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I have a friend who said "I have a false belief that I might be able to do [some activity]." When I asked her to clarify this statement, she said, "I believe I can do it, but I also believe that I'm wrong about that."

Is this even possible? Is there an epistemological theory which addresses these kinds of thoughts? To me, it seems self-contradictory when we formulate them strictly as follows:

  • I believe I can run three miles.
  • I believe that my belief that I can run three miles is false.

The latter seems to encapsulate the first and invalidate it -- but this is only my intuition. At the same time, there seems to be some kind of "layering" of cognition which might make this plausible. I don't remember reading any papers or texts that addressed a situation like this. Is there any?

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    I think some context might clarify the nature of this apparent paradox. Did your friend indicate somehow how the "false" belief applies (counts as a belief) or why they indicate (as opposed to actually believing) that it is false? – Niel de Beaudrap Mar 30 '13 at 20:48
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    Related (maybe duplicate?): Can one choose to believe a claim that one rationally agrees to be false? and my answer. – DBK Mar 31 '13 at 8:20
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    You can have a feeling that something is true, as well as a rational belief that this feeling is false. An arachnophobe might feel spiders are terrifying while rationally accepting that they're harmless. – Jack M Mar 31 '13 at 23:49
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Yes, it is self-contradictory in a similar way as Moore's Paradox. (In fact, one might consider it merely a variant of Moore's Paradox by applying some disquotation principle to the latter.)

However, you should be aware that some philosophers, A.I. researchers, and psychologists consider human beliefs to be compartmentalized, allowing for contradicting beliefs as long as they do not manifest themselves directly in action conflicts. More radical thinkers would say that human belief systems are irrational anyway and the whole idea of 'rational belief' is a chimera. I personally think that there is not just one notion of belief but many, that our everyday notions are not very sharp with respect to boundary cases, and that you need to pick whichever notion is fruitful for philosophical theorizing in a given theoretical context.

Regarding the layers: This has been discussed as well. In 'standard' epistemic logic such as KD45 you have axioms for positive introspection - if you believe that p then you believe that you believe that p - and negative introspection - if you don't believe that p then you believe that you don't believe that p. If these principles don't hold you get a layering.

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In order to resolve the paradox one could rephrase the statement into something trivial:

  • I believe that I either can run three miles or I cannot run three miles.

One of those thing will be true so the statement is always true. Yet is says nothing about the actual ability. Trivial sentences say nothing.

So as a different approach, let us look at the term believe. It is often used to convey an assumption. So the statement might as well be:

  • I assume I can run three miles. I am not sure though and could be wrong. I would have to test it first.

So it becomes clear that the person does not both believe both p and NOT p. He also does not state something trivial, as it conveys a self-assessment. One could question the reason for the self-assessment in order to determine how valid it is. It is nonetheless a useful statement for us humans and we use this approach in our everyday life a lot in order to deal with uncertainties.

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