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The pragmatic theory of truth is a philosophical theory of truth. The theory states that something is true only if it is useful to believe.
James's version of pragmatism was been taken up by later philosophers such as John Dewey and, most controversially, Richard Rorty.
Objections to pragmatic accounts
Several objections are commonly made to pragmatist account of truth, of either sort.
First, due originally to Bertrand Russell (1907) in a discussion of James's theory, is that pragmatism mixes up the notion of truth with epistemology. Pragmatism describes an indicator or a sign of truth. It really cannot be regarded as a theory of the meaning of the word "true". There's a difference between stating an indicator and giving the meaning. For example, when the streetlights turn at the end of a day, that's an indicator, a sign, that evening is coming on. It would be an obvious mistake to say that the word "evening" just means "the time that the streetlights turn on." In the same way, while it might be an indicator of truth, that a proposition is part of that perfect science at the ideal limit of inquiry, that just isn't what "truth" means.
Russell's objection isn't so much an argument against pragmatism, so much as it is a request -- that we make sure that we aren't confusing an indicator of truth with the meaning of the concept truth. There is a difference between the two and pragmatism confuses them.
There are many other objections to pragmatism. For example, how do we define what it means to say a belief "works"? Or that it is "useful to believe"? Presumably, it is sometimes useful to tell lies. In this case, pragmatism implies that lies can be true. Presumably this is an absurd conclusion. Suppose that religion is useful to believe. Then, according to James's theory, it is true. But why should it follow that God exists merely because believing that God exists is useful? More worryingly, in the Soviet Union under Stalin, certain beliefs concerning biology were adopted because they were "useful to believe" and this led to what is called Lysenkoism.
Another objection---which can be applied to all of the epistemic theories---is that pragmatism appears to be incompatible with the T-scheme mentioned above (and Tarski's inductive definition, in relation to the connecitves ~, & and so on). According to the T-scheme, if ~A is true, then A is not true. But presumably both a proposition A and its negation ~A might be useful to believe, which contradicts the T-scheme. For any determinate proposition A, either A is true or ~A is true. But it might be that neither is useful to believe. And so on.
A final objection is that pragmatism of James's variety (and Rorty's) entails relativism. What is useful for you to believe might not be useful for me to believe. It follows that "truth" for you is different from "truth" for me (and that the relevant facts don't matter). This is relativism.
A viable, more sophisticated consensus theory of truth, a mixture of Peircean theory with speech-act theory and social theory, is that presented and defended by Jürgen Habermas, which sets out the universal pragmatic conditions of ideal consensus and responds to many objections to earlier versions of a pragmatic, consensus theory of truth. Habermas distinguishes explicitly between factual consensus, i.e. the beliefs that happen to hold in a particular community, and rational consensus, i.e. consensus attained in conditions approximating an "ideal speech situation", in which inquirers or members of a community suspend or bracket prevailing beliefs and engage in rational discourse aimed at truth and governed by the force of the better argument, under conditions in which all participants in discourse have equal opportunities to engage in constative (assertions of fact), normative, and expressive speech acts, and in which discourse is not distorted by the intervention of power or the internalization of systematic blocks to communication.
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