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I'm able to tell this is an example of argumentum ad ignorantiam,

"I can't prove the existence of god, therefore, god doesn't exist."

But what about the sentence

"One should never claim that "God doesn't exist" because one cannot prove this nonexistence".

Is this an example of argumentum ad ignorantiam?

I personally think that it's not a case of argumentum ad ignorantiam because the sentence doesn't lead to any conclusion whether god exists or not. The sentence only shows an opinion (exposition?) of the fact of the author which is he never stated that statement simply because of his inability to prove so.

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The fallacy is more general than on the existence of God. –  Mechanical snail Feb 16 '13 at 0:04
    
yeah I know. I used the existence of god in my sample sentences simply because it was the examples that spontaneously popped into my mind. –  Coderama Feb 16 '13 at 2:47
    
As I understand it, it is impossible to PROVE that anything at all does NOT exist.. –  joe theengineer Feb 17 '13 at 9:16

2 Answers 2

up vote 6 down vote accepted

One should never claim that "God doesn't exist" because one cannot prove this nonexistence.

Is this an example of argumentum ad ignorantiam?

No, it's not an argumentum ad ignorantiam. It only says that one should never claim that God doesn't exist [with absolute certainty] because there is indeed no way to prove this nonexistence. One can make claims about the likelihood of the existence or nonexistence of God, but there is no way to disprove with absolute certainty that he doesn't exist. If someone said that he is absolutely, 100% certain that God does not exist, he would make a mistake, and that is all your quote says.

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No, it's not an argumentum ad ignorantiam.

The argumentum ad ignorantiam assume that since something has not been proven false, it is therefore true. Conversely, such an argument may assume that since something has not been proven true, it is therefore false. It assumes that all propositions must either be known to be true or known to be false. Lack of proof is not proof.

There are a few types of reasoning which resemble the fallacy of Appeal to Ignorance, and need to be distinguished from it:

The burden of proof is usually on a person making a new or improbable claim, and the presumption may be that such a claim is false. For instance, suppose that someone claims that the president was taken by flying saucer to another planet, but when challenged can supply no evidence of this unusual trip. It would not be an Appeal to Ignorance for you to reason that, since there is no evidence that the president visited another planet, therefore he probably didn't do so. Another example: Invisible Pink Unicorn's incarnation requires both that Invisible Pink Unicorn become human and that Invisible Pink Unicorn remain wholly other. There is no evidence of Invisible Pink Unicorn's incarnation, therefore he probably didn't do so.

When extensive investigation has been undertaken, it is often reasonable to infer that something is false based upon a lack of positive evidence for it:
If there really were a large and unusual type of animal in Loch Ness, then we would have undeniable evidence of it by now. We don't have undeniable evidence of a large, unfamiliar animal in Loch Ness. Therefore, there is no such animal.
Another example: If there really were Invisible Pink Unicorn, then humanity would have undeniable evidence of it by now. We don't have undeniable evidence of Invisible Pink Unicorn. Therefore, there is no Invisible Pink Unicorn.

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