I have wanted to comment for some time about a number of available “theories of truth.” The occasion has now been presented by the fact that I am writing the fourth chapter of my new book (on whether and how philosophy makes progress, forthcoming from Chicago Press), which is about the surprisingly not-so-straightforward concept of progress (and truth) in science itself, the very discipline normally held to be the paragon of a truth seeking enterprise.

Every scientist I have talked to about these matters (though, of course, mine is an anecdotal sample, and actual sociological research would be welcome!), implicitly endorses what philosophers refer to as the Correspondence Theory of Truth (henceforth, CToT). This also likely captures the meaning of truth as understood by lay people. Interestingly, most philosophers up until modern times have also endorsed the CToT, and have done so without even bothering to produce arguments in its favor, since it is usually considered self-evident. Indeed, Descartes famously put it this way in his Letter to Mersenne: “I have never had any doubts about truth, because it seems a notion so transcendentally clear that nobody can be ignorant of it... the word ‘truth,’ in the strict sense, denotes the conformity of thought with its object.”

But what, exactly, is the CToT? Here is how Aristotle put it, in his Metaphysics: “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true.” Not exactly the most elegant rendition of it, but a concept that we find pretty much unchanged in Aquinas, Descartes, Hume, Kant and several other medieval and early modern writers. Its modern rendition dates to the early days of analytic philosophy, and particularly to the work of G.E. Moore and Bertrand Russell. Truth, according to the CToT, is correspondence to facts: to say that statement / theory X is true just means that there is a factual state of affairs Y in the world that is as described by X. It seems pretty straightforward and hard to dispute, and yet much 20th century philosophy of science and epistemology has done just that: challenge the CToT with the aim of carefully unpacking the notions on which it is based, and — if necessary — to replace it with a better theory of truth.

The first problem lies in the very use of the word “truth.” It seems obvious what we mean if we say that, for instance, it is true that the planet Saturn has rings in orbit around its center of gravity. But it should be equally obvious what we mean when we say things like the Pythagorean theorem is true (within the framework of Euclidean geometry). And yet the two senses of the word “truth” here are quite distinct: the first refers to the sort of truth that can be ascertained (insofar as it can) via observation or experiment; the second one refers to truth that can be arrived at by deductive mathematical proof. We can also say that the law of the excluded middle — which says that either a proposition or its negation are true, but not both — is (logically) true within the framework of classical logic. This is related to, and yet somehow distinct, from the sense in which the Pythagorean theorem is true, and of course it is even more distinct from the business about Saturn and its rings. There are yet other situations in which we can reasonably and more or less uncontroversially say that something is true. For instance, according to every ethical system that I am aware of it is true that murdering someone is wrong. More esoterically, philosophers interested in possible world semantics and other types of modal logic may also wish to say that some statement or another is “true” of all nearby possible worlds, and so on.

The bottom line is that the concept of truth is in fact heterogeneous, so that we need to be careful about which sense we employ in any specific instance. Once appreciated, this is not an obstacle unless a scientistically inclined person wants to say, for instance, that moral truths are the same kind of truths as scientific ones. Needless to say, one easily encounters a number of such cavalier statements, which makes the point that the apparently obvious differences among the above mentioned meanings of truth do, in fact, need to be spelled out and constantly kept in mind. So, the CToT — within the specific context that interests us here — is limited to empirical-scientific truths about the way the world is and works. To speak of a CToT in the case of, say, mathematics or morality would be a highly metaphysically treacherous enterprise, one on which we are not going to embark (but see here).

Even if we are now clear that the CToT in science makes sense only for a restricted meaning of the word “fact” we still need to examine a number of objections and alternative proposals to the theory, as they will help appreciate why talk about progress in science is not quite as straightforward as one might think. There are several issues that have been raised about the soundness of the CToT, one of which is that it simply does not amount to a “theory” of any sort; it is rather a trivial statement, a vacuous platitude, and so forth. This is somewhat harsh, but not far from the mark, I think. The CToT really isn’t anything that we might reasonably label with the lofty term of “theory.” Then again, this doesn’t mean that it is either trivial or vacuous. I consider the CToT rather as a definition of what truth is, particularly in science (some philosophers refer to these situations as “mini-theories,” or perhaps better, “accounts”). Definitions are useful, if not necessarily explanatory, as they anchor our discussions and provide the starting point for further exploration.

Perhaps a more serious objection to the CToT is that it relies on the somewhat obscure concept of “correspondence,” which needs to be unpacked. One of the possible answers here is that defenders of the CToT can invoke the more precise (at least in mathematics) idea of isomorphism as the type of correspondence they have in mind. But — unlike in math — it is not at all straightforward to cash out what it means to say that there is an isomorphism between a theory (which is formulated in the abstract language of science) and a physical state of affairs in the world. This is a good point, but as Marian David retorts, this sort of problem holds for any type of semantic relation, not just for isomorphisms in the context of the CToT, and a discussion of that topic would veer too far into philosophy of language to be appropriate here.

