Justification and the growth of error
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It is widely thought that in fallible reasoning potential error necessarily increases with every additional step, whether inferences or premises, in the same way that the probability of a lengthening conjunction shrinks. However, this has the absurd consequence that consulting an expert, proof-checking, filling gaps in proofs, and gathering more evidence for a given conclusion necessarily make us worse off, since they also add more steps. I will argue that the self-help steps listed here are of a distinctive type, involving composition rather than conjunction. Error grows differently over composition than over conjunction, I argue, and this dissolves the apparent paradox.
KeywordJustification Growth of error Internalism Externalism Connection thesis Consulting experts Reliability Proof-checking Reliability-checking Double-checking Evidence Gap-free proof Total probability
This study was supported in large part by NSF grant SES-0823418.
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