Justification and the growth of error

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. Keyword Justification Growth of error Internalism Externalism Connection thesis Consulting experts Reliability Proof-checking Reliability-checking Double-checking Evidence Gap-free proof Total probability It is widely accepted that in fallible reasoning potential error necessarily increases with every additional step, whether inferences or premises, because it grows in the same way that the probability of a lengthening conjunction shrinks. As it stands, this is disappointing but not unintuitive. However, consulting an expert, proof-checking, filling gaps in proofs, and gathering more evidence for a given conclusion also add more steps, and we think these actions have the potential to improve our reliability or justifiedness. Thus, the received wisdom about the growth of error implies a skepticism about the possibility of improving our reliability through effort. Paradoxically, and even more implausibly, taking steps to decrease your potential error necessarily increases it. I will argue that the self-help steps listed here are of a S. Roush (&) Department of Philosophy, University of California, Berkeley, CA, USA e-mail: [email protected] 123 Philos Stud DOI 10.1007/s11098-012-9967-7 Author's personal copy