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Proving a Negative? Or Not?

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We know that the onus of proof is on the one making a positive claim. For example, someone claiming "X exists" must back up that assertion with evidence and reasoning. It's not anyone's responsibility to prove the negative "It is not the case that X exists."

But, what if I state "X does not exist"? Is that a positive assertion which I must defend? Or is it no different than "It is not the case that X exists" as the negative of "X exists," even if the latter has not been asserted?

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But, what if I state "X does not exist"? Is that a positive assertion which I must defend?

Yes.

Or is it no different than "It is not the case that X exists" as the negative of "X exists," even if the latter has not been asserted?

The state of knowledge without any assertion being proven (or having other relevant evidence) is "I have no information about whether X exists", not "It is not the case that X exists".

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But, what if I state "X does not exist"? Is that a positive assertion which I must defend?

Yes.

Or is it no different than "It is not the case that X exists" as the negative of "X exists," even if the latter has not been asserted?

The state of knowledge without any assertion being proven (or having other relevant evidence) is "I have no information about whether X exists", not "It is not the case that X exists".

"I have no information ..." isn't the same as not being provided information by someone making a claim. If he doesn't provide evidence, then cognitively it is as if nothing had been asserted. If he tries to make a case for it, then that must be considered and rebutted (which is often easily done given what is passed off as evidence these days) before rejecting the conclusion as unsubstantiated.

If you don't know anything about it you can still say "I have no information ...", but that is not the same thing as rejecting an assertion made with no evidence provided (and of course is still not the same as the positive statement of saying it is wrong). If you do consider his evidence and it doesn't support his conclusion, then you are back to the state in which cognitively it is as if nothing had been said. If you don't consider it, then that still doesn't justify saying it is wrong, but you have to decide (if it is importantant enough for some reason to matter) whether there are grounds on which to consider it a legitimate hypotheses.

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We know that the onus of proof is on the one making a positive claim. For example, someone claiming "X exists" must back up that assertion with evidence and reasoning. It's not anyone's responsibility to prove the negative "It is not the case that X exists."

But, what if I state "X does not exist"? Is that a positive assertion which I must defend? Or is it no different than "It is not the case that X exists" as the negative of "X exists," even if the latter has not been asserted?

In logic, a positive statement can take the form of "S is P" or "S is non-P" while a negative statement has the form of "S is not P". So your statement is negative in form. One must consider the context in which you are making your statement to make sure it is an accurate assertion of your meaning. Are you making the assertion against what someone else is arguing or are you beginning an argument with your assertion? If the latter, then the appropriate form should be "X is non-existent" which is a positive statement. And you would need to offer evidence. For example, if you asserted "Gravity does not exist" that may be negative grammatically, but you are logically saying "gravity is non-existent," a positive statement for which you'd need to offer proof because there is ample evidence for gravity. On the other hand, after hearing an argument about God, and you concluded that "God is not an existent" because there is no evidence for it, then you do not need to offer evidence.

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We know that the onus of proof is on the one making a positive claim. For example, someone claiming "X exists" must back up that assertion with evidence and reasoning. It's not anyone's responsibility to prove the negative "It is not the case that X exists."

But, what if I state "X does not exist"? Is that a positive assertion which I must defend? Or is it no different than "It is not the case that X exists" as the negative of "X exists," even if the latter has not been asserted?

In logic, a positive statement can take the form of "S is P" or "S is non-P" while a negative statement has the form of "S is not P". So your statement is negative in form. One must consider the context in which you are making your statement to make sure it is an accurate assertion of your meaning. Are you making the assertion against what someone else is arguing or are you beginning an argument with your assertion? If the latter, then the appropriate form should be "X is non-existent" which is a positive statement. And you would need to offer evidence. For example, if you asserted "Gravity does not exist" that may be negative grammatically, but you are logically saying "gravity is non-existent," a positive statement for which you'd need to offer proof because there is ample evidence for gravity. On the other hand, after hearing an argument about God, and you concluded that "God is not an existent" because there is no evidence for it, then you do not need to offer evidence.

Rejecting a statement without evidence as if cognitively it had never been asserted is not the same thing as stating it is false. "God is not an existent" is an epistemologically positive statement even though it is a grammatical negative -- it means there is no God. What you do with rejecting assertions claiming the existence of god depends on what it is meant be. If it contradicts what you do know -- as in rejecting identity through claims of omniscience, i.e., unlimited knowledge about the past, present, and future, etc. -- then you can conclude it is false. If it does not contradict what you know, then you can only say that you reject it as a cognitively useless assertion of no consequence because there is no evidence for it. Most such assertions are so vague as to be meaningless non-assertions to begin with, which is worse than saying something definitive without evidence because there is nothing to even consider.

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