[Guest]

This paradox, in the self-referential category, begins with a sentence such as:

If this sentence is true, then God exists.

The sentence is of the form "If A, then B"

where A = "this sentence is true",

B = "God exists"

"this sentence" = "if A, then B"

therefore A= '"if A, then B" is true'; and we could go the route of and endless circular argument, called infinite regress

OR, we can go through a formal logical proof, as follows:

1. A = (A --> B) is true (as stated above)

2. A --> A (by identity)

3. A --> (A --> B) is true (by substitution)

4. A --> B is true (by contraction)

5. A without qualification, i.e. A is true (by substitution of 1. into 4.)

6. B is true (from 4. and 5.)

So B = "God Exists" is true, period. End of discussion.

Discuss.

[Izzy]

If this sentence is true, then I am a flying monkey with a mohawk and magical healing powers.

Apply same logic.

[Guest]

If this sentence is true, then I am a flying monkey with a mohawk and magical healing powers.

Apply same logic.

That's hilarious. Way to utilize the same logic to prove another ridiculous statement.

[hugemonkey]

This sounds like Ontological argument for the existence of God.

It basically goes like this:

1. God is by definition a "Perfect Being".

2. A "Perfect Being" would have many attributes among which would be "existence".

3. Lack of existence would be an imperfection so by definition would not be an attribute of God.

4. So therefore God exists.

As with many logical fallacies, this one has more to do with the many specific meanings the words used, in this case the words "perfect" and "existence". I could go into this more but my posts tend to ramble.

To your original quote:

I think you break down at step 5. "A" still contains the qualification "IF" since A= '"IF A, then B". Basically you are saying "It is true if it is true." Which is, of course, a true statement.

Substitute the word "false".

"If this statement is false, then God exists."

It reminds me of the Discordian proverb : "All things are true, even false things."

There is no prohibition in language from saying nonsense or making illogical statements.

(See what I mean about rambling?)

[Guest]

This sounds like Ontological argument for the existence of God.

It basically goes like this:

1. God is by definition a "Perfect Being".

2. A "Perfect Being" would have many attributes among which would be "existence".

3. Lack of existence would be an imperfection so by definition would not be an attribute of God.

4. So therefore God exists.

As with many logical fallacies, this one has more to do with the many specific meanings the words used, in this case the words "perfect" and "existence". I could go into this more but my posts tend to ramble.

This is off topic, but briefly, step 3 doesn't necessarily work. Neoplatonism and Taoism define their deity as "above existence". One cannot correctly describe "The One" or "That which cannot be named" as either existing or not existing. It is only lesser things, that have emanated from the deity, and thus lost some of their unity - things that exist - that have imperfections.

I think you break down at step 5. "A" still contains the qualification "IF" since A= '"IF A, then B". Basically you are saying "It is true if it is true." Which is, of course, a true statement.

The notation A-->B does contain the "if". This paradox is not so easily dismissed. Current philosophical scholars are still debating it. Curry's paradox is widely recognized by the experts as one that remains unresolved.

Substitute the word "false".

"If this statement is false, then God exists."

It reminds me of the Discordian proverb : "All things are true, even false things."

There is no prohibition in language from saying nonsense or making illogical statements.

Again, the problem goes beyond semantic language. The formal symbolism of logic that I used demonstrates that. (Yes that is a language in itself, however it is the language of mathematics. Curry's paradox is one that eludes even that discipline.)

[Guest]

I'll post my own "answer" later. Think "outside the box." Give this contradiction some hard thought. It's a great brain teaser.

[Guest]

When I first saw the sentence:

If this sentence is true, then God exists.

The first thing I think is to look for the sentence that can prove the existence of God. But when I read the rest, I am confused...

1st substitution:

If this sentence is true, then God exists.

------> this sentence: If this sentence is true, then God exists. so:

If if this sentence is true, then God exists is true, then God exists.

(don't want to continue)

so confusing, my brain can't picture how a sentence like "if this sentence is true, then God exists" can be true or false, if the sentence doesn't refers to another sentence. I think that's why it's a paradox... hahaha

[Guest]

so ok! he exists, but Stop making my head hurt with illogical statements

[Izzy]

so ok! he exists

Prove it? Perhaps with statements that aren't 'illogical'?

[Guest]

This paradox, in the self-referential category, begins with a sentence such as:

If this sentence is true, then God exists.

The sentence is of the form "If A, then B"

where A = "this sentence is true",

B = "God exists"

"this sentence" = "if A, then B"

therefore A= '"if A, then B" is true'; and we could go the route of and endless circular argument, called infinite regress

OR, we can go through a formal logical proof, as follows:

1. A = (A --> B) is true (as stated above)

2. A --> A (by identity)

3. A --> (A --> B) is true (by substitution)

4. A --> B is true (by contraction)

5. A without qualification, i.e. A is true (by substitution of 1. into 4.)

6. B is true (from 4. and 5.)

So B = "God Exists" is true, period. End of discussion.

