1. The Question

The first preliminary is the meaning of the title's question. I mean the question like this: There are some properties that confer value on entities that have those properties. Beauty, for example, the property of being beautiful, is valuable if beauty makes things valuable, if the reason a thing ought to be loved is that it is beautiful. Moral goodness is valuable if it makes actions valuable, if the actions ought to be performed because they are good. Such properties are often called ‘evaluative’ properties, and they are contrasted with ‘descriptive’ properties. Evaluative properties are governed by norms – that thing ought to be pursued, that action ought to be performed – and descriptive properties are not. The question is whether truth is an evaluative property.Footnote ¹

It is important to contrast the claim that truth is valuable with two other claims. The first is that it is valuable to believe truths. It is often valuable to believe truths, but it is not invariably so. A belief is valuable if it helps one achieve one's goals, and there are countless true propositions that wouldn't help me achieve my goals by believing them (e.g., I have no goals that would be helped along by believing the truth about exactly how many gnats were swirling about my head on that hike last summer), and sometimes false beliefs are useful (e.g., I would run faster if I believed I was being chased by a lion). But here, ‘valuable’ means ‘extrinsically valuable’, and the issue is about the action of believing, rather than the object. In any case, this is a different question.Footnote ² The second contrasting claim is that a truth p is valuable if it is good that p is true. Surely there are many unfortunate truths. If it is true that the city of Pompeii was destroyed by Vesuvius, it is not therefore good that the city of Pompeii was destroyed by Vesuvius. It may, however, be good to find out whether Pompeii was destroyed by Vesuvius, and believe it if it was.

This is the question I am asking: Are truths valuable, and hence ought to be sought for and believed? I am not asking whether believing them is valuable, and not whether truth is always pleasant. Assuming that truths – true propositions – are valuable, i.e., that there is some norm governing their pursuit and acquisition; the question of this paper is whether this value comes from their truth or from some other property.

The norm governing truth is, roughly, that we ought to seek to find out what is true, and believe it when we have found it. That is, the norm is not only about belief. It is also about seeking. We sometimes want to find out whether p, that is, whether p is true. We seek for beauty when we go to the museum or the library to see a marble or read a poem. We seek for truth when we go to the laboratory or to our armchairs. Why do we seek truth? Is it simply because it is true, or is there some other reason?

In this paper, I'll use a pair of examples as paradigmatically valuable truths. The first is that God exists. That is, if God exists, then the proposition that God exists is valuable. This could be so in several ways. One is that if God exists, we will be rewarded for believing that God exists – there will be great rewards in heaven for getting the truth of this proposition right. Thus, the proposition might be extrinsically valuable. Another way the proposition could be valuable is independent of any reward – it is good to possess the truth that God exists much as it is good to perform a good action. (Of course, I ought to say, ‘If God exists, the proposition that God exists is valuable; and if God doesn't exist, the proposition that God doesn't exist is valuable’. Take my discussion of the proposition to be expressed conditionally, covering both alternatives.) One prima facie reason to think that this proposition is valuable in the second way rather than the first (valuable in itself instead of for its rewards) is that the value of these two propositions – that God exists, and that God doesn't exist – is at least roughly symmetrical, but that the value of the rewards of being right are not at all symmetrical. If God exists and I'm right (assuming God rewards being right about this proposition), I will have infinite (extrinsic) rewards. But there are no extrinsic rewards for being right about the proposition that God doesn't exist, or at least very few.

The other example I'll use as a paradigmatically valuable truth is that quarks are not composed of smaller particles – and again I mean that this is valuable if it's true, and likewise for its denial. There may well be some reward for being right about this – past scientific discoveries have sometimes been technologically valuable. But there's no reason to think it will be. And yet, the proposition is still valuable. Or, at least, that's the view that I take to be intuitive, and the view that I examine in this paper.

