The theory

Here is a version of the coherence theory of propositional truth, general enough for most proponents of a coherence theory to endorse:
CT: For a proposition to be true is for it to cohere with certain other propositions (call these the comparison propositions)

It remains for more specific versions to clarify (a) the nature of the coherence relation (i.e. what it is to cohere), and (b) which propositions are the comparison propositions. It is generally agreed that the comparison propositions must be ones that are believed, but by whom and when is controversial.

Those who are often thought to have held a version of the coherence theory include: Leibniz, Spinoza, Hegel, Bradley, Blanshard, Neurath, Hempel, Dummett, Putnam. (It used to be much more popular than it is today.)

Note that coherence theories are fairly plausible for some other things, such as plausibility (for a proposition to be plausible is for it to cohere with what is believed), or justification (for someone to be justified in believing a proposition, p, is for p to cohere with her beliefs). So why not truth as well? (Well, perhaps truth is more objective than plausibility and justification.)
Motivation

Why might anyone be attracted to CT?

Perhaps because they are dissatisfied with the alternatives (i.e. the other accounts of propositional truth), but still inclined to think that there must be some account.
This might not be a good reason to think that CT is true, but it might at least be a good reason to take it seriously. Then again, being philosophers, we should take every theory seriously. (Dawkins: "... you could almost define a philosopher as someone who won't take common sense for an answer.")

Perhaps because they are idealists  i.e. they think that our world is just a bunch of ideas. Actually, perhaps idealists will deny even the existence of propositions, in which case they will not endorse of coherence theory of propositional truth. So perhaps it is because they accept the existence of propositions, taking them to be minddependent things, but reject the existence of any mindindependent facts, in terms of which propositional truth can be accounted for. Then they might find it natural to account for the truth of a proposition in terms of its coherence with other propositions.
But is idealism correct? It was once popular, but these days has fallen into disrepute. And if it is correct, perhaps a pragmatic account of truth will serve the idealist's purposes equally well. Also, if CT entails idealism (as some argue  see the exercise for this week), and if idealism is false, then this turns out to be a problem for CT.

Perhaps because they are impressed by the epistemological argument that we considered last week, that if the correspondence theory is correct then we cannot know anything, and think that CT is immune to the objection, because even if we cannot know whether a proposition corresponds with a fact, we can know wether it coheres with other propositions.
But we saw reasons to reject that argument, and besides, are we really betterpositioned to know that a propositions coheres with other propositions?

Perhaps because of considerations about the conditions under which we accept that a proposition is true. They might observe this: we accept a proposition as true if and only if it coheres with everything else that we believe  if it does cohere, then we accept it as true; if it does not cohere, then we do not accept it as true (unless we can adjust our existing beliefs until it does cohere). Why is this? Because, they might argue, that's what it is for the proposition to be true: for it to be true is for it cohere with what we believe.
But is the best explanation? Note that it seems to make us infallible about what is true: we accept a proposition as true iff it coheres with what we believe, i.e. iff it is true. Perhaps we'd be better to stick to a coherence account of accepting as true, rather than of being true.

Perhaps because they think that truth comes in degrees, and that CT is the only account which allows for this: a proposition is more or less true according to how well it coheres with certain propositions.
But does truth come in degrees? And if it does, is CT the only explanation of this?

Perhaps because they think that truth is relative, and that CT is the only account which allows for this. What is meant by truth being relative? Consider the proposition that wifebeating is wrong. The truth of this is relative if there are communities C1 and C2 such that it is true for C1 but not true for C2. This does not mean that C1 believes it to be true, whereas C2 does not believe it to be true  it means that it actually is true for C1, and actually is not true for C2.
But is truth relative in this way? If it is not, and if CT entails that truth is relative, then this turns out to be a problem for CT.
Is there a devil in the details?

We can't really understand CT, and subject it to careful scrutiny, until we are told more about (a) what it is to cohere, and (b) which propositions are the comparison propositions.

What is it to cohere? There are at least two possibilities:
 Coherence is consistency. i.e. for a proposition, p, to cohere with the propositions, P, is for p to be consistent with the Ps.
 Coherence is entailment. i.e. for a proposition, p, to cohere with the propositions, P, is for p to be entailed by the Ps.
Consistency

If coherence is consistency then we have to be careful about which propositions are the comparison propositions. Suppose the comparison propositions are the propositions that I currently believe. Since it is compatible with what I currently believe that Descartes had 100 books on his bookshelf (I have no opinion on the matter, and my beliefs do not rule it out), and compatible with what I believe that Descartes had 200 books on his bookshelf, the present approach to CT yields that both of these propositions are true. But that seems like the wrong result, and proponents of CT would agree.

We get a similar problem if we take the comparison propositions to be any propositions that are currently believed by any person or group of people  since any such system of beliefs will leave all sorts of matters open, there will in every case be a pair of similarly problematic propositions.

