This post is inspired by a fun thread from Michael Bench-Capon:
This is a nice question. In Problems (pages 191-192 in this edition from Archive.org) Russell gives two objections—in typical fashion, he calls them “great difficulties”—against the coherence theory of truth:
The first [objection] is that there is no reason to suppose that only one coherent body of beliefs is possible. […] The other objection to this definition of truth is that it assumes the meaning of “coherence” known, whereas, in fact, “coherence” presupposes the truth of the laws of logic.
I ignore the first argument here because Bench-Capon’s thread does not concern the first argument. Russell next argues for his second claim about coherence theories:
Two propositions are coherent when both may be true, and are incoherent when one at least may be false. Now in order to know whether two propositions can both be true, we must know such truths as the law of contradiction. For example, the two propositions “this tree is a beech” and “this tree is not a beech” are not coherent, because of the law of contradiction. But if the law of contradiction were itself subjected to the test of coherence, we should find that, if we choose to suppose it false, nothing will any longer be incoherent with anything else. Thus the laws of logic supply the skeleton or framework within which the test of coherence applies, and they themselves cannot be established by this test.
The idea here is that one cannot specify what coherence means without invoking the notion of truth. That is, in order to explain what it means for a collection of beliefs to be coherent, we will need to say that they can all be true. But this is just to invoke the notion of truth, or at least the possibility of their all being true, to explain their coherence. And because the coherence theory was supposed to explain what truth is, this is just to explain what truth is by appealing to what truth is.
Russell points out that one will need the logical laws to be true independently of their coherence with any given body of beliefs in order to give any belief-system independent criterion of coherent bodies of beliefs. How does that go? The example of the beech tree indicates what Russell has in mind. Suppose I accept the coherence theory of truth, and that I further think that a collection of beliefs is coherent when all the beliefs in question could be true. But now I say that the collection of beliefs B containing p and not-p is incoherent. And somebody asks, “Why is B incoherent?” Presumably, I will need to explain this by appealing to the impossibility of both p and not-p being true. But now we have completed the circle and arrived back at truth, which was our starting point.
Russell puts the same point in a slightly different way in a 1907 essay, “The Nature of Truth” (pages 156-157 of this edition from Archive.org). He in effect argues that the coherence theorist cannot explain why some collections of beliefs are coherent (somehow correct) and others incoherent (somehow in error) without appealing to the notion of truth:
…we are concerned with the question, not how far a belief in the coherence-theory is the cause of avoidance of error, but how far this theory is able to explain what we mean by error. And the objection to the coherence-theory lies in this, that it presupposes a more usual meaning of truth and falsehood in constructing its coherent whole, and that this more usual meaning, though indispensable to the theory, cannot be explained by means of the theory. The proposition “Bishop Stubbs was hanged for murder” is, we are told, not coherent with the whole of truth, or with experience. But that means, when we examine it, that something is known which is inconsistent with this proposition. Thus what is inconsistent with the proposition must be something true; it may be perfectly possible to construct a coherent whole of false propositions in which “Bishop Stubbs was hanged for murder” would find a place. In a word, the partial truths of which the whole of truth is composed must be such propositions as would commonly be called true, not such as would be commonly called false; there is no explanation, on the coherence-theory, of the distinction commonly expressed by the words true and false, and no evidence that a system of false propositions might not, as in a good novel, be just as coherent as the system which is the whole of truth.
I like this passage because it shows that Russell is concerned with the ability of the coherence theorist to explain truth using coherence. Russell’s challenge is to specify what coherence means independently of the notion of truth. Russell’s view is that this cannot be done.
It might be useful to put it a little differently. Suppose I am a coherence theorist. Let B be a collection of beliefs that is incoherent because, say, it contains p and not-p. In explaining what coherence is, I have two choices: (a) I can say that B is incoherent because p and not-p violate the logical principles included in B, or (b) I can say that B is incoherent because p and not-p violate logical principles not included in B.
Strategy (b) gives up the coherence theorist’s game. Appealing to logical laws that are true independently of their coherence with the body of beliefs B is just to give a test of truth of beliefs contained in B using the impossibility of their both being true. But truth was the very thing that coherence was supposed to explain.
On the other hand, strategy (a) does not explain why some collections of belief are true and others are not. If the only test of coherence is through internally accepted logical principles, then there is no way to say, of a given body of beliefs, that it is coherent or incoherent. One cannot give a belief-independent explanation of coherence at all. There is nothing to which you can appeal in making this judgment besides the internal logical principles of a given collection of beliefs.
Well, why should that be so bad? Assume that all judgments of coherence are, to borrow a Carnapian phrase, internal questions. Russell’s objection still stands: it is just that the coherence theorist is not able to offer an account of what makes a given body of beliefs coherent. Even on strategy (a), to say what coherence is, one would first have to pick a coherent belief system, then explain what coherence means in general. But if all questions about coherence are internal, then this is precisely what we cannot do.
As a side note, the Stanford Encyclopedia of Philosophy article on the Coherence Theory of Truth calls Russell’s objection the specification objection. I do feel that the summary there overlooks that strategy (a) does not answer Russell’s objection of stating what it means in general for a given collection to be false and for another to be true, but the clear distinction of internal and external questions may be, in Russell’s development, a post-Carnap conceptual development that should not be held against the 1907-1912 fellow.