Negative proof fallacy:

Formal Fallacy
Definition Example
When it is claimed or implied that, because a premise cannot be proven false, the premise must be true, or that, because a premise cannot be proven true, the premise must be false. Can you prove I’m not wearing an invisible hat? If you can’t, I’m justified in believing I am.
  Notes
The degree of warrant for a given proposition is the balance of evidence that favors that proposition, not the absence of evidence that would falsify the proposition. The ability to say “You can’t prove I’m not right” does not mean you are warranted in believing you are right.


Note that there are cases in which you can logically prove a negative by demonstrating logical incoherence in a concept. A married bachelor is an example of such a concept.

Case Study One

If someone claims that global warming is due to human activity, then justifies their position by saying “You can’t prove human activity is not the cause of global warming”, they have committed this fallacy.


Case Study Two

In the U.S., until someone accused of a crime has been found guilty based on sufficient evidence, they are legally presumed innocent. This does not mean they are innocent of the crime. It is just that the legal institutions start with the assumption that they are innocent until (if ever) sufficient evidence warrants judging them guilty. This is artificially binary. As individuals, we rationally reposition our degree of belief as the arrival of new confirming/disconfirming evidence arrives.


Keep in mind that a fallacious argument does not entail an erroneous position.


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