So too if we take the comparison propositions to be any propositions that were or will be believed by any person or persons. No system of actual beliefs will ever be sufficiently comprehensive to avoid there being a pair of problematic propositions.

Besides, here is another concern about taking the comparison propositions to be propositions that were, are, or will be believed by any person or persons: we typically hold inconsistent beliefs, without even realizing it (e.g.: many of us believe both that absence makes the heart grow fonder, and that out of sight means out of mind). But if the comparison propositions are inconsistent, then no proposition is consistent with them, and so no proposition is true, on the present approach. That seems like the wrong result, and proponents of CT would agree.

What if we take the comparison propositions to be the propositions that we would ideally believe (even if we never do)? Well, to avoid the Descartes problem we would need these propositions to be such that there is no pair of numbers n and m such that the proposition that Descartes had n books on his bookshelf, and the proposition that Descartes had m books on his bookshelf are both consistent with them. But why is that a condition on being ideal to believe? Not because it would make any practical difference (it wouldn't). Perhaps because they cannot both be true. But a proponent of CT cannot say this on pain of circularity. Besides, moving away from what we actually believe to what we would ideally believe seems like a move towards making truth less subjective and more objective, a move that goes against the spirit of CT.

It is similarly problematic to appeal to what is actually believed by an ideal believer (or omniscient being), rather than by people like us.

Finally, consider the question: What is it to be consistent? The standard account of consistency goes as follows:
for a proposition, p, to be consistent with the propositions, P, is for there to be a possible situation in which p and the Ps are all true. But propopents of CT cannot say this, on pain of circularity: CT gives an account of propositional truth in terms of consistency, so it cannot give an account of consistency in terms of propositional truth. There is a challenge, here, for proponents of CT: to convince us that consistency can be accounted for without appealing to truth.
Entailment

If coherence is entailment, then again we have to be careful about which propositions are the comparison propositions. Suppose the comparison propositions are the propositions that I currently believe. Since it is not entailed by what I currently believe that Descartes had 100 books on his bookshelf, the present approach to CT yields that it is not true that Descartes had 100 books on his bookshelf. Moreover, since, for every n, it is not entailed by what I currently believe that Descartes had n books on his bookshelf, the present approach to CT yields that, for every n, it is not true that Descartes had n books on his bookshelf. But that seems like the wrong result  intuitively, there is some n such that it is true that Descrates had n books on his bookshelf.
Note: a proponent of CT could bight the bullet on this, and accept that there is indeed no n such that it is true
that Descartes had n books on his bookshelf. She could even accuse her opponent of begging the question against CT if he claims that there is any such n.

We get a similar problem if we take the comparison propositions to be any propositions that were, are, or will be believed by any person or group of people  we will always be able to come up with a similarly problematic proposition.

And again, we often have inconsistent beliefs (without realizing it). But if the comparison propositions are inconsistent, then every proposition is entailed by them, and so every proposition is true, on the present approach. That seems like the wrong result.

What if we take the comparison propositions to be the propositions that we would ideally believe (even if we never do)? Well, to avoid the Descartes problem we would need these to entail the proposition that Descartes had n books on his bookshelf (where n is the number of books that he actually had). But why is it ideal to believe propositions that entail this? Not because it would make any practical difference (it wouldn't). Perhaps because it is true. But a proponent of CT cannot say this on pain of circularity (it would amount to saying that it is ideal to believe it because it is ideal to believe it). Similarly if we appeal to an ideal believer or (omniscient being).

Finally, what about entailment  what is it to entail? The standard account of entailment goes as follows:
for a proposition, p, to be entailed by the propositions, P, is for there to be no possible situation in which the Ps are all true but p is not true. But proponents cannot give this account, on pain of circularity: they give an account of propositional truth in terms of entailment, and so cannot, without circularity, give an account of entailment in terms of propositional truth. There is a challenge, here, for proponents of CT to convince us that entailment need not be accounted for in terms of truth.
Something else?

There are thus problems if we take coherence to be either consistency or entailment. Can proponents of CT avoid these? Or is there some other understanding of coherence that is less problematic? (For an explanation of coherence in terms of mutual explanatory support see Bradley, F. (1914), Essays on Truth and Reality (Oxford: Clarendon Press).)
A regress problem?

Ralph Walker has recently offered a new argument against CT (Walker, R. C. S. (1989), The Coherence Theory of Truth (London and New York: Routledge). He argues that CT suffers a vicious infinite regress. For a discussion of this see Crispin Wright's review in Synthese 103 (1995), pp. 279302. For a defence of CT against Walker see Young, J. O. (2001), 'A Defence of the Coherence Theory of Truth', The Journal of Philosophical Research 26, pp. 89101.
In McGinn, C. (2002), 'The Truth about Truth', in Richard Schantz (ed.), What is Truth? (Berlin: Walter de Gruyter), pp. 194204, Colin McGinn argues that the coherence theory of truth is committed to idealism and is therefore false. What is McGinn's argument? Can you think of any problems for it? (The argument appears in the first two pages; you can read these via google books.)