Abstract
A paradox is presented that the poses new problems for both the truth norm and the knowledge norm of belief.
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Notes
Cf. ‘a belief is correct if and only if the proposition believed is true’ (Wedgwood 2002:267). ‘that truth is the standard of correctness for belief … is expressed in the prescription to believe that p only if p is true’ (Shah 2003:448). The most recent example I know: ‘More generally, true beliefs are correct or right, false beliefs are incorrect or wrong’ (Whiting 2013b:121).
e.g. walking is required iff it is not permissible not to walk.
e.g. walking is required iff it is forbidden not to walk.
e.g. walking is permitted iff it is not forbidden to walk.
Such competent deduction retaining knowledge throughout fits Hawthorne’s Single-Premise Closure principle, see Hawthorne (2004:34).
By my counting there are 4 undischarged premisses: two logical truths, factivity for knowledge and the knowledge norm. For discussion of multi-premiss closure see Hawthorne (2004:46) ff.
Note that we have two separate proofs for two separate contradictions, which proofs happen to have parts in common. It is, of course, also true that from each of these contradictions we can derive the other.
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Shackel, N. The Nought Belief Paradox. Erkenn 79, 523–529 (2014). https://doi.org/10.1007/s10670-013-9521-9
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DOI: https://doi.org/10.1007/s10670-013-9521-9