Discuss.

lol I'm reminded of my geometry class...my head is almost spinning.

[Guest]

Simplicity, simplicity, simplicity.

There is no paradox here.

The effort attempts to complicate the thought that is a play on words.

If this sentence is True, then G-d exists..

The issue becomes something that presents an abstract with the indecision of the word, "If"..

In many circles it is of a belief that there are no Athiests in the Foxhole when the enemy is upon you..

Is A>B? A is not defined. What sentence is being referenced..

The question should have asked,,

Prove the existance of G-d..

and you cannot.. But, that power does exist...

[Guest]

my brain can't picture how a sentence like "if this sentence is true, then God exists" can be true or false, if the sentence doesn't refers to another sentence. I think that's why it's a paradox... hahaha

The question should have asked,,

Prove the existance of G-d..

Both of these responses point to what I'd call "practical" flaws in the logic. Probably the most respected philosopher of the 20th century, Ludwig Wittgenstein, said that philosophy "puts everything before us, and neither explains nor deduces anything".

Curry's Paradox allows the addition of any random, arbitray bit of information to the set of true facts. Inductive reasoning (which in itself is rooted in the paradox that it requires induction to demonstrate that it works), tells us that arbitrary random information is not to be accepted without other corroborating evidence. Therefore we are still obligated to provide *additional* evidence that God exists before we can accept it as a fact.

[Guest]

I'm always amused when sentences are expected to support themselves like this. There is nothing that can be called true or false in the sentence to begin with. Its just an algorithm. "If this sentence is true, then God exists." There is no solid matter in the sentence to be disputed as true or false. It just causes infinite regression.

[Guest]

There doesn't even appear to be infinite regression. It's just an incomplete test is all. Another example; If N is true, then God exists.

However you might be able to force the issue with; If this sentence is a sentence, then God exists. And then we would get into a discussion about what opinions are.

If you want to prove that anything exists, just look into the Better Logic Paradox. (Nothing is better than God. N is better than nothing. Thus N is better than God.)

[Guest]

There doesn't even appear to be infinite regression. It's just an incomplete test is all. Another example; If N is true, then God exists.

However you might be able to force the issue with; If this sentence is a sentence, then God exists. And then we would get into a discussion about what opinions are.

If you want to prove that anything exists, just look into the Better Logic Paradox. (Nothing is better than God. N is better than nothing. Thus N is better than God.)

In the Better Logic Puzzle however, nothing is employed with two usages. "Nothing is better than God" - states that there is not a thing better than God. Whereas "N is better than nothing" - states that N is better than a lack of anything.

The infinite regression comes in when you replace the "this sentence" portion with the actual sentence.

"If this sentence is true, then God exists." >>> "If [if this sentence is true, God exists] is true, then God exists." and so on.

[Guest]

personally i don't see any difference between:

if this sentence is true, then God exists.

and

if 4*6 = 24, then God exists.

what does the existence of God have to do with multiplication?

what does the existence of God have to do with the truth-hood of that sentence?

in both cases absolutely nothing.

we can all agree 4*6 is 24, we can all agree that "this sentence is true" is a true statement, but neither one logically leads to the conclusion.

[Guest]

basically i would propose a new law of logic to handle this paradox.

A -> B

A -> ~B

-----------

A -/-> (B v ~B)

if 6*4 = 24, then God exists

if 6*4 = 24, then God does not exist

both are logically true statements, therefore 6*4 = 24 does not imply the existence or non-existence of God.

[Guest]

Simplicity, simplicity, simplicity.

There is no paradox here.

The effort attempts to complicate the thought that is a play on words.

If this sentence is True, then G-d exists..

The issue becomes something that presents an abstract with the indecision of the word, "If"..

In many circles it is of a belief that there are no Athiests in the Foxhole when the enemy is upon you..

Is A>B? A is not defined. What sentence is being referenced..

The question should have asked,,

Prove the existance of G-d..

and you cannot.. But, that power does exist...

It is indeed a paradox. It is in the form of Curry's paradox. Curry's paradox is a paradox that allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently logical deduction rules.

[Guest]

If you ask me, "Curry's Paradox" isn't a paradox at all, it's just a logical mismatch.

"If this sentence is true, then god exists" does not actually suggest anything that could be defined as true or false. "then god exists" is not claiming anything, because it is solely dependent on the illogical first part of the sentence.

You might as well ask the question like this:

"If this sentence is purple, then god exists"

The sentence does not have a color.

There is a logical mismatch in the "if" part of the statement, and as a result the "then" part of the if/then statement is irrelevant.

Edited January 22, 2010 by Accipter

[Guest]

Simple answer.

An argument can be logical and the conclusion follow from the premises, but that does not mean that the premises are true.

[Guest]

Impossible to discuss, as it is said to be the "end of discussion", therefore, by that logic, all of these preceding statements are rendered invalid.