2. Truth varying

On one theory of value, due to Brentano, a thing is valuable if and only if it is correct to love that thing in itself, and one thing is more valuable than another if and only if it is correct to prefer the first in itself to the second.Footnote ³ Stated like this, Brentano's theory is not complete. A theory like this gives only a criterion, a test whether a thing (act, proposition) is valuable; this test is whether the thing has a norm governing its pursuit. If there is a norm that says it's right to love it, or pursue it, or possess it (perform the action, believe the proposition), then the thing is valuable – but the theory is silent as to why. It does not explain what it is about this thing that makes it valuable. A full and satisfactory explanation of what makes something valuable will explain why, will explain what properties the thing has that make it valuable.

And so it is with truth. If truths are valuable, according to this theory, there will be some norm governing their pursuit. But a full and satisfactory theory about the value of truths will explain what it is that makes them valuable. The most obvious answer is their truth. If truths really are valuable, the most salient property they have in common is their truth. This is a prima facie reason to believe that truth is an evaluative property, that it is truth that makes truths valuable. Another prima facie reason to believe it is found in the fact that our interest in truth is an interest in reason. Just as we value beauty because we are perceivers and moral goodness because we are agents, so we value truth because of the role truth plays in reasoning. And so, because reasoning is concerned only with the truth of propositions – a valid argument is just one that preserves truth – it is the truth of truths that is valuable.Footnote ⁴

Brentano's theory also states a comparative, what makes one thing more valuable than another, and the weakness in such a theory is the same: a satisfactory explanation of why one thing is more valuable than another will involve the properties the two things have. According to Brentano's theory, one true proposition is more valuable than another iff it is correct to prefer it to the other. But what lies behind this correctness? Again it seems that a satisfying answer to this question will make use of the properties of the propositions. Comparing values is tricky. Often values will be incommensurable, and it may be that values are sometimes not transitive.Footnote ⁵ The study of truth's value avoids most of these problems by limiting its concern to a single class of things. We are not comparing truths with beauties, but truths with truths.

The question of comparing truths arises because value comes in degrees. Some things are more valuable than others. It is better to save a life than to save a dollar (and saving a dollar is good); Michelangelo's David is more beautiful than Donatello's or Bernini's (and these are beautiful). So, if truth is valuable, this value should come in degrees. What explains the difference in value? If one set of marbles weighs more than another set, either the first marbles are heavier, or there are more of them. In making comparisons of things with different evaluative properties – comparing something beautiful to something morally good, for example – it may be that one evaluative property has more weight. But in comparing things with the same property – two beautiful things, or two morally good actions – one can be more valuable than the other only if there is more of the evaluative property. That is, evaluative properties are variable. Beauty comes in degrees, and this explains why it is that Don Giovanni is more valuable than Don Pasquale. Moral goodness likewise. If it is an evaluative property, it should be the same with truth. If truths vary in their degree of value, it must be that some truths are truer than others.

This sounds surprising. The most pedestrian trivium is no less true than the deepest mystery, or at least so it seems. Even if some proposition is more valuable than another, it is no more true. Truth is binary; either a proposition is true or it's not. Even though there are degrees to the value of truth, there are no degrees to truth.

So we have a puzzle. We can pose this puzzle as a trilemma: all three of these propositions seem true, but they are inconsistent.

1. 1. Some true propositions are more valuable than others.

2. 2. One truth can be more valuable than another only if it is more true.

3. 3. No true proposition is more true than another true proposition.

Which should we deny? The next three sections will examine each in turn.

3. Value unvarying

Denying 1 means claiming that all truths are equally valuable. This is wildly counter-intuitive.

To say that truths are valuable, again, is to say that there is a norm that governs the pursuit of truth. Following James, it is common to take this norm as consisting of two parts: ‘Pursue Truth! Shun Error!’Footnote ⁶ But by itself this does not explain our intuitions about what makes truth valuable. Some truth simply isn't worth knowing. It would take some effort for me to learn exactly how many gnats were swirling about my head on my hike last summer, and this would be effort wasted. It would also take some effort for me to learn whether there are any particles smaller than quarks, but this, in most cases, is not effort wasted.

