E.G.

Our everyday methods of evaluating arguments make both foundationalist and coherentist chains of inference appear to be unsound.  In this post I’ll say a few things about the possible implications of this fact.

Chains of inference, like regular metal chains, come in only a few different shapes.  I think chains of inference must take one of the following two shapes:

1. Chains can be finite in length and non-circular.

2. Chains can be infinite in length and circular.

A chain of type 1 is a foundationalist chain: it begins with an original, non-inferred belief — a "foundational" belief — from which all subsequent beliefs in the chain are inferred.  A chain of type 2 is a coherentist chain: it does not involve any foundational beliefs, so all beliefs in the chain are inferred from (at least one) other belief(s) in the same chain. 

(A discussion of the reasons for limiting our options in this way can be found in more than one place, but here I am, I think, adhering pretty closely to the schematization given by Brink in his Moral Realism and the Foundations of Ethics, ch. 5.)

Suppose I say, "The gardener must already have mowed the lawn, because the grass is cut."  Then you ask me how I know the grass is cut, and I say, "Well, it must be cut, because the gardener has already mowed the lawn."  You’ll likely say: "But, that’s circular reasoning!" and take this to be a damning criticism of my argument.

Suppose, on another occasion, I again say, "The gardener must already have mowed the lawn, because the grass is cut."  Again you ask me how I know the grass is cut, but this time my answer is different.  I say, "Well, I just know it is cut.  I didn’t infer it from anything; it just came to me."  Once again, you’re not likely to accept my argument.  You’d be right, I think, if you said to me: "If you think you ‘just know’ it, you don’t know it at all."

In the first case, you reject my argument on the basis of what we might call the "anti-coherentist principle," according to which circular arguments are, because circular, unsound.  In the second case, you reject my argument on the basis of what we might call the "anti-foundationalist principle," according to which beliefs for which no inferential support can be given are unjustified — and therefore any argument proceeding from them is unsound.

If a chain of inference is circular, it falls under the purview of the anti-coherentist principle.  Yet if a chain of inference is not circular, it must originate in a non-inferred belief, and in that case it falls under the purview of the anti-foundationalist principle.  But all chains of inference are either circular or non-circular.  Thus, if we apply these two principles across the board, to every chain of inference, all chains of inference are unsound.  But this is nonsense; there obviously are sound chains of inference.  Thus, one or the other of these principles must be limited in scope: Either not all circular chains of inference are unsound, or not all non-circular chains of inference are unsound.

Still, I feel a tug of approximately equal force from both principles, and feel equally compelled to assent to their verdicts no matter which cases I examine.  For instance: Expanding the size of a circular chain of inference does not make its circularity any less bothersome to me — even if the chain becomes so large it includes all or almost all of a subject’s beliefs.  Likewise, neither the immediacy of certain especially cautious claims about sense-data, nor the apparent self-evidence of certain claims about logical or mathematical law, makes me any less wary if there is a lack of inferential support underlying such beliefs.

I see three ways to proceed:

1. Look more deeply; hope that upon further reflection, the tug I feel from one or the other of these principles will go away or at least diminish.

2. Ignore the principles’ tuggings.  Find reasons other than some "tug" to choose among theories of justification.

3. Accept the tugs.  Sigh.  Put head in hands.  Then leap from chair and announce: "Two equally demanding principles of reason have an equal hold upon me; yet when they are both applied to the totality of my system of inference, they make it look like nonsense.  So the totality of my system of inference is an illusion."

#3 would be going overboard.