Philosophical Studies

, Volume 165, Issue 2, pp 527–551 | Cite as

Justification and the growth of error

  • Sherrilyn Roush


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.


Justification 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.


  1. Detlefsen, Michael, & Luker, M. (1980). The four-color theorem and mathematical proof. The Journal of Philosophy, LXXVII, 803–820.CrossRefGoogle Scholar
  2. Garber, D. (1983). Old evidence and logical omniscience in bayesian confirmation theory. In J. Earman (Ed.), Testing scientific theories (Vol. X, pp. 99–131). Minneapolis: Minnesota Studies in the Philosophy of Science.Google Scholar
  3. Goldman, A. (2008). What is Justified Belief? In Epistemology: An anthology, 2nd edn. (pp. 333–347. Malden: Blackwell Publishing.Google Scholar
  4. Hacking, I. (1967). Slightly more realistic personal probability. Philosophy of Science, 34(4), 311–325.CrossRefGoogle Scholar
  5. Jeshion, R. (1998). Proof checking and knowledge by intellection. Philosophical Studies, 92, 85–112.CrossRefGoogle Scholar
  6. Kitcher, P. (1984). The nature of mathematical knowledge. Oxford: Oxford University Press.Google Scholar
  7. Resnik, M. D. (1989). Computation and mathematical empiricism. Philosophical Topics, XVII, 129–143.CrossRefGoogle Scholar
  8. Vogel, J. (2006). Externalism resisted. Philosophical Studies, 131, 729–742.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of CaliforniaBerkeleyUSA

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