I just read this interesting article. Here's what is says:

quote:

Define the adjectives "autological" and "heterological" as follows:

A word is autological if and only if it describes itself. For example "short" is autological, since the word "short" is short. "Sophisticated" and "polysyllabic" are also autological.

A word is heterological if and only if it does not describe itself. Hence "long" is a heterological word, as is "monosyllabic".
Since autological and heterological are opposites, all words are members of either the set of "autological" words, or the set of "heterological" words.

The paradox is this: is the word "heterological" heterological? There is no consistent answer: if it is, then it isn't; if it isn't, then it is.

If "heterological" is heterological, as "heterological" is by definition an autological word, it is thus not heterological. If not, then "heterological" has the property it designates and therefore it is heterological. Hence, "heterological" is heterological if and only if it is not heterological.

This got me thinking.

Define God as all-powerful.

God could not create something that he could not lift. However, if God can't create something, He isn't all-powerful. Hence, "God" is all-powerful only if He is not all-powerful.

Likewise, we could define God as all-good and all-powerful. A perfectly good being could not create a world in which suffering happens and still be all-good. However, if God can't create something, He isn't all-powerful. Therefore, "God" is all-powerful and all-good only if He is not all-powerful and all-good. ("God" is God only if He is not God).

This has always been one of the strongest arguments for me that God doesn't exist. This is a clear contradiction. God doesn't fit the definition of God, so He must not exist. However, we would not make the same statement about heterologies. If a "heterology" exists despite the fact that a heterology cannot be defined as either a heterology or not a heterology, couldn't a "God" exist despite the fact that a God cannot be defined as either a God or not a God?

I recognize that this doesn't prove that God does exist, but I think it puts serious doubt into the strongest arguments I know of against God's existence. The fact that something is a paradox doesn't make it untrue, as the heterological paradox demonstrates.

What is your reaction to this comparison of the two ideas?

I don't really think there is a strogest argument for non-existence for God. There seems to just be lots of little odd things. The lack of solid evidence, such as his great goodness, is one of them.

I'm currently taking a philosophy of religion class and we've been reading about various arguments for the existence of evil and the imperfect world. For example, St. Augustine who says we are intentionally made imperfect so that we contribute to the beauty of the universe. So there may be bad in the world, but in God's eyes, it's actually good in the end. And since it's good as a whole, God is still being all-good. This certainly seems like a very reasonable argument, assuming a God existed, and I see no reason to not think it were true if God was real. I'd suggest reading a lot of these arguments and you might actually break down that little argument that seems to be holding you back. Should I let you know about some of the people who have these arguments in my book? Or maybe the name of my book?

Ok, I've been thinking about this very interesting idea. I think I've figured it out. The word heterological exists because its existence still makes sense. It's a logical paradox. The paradox of this word is only significant within the word itself. It has no other consequence in any of the other heterologies, any other words, it doesn't weaken our language, our existence, or anything else except the concept of the word. This God paradox, however, can't exist because its existence would be impossible in this world. The God paradox is rooted in literally everything. The consequence of the paradox is in everything. If God actually existed, nothing would make sense given this paradox. It's an illogical paradox. And I can't think of any other reason for it being an illogical paradox except for because it simply has consequnce. If the word heterological somehow existed as more than a concept, I guess it would be in the same position as the idea of God. Very interesting, Sarai. Thanks.

God has sovereignty: He can do what He wants how He wants. Now, we can think that we know with certainty what God cannot do, for example, sin; however, the Bible gives instances in which we are informed that God caused destruction of lives. So how does God "get away with" being a hypocrite . . . so it seems. Well, God speaks the Word, and anything which He speaks occurs. Believe it or not, God also is the Word. In other words, God can project Himself in ways which humans deem contrary to His nature. Again, God has sovereignty, which is why He is to be feared, although He prefers to be loved, as He also projects as love.

Grelling's Paradox is the name attached to the "heterological" paradox involving non-self-describing adjectives. Similarly there is (Bertrand) Russel's Paradox, involving the set of all sets that do not contain themselves as members. Epimenides' Paradox is perhaps the most famous of this type, wherein a man from Crete declares, "All Cretins are liars." In essence it boils down to the ambiguous truth value of the statement, "This statement is false."

Douglas Hofstadter used such examples of self-referential paradoxes to lead into a discussion of Gödel's Undecidability Theorem, involving the existence of propositions in formal logical systems which can be neither proven true nor false. In essence, these difficulties can be circumvented only by "stepping out" of the system and viewing it from the outside at a higher level.

But I'm talking about math, not religion.

The God paradox I've most often heard can be summed up by asking why God doesn't banish evil. Either he can't or he won't. If he can't then he's not all-powerful; if he won't then he's not all-good. Either way it's un-godlike.

Does that constitute a disproof of God? Well, I think in an earlier era when science, religion philosophy, and logic were all rolled up into one intellectual tradition, the great thinkers commonly attempted such religious proofs or disproofs. But in a modern context it strikes me as quaintly irrelevant.

You either believe or you don't, and depending on your world view it's either inspired revelation or deep self-delusion. But I can't see how formal mathematical logic ultimately has any real bearing on religious questions.

quote:

Originally posted by Professor:
But in a modern context it strikes me as quaintly irrelevant.

You either believe or you don't, and depending on your world view it's either inspired revelation or deep self-delusion. But I can't see how formal mathematical logic ultimately has any real bearing on religious questions.

Why? I don't understand why it would be any less relevant today than it was in the past. Could you explain your reasoning further?

quote:

The God paradox I've most often heard can be summed up by asking why God doesn't banish evil. Either he can't or he won't. If he can't then he's not all-powerful; if he won't then he's not all-good. Either way it's un-godlike.

Some Jewish sages explained this by saying that God created evil in order for man to have free will, the opportunity to choose.

Well, I guess by "modern" I meant "scientific," which is generally taken to mean a philosophical approach to reality known as logical positivism, a Platonic concept that assumes that there is physical reality "out there" independent of our minds, which can be discovered and verified by all rational observers (bear with me -- I'm not a philosopher!).

This makes it impossible to prove a negative, and almost by definition puts supernatural or metaphysical phenomena out of reach of the scientific method, because if you have hard physical evidence of something, then it belongs to the natural world and is not supernatural.

For every "disproof" of God such as the one I repeated earlier, there are inevitably reubttals such a tsaeb's above. Outside the realm of physical observation, nobody is right and nobody is wrong.

Isaac Newton was the greatest scientist and philosopher of his day. He made huge strides in mathematics and physics. Yet he was more preoccupied with religion and alchemy than he was with what we would today call "science." In his day the distinction between physical reality and metaphysical intangibles was fuzzy at best. Today that distinction is important and usually clear to us.

Sarai, I'm afraid I'm not equipped to explain myself any better. I'll defer to others to rescue me.

No such need; what you wrote makes perfect sense.