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To know absolutely that there is no God one must have infinite knowledge. But to have infinite knowledge one would have to be God. it is impossible to be God and an atheist at the same time. Atheists cannot prove that God doesn't exist.

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    1) How do you define God? 2) Does it really require infinite knowledge to know that God does not exist? 3) How do you know God has infinite knowledge? I can't name the fallacy off the top of my head, but these are some of the flaws in your argument. – David Blomstrom Dec 30 '18 at 7:14
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    To know absolutely that X one would have to be God. Therefore, people know nothing absolutely. This seems to have nothing to do with atheists in particular. We do not know absolutely even that the Sun will rise tomorrow, or 1+1=2, but they are beyond reasonable doubt. The problem is with the wrong standard of knowledge and proof, which is irrelevant to the issues discussed by humans. – Conifold Dec 30 '18 at 7:58
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Because it is necessary to have infinite knowledge in order to be God - a premise granted for the sake of argument - it does not follow that to have infinite knowledge is sufficient to be God. God is generally credited with other attributes unconnected with infinite knowledge - omnipotence and omnibenevolence, for example.

This appears to be a form of affirming the consequent : If p then q, q therefore p. In terms of the example, if X is God then God has infinite knowledge; Y has infinite knowledge; therefore Y = X = God.

Also if the concept of God should prove to be demonstrably incoherent or self-contradictory, which is a logical possibility, one would not need infinite knowledge in order to demonstrate that God does not exist. It would be sufficient to deduce that, qua incoherent or self-contradictory, the concept of God cannot be instantiated.

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P1: To know absolutely that there is no God one must have infinite knowledge.

P2: But to have infinite knowledge one would have to be God.

P3: It is impossible to be God and an atheist at the same time.

C: Atheists cannot prove that God doesn't exist.

Comments:

Argument from ignorance at C due to circular reasoning (between P1 and P2) and contradiction (between C and P3):

  1. Contradiction between C and P3: an atheist, who is a god, and cannot prove or disprove itself a god, would not be a god, and thus counters C, proving god doesn't exist, which makes C false.

  2. Argument from ignorance at C: true because it has not been proven false from P1 and P2- even god cannot prove god doesn't exist as infinite knowledge would still lack contrary evidence.

  3. Defining what "God" and "infinite" means would be helpful too since these are vague terms. We shall assume god is a solely an entity that has all knowledge.

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