Premises.
1. There exists an entity, G, that is omniscient.
2. If an entity is omniscient, the entity is sound (if the entity believes something, it is in fact true).
3. If an entity is omniscient, the entity is complete (if something is in fact true, the entity believes it).
4. The sentence S is defined as "G does not believe S is true"
Argument.
5. G is sound (1, 2)
6. G is complete (1, 3)
7. >> Assume S is true (Assumption)
8. >> G believes S is true (6, 7)
9. >> G does not believe S is true (4, 7)
10. >> Contradiction (9)
11. S is not true (Reductio from 7-10)
12. G does not believe S is true (5, 11, Modus Tollens)
13. G believes S is true (4, 11)
14. Contradiction (13)
Conclusion.
One of the premises is incorrect. Since 2, 3 are obvious, and 4 is just a definition, 1 must be incorrect. Thus, an omniscient God does not exist.
>>7459163
This is a very shitty argument.
Oh and this sentence is not true.
>>7459173
Thank you for your well-reasoned argument!
Anon, you can't really explain God. You just have to believe.
>>7459175
You never said if the entity doesn't believe in something then that makes it false.
And this assumes God can only be defined as an omniscient being and not the Creator of Truth itself.
>>7459163
Assuming an all powerful God implies he cannot be within our existence, as that would put him under the constraints of logic and mathematics, but that does not mean he can not be outside or inside 'all of it'.
>>7459188
It follows from 2 and modus tollens. Here's a proof.
Premises.
1. If P, then Q
2. Q is false
Argument.
3. >> Assume P
4. >> Q (1, 3)
5. >> not Q (reiterating 2)
6. >> Contradiction
7. not P (Reductio from 3-6)
What do you mean by Creator of Truth?
>>7459200
No. 13 doesn't necessarily follow from 12.
If there exists a being that created Truth, then whatever it exists outside the scope of Truth itself.
>>7459209
I mean 12 from 11
>>7459209
Okay, so then what does omniscient even mean?
>>7459220
Problem is there are states distinct from "believe" and "not believe". If S is not true, then G can be in another state, such as neutrality or doubt.
Omniscient means to be All-Knowing but religions define God as more than just omniscient.
Your argument is against G, which would be defined by a Christian/Jew/Muslim as an omniscient being created by the Abrahamic God.
>>7459244
How could an all-knowing being be in neutrality or doubt over the truth of a statement?
Can you more clearly define all knowing?
>>7459259
You defined omniscience as being sound and complete. Under your definition, those states can still exist.
I guess because there are things that aren't true or false but a mixture of both.
>>7459259
And once again, a traditional religious person would consider God as not subject to Truth but to be the Definer of Truth itself.
>>7459265
Like what?
For example, take the statement "Chocolate ice cream tastes good"
This statement is either true or false given a complete definition of good. For example, it's true if I define good as 'stimulates 90% of the populations' taste buds to release some number of milligrams of some hormone'. Then, the statement is either true or false.
>>7459268
I asked before what it means to define truth.
>>7459259
Or like with future contingents.
>>7459272
Define God as the Creator of everything. It follows that God creates everything including "Truth". Define God as apart from His creation and not subject to its laws. Thus, God is not subject to Truth.
>>7459278
If you want to say you can define God however you want to combat logical arguments, yeah that's the point and you did that as well. That's why reason cannot answer everything alone.
>>7459278
So do you also disagree with ontological arguments, first mover arguments, etc., and believe solely on faith without appealing to logic at all?
>>7459292
I don't really have a set opinion on the existence of a god or not
>>7459295
All right then. I agree if you define God such that you can't say anything about God with any deductive certainty, this argument fails.
>>7459317
Yeah but your insistence on bivalence for S and G's reaction towards S if S is not true also hurts the argument.
If you're more interested in faith vs. reason stuff with God, I recommend al-Ghazali and Kierkegaard.
>>7459323
Can you give me an example of a sentence that, when sufficiently defined, is neither true nor false?
>>7459333
Any future contingent or statements about objects that are too vague to be defined.
>>7459163
I see an obvious problem with this argument, and it looks like >>7459173 was trying to point it out.
The issue is that S is a paradoxical statement. Given your premises, there is no difference between saying "God does not believe S is true" and "S is false." And since "S is false" is the definition of S, what S really means is "This statement is false."
Obviously, "This statement is false", when applied to itself, is paradoxical. It's like saying "This statement is a lie." If the statement is a lie, it is true, but if it's true, it can't be a lie.
The reality is that, in both cases, the statement is neither true nor false: it's paradoxical. Thus, among other things, 7. is impossible. We can't assume a paradoxical statement is true. And because S is paradoxical, it would seem that the problem in your argument lies in 4. not 1.
Or have I missed something?
So god's omniscience can't be deduced from his own omniscience, thanks Kurt.
This isn't a very interesting argument outside of formal axiomatic systems unless you grossly misinterpret the conclusion.
