An argument is presented which shows that coherence theories of justification are committed to a conception of epistemic support which conflicts with an axiom of probability theory

Stoneham, Tom

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This is a repository copy of A reductio of coherentism.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/2524/Article:Stoneham, Tom orcid.org/0000-0001-5490-4927 (2007) A reductio of coherentism. Analysis. pp. 254-257. ISSN 0003-2638 https://doi.org/10.1111/j.1467-8284.2007.00683.xeprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. A reductio of coherentism  TOM STONEHAM  I put forward the following argument in the spirit of curiosity. On the face of it, the argument gives a conclusive reductio ad absurdum of any coherence theory of justification. But that cannot be right, can it?  (1) There are finite sets of beliefs such that each member of the set is epistemically supported by some other members (and nothing else). (Coherentism)  Comment: A belief b(p) is epistemically supported by the belief b(q) IFF b(p)’s justifiedness or reasonableness (for a subject at a time) consists in part in b(p) standing in some relation of dependence to b(q). Exactly what that dependence relation is will be a matter of debate amongst coherentists. While a coherentist will typically prefer to say that a belief is justified in virtue of it being a member of a coherent set of beliefs, it will be epistemically supported by individual members of the set precisely when the condition just stated is met.  (2) The relation of epistemic support is transitive. (Axiom)  Comment: The coherentist will probably want to allow exceptions to transitivity in order to prevent a belief epistemically supporting itself. Thus we might replace (2) with the weaker:  (2*) ∀xyz((x≠z & Exy & Eyz) → Exz).  (3) The relation of epistemic support is not asymmetric. (From 1 and 2 or 2*)  Reasoning: From (1), b1 is supported by b2 and b1≠b2, b2 is supported by b3 and b2≠b3, b3 is supported by b4 etc. Since the set is finite, for some i and j, bi=bj. Without loss of generality suppose there are only three beliefs and b1=b4. Then b3 is supported by b1. Since b1 is supported by b2 and b2 is supported by b3, by transitivity – or (2*) provided b1≠b3 – b1 is supported by b3. So the relation is not asymmetric.  (4) For some p and q and some thinker at some time, it is possible that the belief that p&q is better supported than the belief that p or the belief that q alone. (From 3)  Reasoning: From (3) it is possible that there is a subject with stock of beliefs S such that b(p) supports b(q) in the presence of S (iff b(p) has positive support) and b(q) supports b(p) in the presence of S (iff b(q) has positive support). Since, in the presence of S, b(p) supports b(q) and vice versa, S+b(p) provides more support for b(q) than S alone and S+b(q) provides more support for b(p) than S alone. Suppose a subject has S but not b(p) or b(q) and that S does not support b(p) or b(q) or b(~p) or b(~q). Then if the subject adds just b(p) or just b(q), he will be adding a belief with no support, but if he adds both he will be adding a belief (viz. b(p&q)) with positive support.  (5) The belief that p epistemically supports the belief that q only if p raises the probability of q. (Axiom)  (6) There is a pair of propositions such that pr(p&q) > pr(p). (From 4 and 5)  Reasoning: These probabilities are credences. Suppose our subject has belief set S and comes to consider p and q, then the credence of p is 0.5 but the credence of p&q is >0.5.  (7) pr(p&q) is always less than or equal to pr(q). (Theorem)  (8) So (1) is false. (RAA on 6 and 7)  Which premise can the coherentist reject? (1) is characteristic of her view. (2) is pretty much analytic. (5) might be a matter for debate, but it is hard to see how there could be counterexamples, and if it is weakened to:  (5*) The belief that p epistemically supports the belief that q only if p does not lower the probability of q,  a great deal more would need to be said to explain why epistemic support is a truth-conducive property. How can p give us any reason to believe q is true if the truth of p does not make q any more likely? Finally, (7) is a theorem of probability theory and, while it may not be much respected in intuitive judgements of probability, no theorist can deny it.  The coherentist might try to reject the inference from (3) to (4). She might question whether a belief set which provided no support at all for b(p) and b(q) could be one in the presence of which b(p) supports b(q) and vice versa. But the reasoning only assumed that S provided no support for b(p) and b(q) to simplify its expression – the only assumption we really needed was that S+b(p) provides more support for b(q) than S alone and S+b(q) provides more support for b(p) than S alone. And that must be the case for any S in the presence of which b(p) supports b(q) and vice versa.   She might also question the inference from (4) and (5) to (6): prior to believing p and q, pr(p)=0.5 and pr(q)=0.5 so pr(p&q)≤0.5, but once she comes to have both those beliefs the probability of each rises and thus pr(p&q) becomes >0.5. Thus the objection is that the inference from (4) confuses epistemic support at a time for something one does not yet believe with the support it will have when one later comes to believe it. So while pr(p&q) at t2 > pr(p) at t1, there is no time at which pr(p&q)>pr(p).  But while we should accept this general distinction, it only makes a difference when there is some other change in the subject's beliefs by the time she comes to believe the proposition in question. Since the only reason why the pr(p&q) is greater after the subject comes to believe p and q can be that she now believes that very proposition, the inference from (4) would only be incorrect if the mere fact that I believe something can make it more reasonable for me to believe it, which is not in general true.  The negation of (1) is:  For any finite set of beliefs all of which have some positive degree of epistemic support, at least one member of that set does not receive its support entirely from the other members of the set.  Which, pace infinitism, is a pretty good definition of foundationalism. Q.E.D.  University of York,  York, YO10 5DD, UK twcs1@york.ac.uk 

A reductio of coherentism

Tom Stoneham

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A reductio of coherentism

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