Another way to take the measure of the CToT is to look at some of its principal rivals, as they have been put forth during the past several decades. One rival is a coherentist approach to truth, which replaces the idea of correspondence (with facts) with the idea of coherence (among propositions). This move works well, I suspect, for logic and mathematics (which are based on deductive logic, and where internal coherence is a required standard), but not for scientific theories. There are simply too many possible theories about the world that are coherent and yet do not actually describe the world as it is (or as we understand it to be) — a problem known in philosophy of science as the underdetermination of theory by the data, and one that from time to time actually plagues bona fide scientific theories, as it is currently the case with string theory in physics.

Another set of alternatives to the CToT is constituted by a number of pragmatic theories of truth, put forth by philosophers like Charles Peirce and William James. Famously, these two authors differed significantly, with James interested in a pluralist account of truth and Peirce more inclined toward a concept that works for a realist view of science. For Peirce scientific (or, more generally, empirical) investigation converges on the truth because our imperfect sensations are constrained by the real world out there, which leads to a sufficiently robust sense of “reality” while at the same time maintaining skepticism about specific empirical findings and theoretical constructs. Here is how Peirce characterizes the process (in The Essential Peirce):
So with all scientific research. Different minds may set out with the most antagonistic views, but the progress of investigation carries them by a force outside of themselves to one and the same conclusion. This activity of thought by which we are carried, not where we wish, but to a foreordained goal, is like the operation of destiny. No modification of the point of view taken, no selection of other facts for study, no natural bent of mind even, can enable a man to escape the predestinate opinion.
For Peirce, therefore, truth is an “opinion” that is destined to be agreed upon (eventually) by all inquirers, and the reason for this agreement is that the object of such opinion is reality. This is actually something that I think scientists and realist-inclined philosophers could live with. By contrast, I find James’ views irritatingly close to incoherence, or at least wishful thinking, as when he claims that truth is whatever proves to be good to believe, or when he defines truth as whatever is instrumental to our goals. It is by way of this sort of fuzzy thinking that James arrived at his (in)famous defense of theological beliefs: belief in God becomes “true” because “[it] yield religious comfort to a most respectable class of minds” (in Pragmatism: A New Name for some Old Ways of Thinking), which ought to be considered prima facie preposterous and accordingly dismissed. While some suggest that Bertrand Russell was a bit unfair to James when he said that the latter’s theory of truth committed him to the “truth” that Santa Clause exists, I am inclined to go with Bertie on this one.

A third alternative to the CToT is represented by one version or another of verificationism. This notion of course goes back at the least to the British empiricists, and particularly to Hume and his famous fork. As he famously put it in the Enquiry Concerning Human Understanding:
All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic ... [which are] discoverable by the mere operation of thought ... Matters of fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. ... If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
(Note, of course, that strictly speaking Hume recognized two types of truths: empirical ones, subject to verificationism, and logical-mathematical ones, for which he seemed to adopt something like a coherence theory of truth.)

Verificationism, of course, had its heyday with the logical positivists of the early part of the 20th century, and fell out of favor after sustained criticisms by W.V.O. Quine, Hilary Putnam and others, although it is making a come back in the form of James Ladyman and Don Ross’s “non-positivist version.” Indeed, Ladyman and Ross are out to rescue metaphysics — the very discipline that logical positivists had ditched on the ground that it cannot abide by (their version of) the verification principle. So perhaps a modified incarnation of verificationism will still turn out to be viable after all.

I find a few other alternatives to the CToT to be far less palatable or promising, even though some of them have been all the rage of late in epistemology. For instance, the identity theory says that true propositions do not correspond to facts, they are facts. It is, however, not at all clear in what sense this is the case, unless we make recourse to a fairly radical kind of pluralism about facts themselves (i.e., one in which theories count as a category of facts), in which case the identity theory may turn out to have solved close to nothing. Or consider deflationist approaches to truth: according to the CToT, “Snow is white” is true if it corresponds to the fact that snow is white; for a deflationist, however, “Snow is white” is true if snow is (in fact) white. The move basically consists in dropping the “corresponds to” part of the CToT. The above mentioned David points out that many CToT statements are not at all so easily “deflated,” however; moreover, this particular debate seems to me to hinge on issues of semantics rather than on any “theory” of what it is for something to be true, rapidly approaching Ladyman and Ross’s “neo-Scholasticism” status (which is not meant to be a compliment).

A more interesting position, in my mind, is represented by alethic pluralism, according to which truth is multiply realizable. As David puts is: “truth is constituted by different properties for true propositions from different domains of discourse: by correspondence to fact for true propositions from the domain of scientific or everyday discourse about physical things; by some epistemic property, such as coherence or superassertibility, for true propositions from the domain of ethical and aesthetic discourse, and maybe by still other properties for other domains of discourse.” This essentially closes the circle, as alethic pluralism conjoins our discussion of theories of truth with our initial observation that “facts” come in a variety of flavors (empirical, mathematical, logical, ethical, etc.), with distinct flavors requiring distinct conceptions of what counts as true.

So, why do we care? Well, to begin with — and contra popular opinion (especially among scientists) — it turns out that it is not exactly straightforward to claim that science makes progress toward the truth about the natural world, because it is not clear that we have a good theory of truth to rely on; moreover, there are different conceptions of truth, some of which likely represent the best we can do to justify our intuitive sense that science does indeed make progress, but others that may constitute a better basis to judge progress (understood in a different fashion) in other fields — such as mathematics, logic, and of course, philosophy.

Originally appeared on Rationally Speaking, June 29th, 2013