sodium

Actually, it does make more sense that way. But this doesn't avoid the problem with the Book of Truth. I don't really consider it a paradox, though.

To Witt,
I don't think I disagree with any of your points, but they do not affect my argument.

Witt

sodium:

Here's a kind of curious argument against God's existence. I'm not sure I buy it myself, but it is kind of interesting. It starts on the assumption that there is an omniscient being we'll call God, and then shows that this leads to a contradiction.

Consider the following statement.

God knows that this statement is false.

Now, what is God's opinion of that statement? If he decides that it is true, then he has obviously made an error, because the statement says that he knows it is false. If he decides that it is false, and he is correct, then he knows it to be false, but then the statement is true, so he is in error. God cannot be in error, because he is omniscient.
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Yes, the contradiction follows from the erroneous assumption that 'God knows that this statement is false' has truth or falsity.
Your argument shows that this cannot be the case.

IMO:

A sentence is an expression of subject-predicate form.

A proposition is a sentence that is purported to be true or false.

It is not the case that all sentences are propositions.

Some sentences are not meaningful, i.e. they do not have the quality of truth nor of falsity.

None of the following have truth or falsity:

God knows that this statement is false.
God believes that this statement is false.
God knows that this statement is true.
God believes that this statement is true.

They are sentences but they are not propositions.
Logic does not apply to them at all.

Propositions are described sentences which do have truth or falsity.

Just as in objects or classes, some described sentences do not refer.

Godel's incompleteness theorem demonstrates that there cannot be a system (your book of truths) that contains all truths, i.e. there is no absolute truth system.

sodium:
Russell wrote "This statement is false" in his essay.

Since you can't successfully assign a level to "This statement is false", it follows that you can't assign a level to the larger statement, and so it must too be meaningless.
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Not so, "This statement is false" refers to the sentence and not to the assumed proposition: This statement is false, is true.

A confusion of name and what is named, I think.

Witt

sodium

To Witt,

Well, I don't follow your argument, if in fact you have presented one. But I don't see the meaninglessness defence to be effective.

To avoid the problem of arbitrary statements being declared meaningless, I'll define a couple of new terms. Let's say that if we have a sentence, and we understand that sentence, and it makes statements about the world that are consistent with reality, then that statement is Struthish. Sentences that we understand, but say things that conflict with how the world really is are Sfalseish.

Now, let's forget about whether sentences are meaningful, and whether they are true or false. I'm only interested in whether they can be successfully assigned values of Struthish or Sfalseish, whether you consider the statement "meaningful" or not.

Now, we'll amend my original proposal to:

God believes this statement is Sfalseish (using my definition of the terms).

So, my argument can continue as normal, without worrying that certain propositions may be meaningless, for unspecified reasons.

azidhak

The 18th century Danish-Norwegian playwright and author Ludvig Holberg mocked the overzealous use of logic and the gullabillity of the common people in his comedy "Erasmus Montanus". Rasmus Berg (latinized as Erasmus Montanus) have returned to his home after being on latin school in the city. Here's an example from the play where he impresses his mom (mor 'Nille) with his impeccable (not!) logic: "A stone cannot fly, ma 'Nille cannot fly, ergo ma 'Nille is a stone" Ma 'Nille becomes horribly frightened and act as if Erasmus have casted a spell on her. Erasmus calms her and tells her "a stone cannot talk or think" and then everything is suddenly ok.
Haakon