Some skeptics do not adhere to critical thinking as consistently as they should. In my experience, atheistic skeptics exhibit this lack of consistency the most. Critical thinking is not a commendable heuristic if it gets abandoned whenever it inconveniences a pre-existing bias. Rather, critical thinking ought reshape one's bias, not be tossed out when it threatens one's bias.
For example, a skeptic who adheres to critical thinking consistently (Smith) would refuse to accept some proposition P if there is inadequate epistemic warrant for it. Now, one who does not adhere to critical thinking consistently (Jones) would likewise refuse to accept P at first. Where the inconsistency in critical thinking arises is when Jones takes it a step further and asserts that because P has not been proven true it is consequently false.
This is made more obvious where P stands for "gods exist." It is consistent with critical thinking for Jones to reject P if for him there has been inadequate epistemic warrant for it. However, Jones promptly abandons critical thinking if he asserts that P ("gods exist") is false because it has not been proven true; that is a logical fallacy, argumentum ad ignorantiam. And he further contradicts critical thinking if he also affirms that a lack of evidence for P is somehow itself evidence for ¬P ("gods do not exist"). An absence of evidence is an empty set; 'nothing' in support of P is still 'nothing' when used as an attempt to support ¬P.
Smith is the consistent skeptic when he refuses to affirm that P is true but also refuses to affirm that P is false. It may be false. Or it may be true. The lack of adequate warrant either way means he cannot affirm either; Smith remains agnostic on the question. Jones, in order to be consistent with critical thinking, must do the same. If what Jones wants to affirm is that P is false, critical thinking dictates that he must provide evidence that either (a) supports ¬P or (b) invalidates P.
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