Hawking Comes Clean

Not requiring a god does not imply that no god exists. The only thing it implies is exactly what it says: if a god does exist, it is not necessary to the universe functioning as normal. If the god does not exist, then we wouldn't notice the difference.There is a marked difference between "necessary" and "exists".
So, nec( = necessary, pos( = possible, not( = negation of. I would use the standard box and diamond and tipped-over L, but they don't work.

1. nec(A) ==> not(pos(not(A): A exists/is true in all possible worlds. This can be demonstrated by assuming A does not exist nd then using RAA to derive a contradiction to show that A cannot not exist/be true.
2. nec(not(A) ==> not(pos(not(not(A): there is no world in which A exists/is true. This can be demonstrated by assuming A exists and then using RAA to derive a contradiction to show that A cannot exist/be true.
3. not(nec(A) ==> not(not(pos(A) ==> pos(A).
4. not(nec(not(A) ==> not(not(pos(not(not(A) ==> pos(not(not(A).

From the third syllogism, there is possible world in which A exists/is true.
From the fourth syllogism, there is a possible world in which not(not(A), therefore there is a possible world in which A exists/is true.
So, if it is not necessary that something does not exist, it is possible that it does. Which follows from the definition, but the above demonstrates it logically.Hence, Hawkings is not and cannot imply that God does not exist simply by saying that God is not necessary. He would have to state that God necesarily does not exist to imply that God does not exist, and by that stage you're getting into gnostic atheism and a whole lot of ugly theology.{abe: how does one insert symbols? I tried copy-pasting the logical necessity box; didn't work.}
{abe: does that notation above make any sense whatsoever? I did try.}Edited by Nij, : As per ABEs.

Agreed. There is. My statement was probably errant, now that you point out the distinction in clear terms.

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Now I'd like to pick on this: If the atheist position is that the universe and its laws are all that exist, and the theist position is that the universe and its laws exist in addition to God -- these are generalised positions because it's simpler to discuss that way -- then the atheist position is necessarily simpler: it uses fewer entities in its explanation of the universe.To say that the inclusion of God in an explanation of the universe is simpler, when you already have the laws and properties known, seems quite contrary to the idea of "simpler" in all senses of the word.
For example, which of the sets {Newton's laws of motion} and {Newton's laws of motion, God} is simpler? Does one explain more about the functioning of the universe than the other?As it happens, let us revise the original statement:
"The only thing it implies is exactly what it says: if a god does exist, it is not necessary to our explanation of the universe functioning as we normally do. If the god does not exist, then we wouldn't notice the difference in our explanations."Which is more accurate and more in line with both our reasoning, I think.