Stephen Law offers a concise and clear summary of C. S. Pierce's consensus theory of truth, and explores some of the philosophical issues that follow from this definition.
Defining "truth" is a notoriously difficult task, because philosophers typically place the definition at a fundamental metaphysical level, before we have defined notions such as "reality" or "correspondence". To tightly couple truth and reality, then, philosophers typically raise notions of reality to the metaphysical level, i.e. metaphysical realism.
According to Law, Pierce defines truth as "what those who investigate a matter will all eventually agree on." Truth is, in (presumably) Pierce's own words, "The opinion which is fated to by all who investigate is what we mean by truth and the object represented by this opinion is the real."
The typical counterexamples to the consensus theory of truth do not seem to directly rebut Pierce's notion. The most common counterexample is the observation that at one time everyone believed the Earth was flat; despite this consensus, they were all mistaken: the Earth is more-or-less spherical. Law offers his own counterexample:
The suggestion that truth is, at root, whatever we agree it to be might seem open to a very obvious sort of counter-example. Suppose I manage to convince both myself and others that Earth is ruled by Lizard-people from outer space. If the truth is what ever we end up agreeing it to be, then it is true that the Earth is ruled by lizard people from outer space. But of course, this is ridiculous – we can’t just make a claim true by collectively agreeing to it, can we?
These sorts of counterexamples, however, trade on the fact that not everyone agrees to the specified premise. We ourselves do not believe that the Earth is flat, nor do we believe that the Earth is ruled by Lizard-people from outer space. Since there is in fact no consensus, we cannot conclude that these propositions are true by virtue of any consensus. Furthermore, it might be the case that we ourselves are mistaken: The Earth really is flat; Lizard-people do indeed rule the world. Anyone who has swallowed Quantum Mechanics can easily be persuaded that it's possible that a common-sense opinion, which seems blatantly obvious, can actually be mistaken at a fundamental level.
Furthermore, it seems reasonable to take Pierce at his word: The opinion which is fated to by all who investigate, not the opinion which some people, even a large number of people, happen to believe. To do the philosophical job, a counterexample along these lines would have to assert the falsity of an opinion to which everyone believes, including the writer and the readers. This bar seems impossibly high. We cannot tell the difference between a proposition that everyone believes, ourselves included, and a proposition that everyone believes because it's true.
We can, however, critique Pierce's definition on technical grounds. Specifically, the qualifiers "fated to" and those who "investigate" seem vague. How do we tell which beliefs are "fated" and which are mistaken? And what precisely does Pierce mean by "investigate"? Even if we charitably presume he means scientifically investigate, he seems to be begging the question: Why should we privilege scientific investigation a priori? Worse yet, it's not an analytic property of scientific investigation that all investigators are in fact fated to come to the same conclusion.
Pierce's definition fails on pragmatic grounds: It does not do the job we typically expect definitions to do. It is not ostensive (we can point to a chair and say "chair"), it's not operational (length is what we measure with a ruler), and it's not analytic (a bachelor is an unmarried man).
As a concept, however, the coupling between consensus and truth seems appealing. If we look at this coupling in an evidentiary sense, the difficulties with Pierce's use of the concept as a definition evaporate.
We are always surprised, in a deep philosophical sense, by consensus. (In the purely phenomenological sense, we are philosophically surprised when our subjective experiences correlate in unexpected ways.) If people were independently making up arbitrary beliefs, we would expect a range of opinion, not a consensus. All consensus -- indeed any agreement between sufficiently large numbers of people -- calls for some sort of explanation.
Therefore we can modify Pierce's definition to remove the problems: Truth is not what we agree on, truth is what causes agreement. Any time we see agreement, there is some sort of truth causing that agreement. This construction allows us to more flexibility in determining specifically what sort of truth underlies agreement.
In Pierce's construction, we say "if everyone agrees that p, then p is true." Too facile. In the modified construction, we can say, "If everyone agrees that p, then some proposition q is true, and q implies that everyone agrees that p." If q also implies that p, then of course p is true as well.
Looking at the evidence of our daily life, we can discern three primary mechanisms which cause people to widely agree on some proposition: reality: a lot of people agree that the Earth is round because the Earth really is round; deduction: a lot of mathematicians agree that 2+2=4 is a theorem of arithmetic because it's deducible from the axioms of arithmetic; and social construction: a lot of Christians agree that Jesus is the son of God because they have been told so and believed it.
In the first two cases, it's easy to see that what causes the belief to be shared also implies the truth of the belief itself; in the third case (social construction) we can determine the truth of what causes the agreement, but the truth of the cause of the agreement does not imply the truth of what is agreed-upon.
Thus in Law's counterexample, if everyone agreed that Lizard-people from outer space rule the Earth, then there should be some cause of that agreement: it's true by definition that something or other causes the agreement, but that cause may or may not imply that Lizard-people from outer space really do rule the Earth.