only if a certain concept of God is not proved as existing with arguments beyond all reasonable doubt empirically].I concede that,at least now,to no concept of God [probably an infinity] can be assigned a truth value of '1' empirically but neither can we assign for the statement 'God [defined merely as the personal creator of the universe or at least the actual order in the universe] does not exist' an 'empirical','objective' probability greater than 'God does exist'.


If by necessary you mean 'noncontingent' then even without resorting to experimental data that sentence is not true.Indeed if I define God as being 'the personal creator of our universe' even if he exists [but I am unaware of that] does not follow from here that this God is 'necessary' in the sense of being self sufficient,not contingent.As in one novel of Arthur C. Clarke this creator could be 'created' at his turn,contingent too.Even for the Christian God from a simple definition does not follow its necessary existence at least logically,indeed the ontological argument in all its known forms today is not sound.


The interpretation of 'necessary' as being the indispensable cause for the observed reality does not make the above statement acceptable either,there other equally acceptable logically possibilities,at least now,as unique essential causes for all observed facts,naturalism for example.
Also there is,virtually,an infinite number of non contradictory logically concepts of God and no possibility to choose between them logically,moreover this does not mean they have necessary existence in reality: that's why the experiment remain the 'supreme court'.Sure this does not mean that God [defined as the personal creator of the universe at least] does not exist but only that we have no basis to affirm D1 logically and/or experimentally at least now.


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.