Can Coherence Generate Warrant Ex Nihilo? Probability and the Logic of Concurring Witnesses

Most foundationalists allow that relations of coherence among antecedently justified beliefs can enhance their overall level of justification or warrant. In light of this, some coherentists ask the following question: if coherence can elevate the epistemic status of a set of beliefs, what prevents it from generating warrant entirely on its own? Why do we need the foundationalist’s basic beliefs? I address that question here, drawing lessons from an instructive series of attempts to reconstruct within the probability calculus the classical problem of independent witnesses who corroborate each other’s testimony. 1. Weak foundationalism and the coherence theory 2. Lewis versus BonJour 3. Hooper’s formula 4. Boole’s formula 5. Blitstein’s formula 6. Huemer’s formula 7. Olsson and Shogenji’s model 8. Keynes's formula 9. Taxicabs and miracles 10. Real coherence 11. An argument for moderate foundationalism 12. Another requirement of initial credibility 13. Conclusions Appendices A. A farrago of formulas B. Condorcet, Hume, Price, and Boole C. Three theorems on corroboration and confirmation D. Concurring witnesses and the principle of the common cause E. Assorted proofs 1. Weak foundationalism and the coherence theory Common to all versions of foundationalism is the thesis that there are basic beliefs— beliefs that have a degree of noninferential justification or warrant, warrant that does not derive from inferential relations to other beliefs. (Throughout this paper I use ‘warrant’ simply as a syllable-saving synonym for ‘justification’, not in Plantinga’s technical sense. 1) All other justified beliefs are justified in virtue of the inferential support they receive directly or indirectly from basic beliefs. Laurence BonJour distinguishes three grades of foundationalism (1985, 26-30). According to strong foundationalism, basic beliefs are "not just adequately justified, but also infallible, certain, indubitable, or incorrigible" (26-27). According to moderate foundationalism, the noninferential warrant possessed by basic beliefs need not amount to absolute certainty or any of the other privileged statuses just mentioned, but it must be “sufficient by itself to satisfy the adequate-justification condition for knowledge" (28). Finally, according to weak foundationalism, basic beliefs possess only a very low degree of epistemic justification on their own, a degree of justification insufficient by itself either to satisfy the adequate-justification condition for knowledge or to qualify them as acceptable justifying premises for further beliefs. Such beliefs are only "initially credible," rather than fully justified. (28) We must rely on coherence among such initially credible beliefs to amplify their level of warrant up to the point where it is adequate for knowledge. Views along these lines have been advocated by C.I. Lewis (1946), Bertrand Russell (1948), Nelson Goodman (1952), and Roderick Chisholm (1977), among others.2 1 According to Plantinga, warrant is “that, whatever precisely it is, which together with truth makes the difference between knowledge and mere true belief” (1993, 3). On many accounts, this will include not merely justification, but also whatever further condition is required to solve the Gettier problem. 2 Russell and Chisholm are not across-the-board weak foundationalists, for they hold that there are some basic beliefs (for example, beliefs about the current contents of sense experience) that are adequately 2