This worry is not that I can't know everything. This is surely true, and yet, even after I acknowledge my limitations I am not obligated to know as much as possible. The pursuit of difficult truth is noble and praiseworthy in a way that stockpiling trivia is not, even if that pursuit is, in the end, unsuccessful.

Some truths are more valuable than others. We praise people for learning some truths, and don't praise them for learning other truths. We give prizes to people who discover the shape of DNA molecules and not to people who discover how many leaves are on that tree. It is better to know only a few important truths than many pieces of trivia. There are truths that are worth every effort to know, and truths that are cheap. The answer to the question of whether God exists is on a different level altogether from the answer to the question of exactly how many gnats were swirling about my head.

None of this has been much of an argument, because the only way to argue that not all truth is of equal value is to show that whatever it is that makes a truth valuable is held more heavily by one truth than another. That argument is not available in the context of trying to determine what it is that makes a truth valuable. A satisfactory theory of the value of truth will explain why truths vary in value, and this will be a measure of an adequate theory. But as a solution to the puzzle, claiming that truths do not vary in value should remain a last resort.Footnote ⁷

4. Fundamentality

Denying 2 means claiming that other properties are involved in the value of true propositions. Assume that p and q are both true, but that p is more valuable than q. Denying 2 means that there is some gradable property other than truth that p has more of than q. If there is such a property, truth is not valuable; this other property is instead.

Formally, denying 2 allows the possibility that there are false propositions that may be proper to seek after and believe. And clearly, in one sense, there may be. If I am offered a large sum of money to believe that Quine was an eminent politician, that proposition would be (extrinsically) valuable for me to believe. Or a falsehood might be comforting, making it valuable to believe. Or it might put me on a path that leads me to discover an important truth, like a ladder that must be kicked away. But the sense in which it is valuable to believe a false proposition is irrelevant to the sense in which truth is supposed to be valuable. Hence, I will consider only true propositions. Because of this, denying 2 is the same as claiming that truth is merely a necessary, but not a sufficient, condition for a proposition to be valuable. A proposition must be true to be valuable, but the degree of value comes from some other property.

The propositions I have been using as typical valuable truths – that God exists and that quarks are the most basic particles – are explanatorily important, and it seems to me that they are valuable because they are explanatorily important. In fact, it seems plausible that all important truths are important to explanation just like these. I'll call this the ‘fundamentality intuition’ – the most important truths are the most explanatorily fundamental, and the less fundamental a truth the less valuable.

To turn this intuition into a theory that denies thesis 2, we would need to find a way to order the true propositions in terms of their importance, and find a way to measure this importance. I cannot find a way. There are two initially plausible ways to arrange the propositions. The first exploits their relations of logical dependence, and the second their (putative) relations of ontological dependence.

The most obvious relations that proposition bear to each other are logical, primarily entailment. So we might try to order the propositions in terms of logical entailment. Take, as a first approximation of this task, the truths to be arranged axiomatically, with a set of ‘first principles’ as axioms. (The term ‘first principles’ betrays the Aristotelian ancestry of this theory.) These first principles are the most explanatorily fundamental propositions – these propositions are sufficient to explain every truth. All other true propositions follow from the axioms, some immediately, some only at length. The theorems are less fundamental than the axioms (Aristotle says the axioms are ‘prior to’ the theorems), and the degree of fundamentality diminishes in each step from the axioms. This answers our intuitions that the most valuable truths, those that we should devote the most energy into seeking, are those that are the most important in explanations.

The axiomatic picture, however, is probably too tightly structured to be adequate. There are two ways in which it's too tightly structured. The first is that it confuses logical entailment with deduction via some set of rules. Which of two theorems is more immediately entailed by the axioms? It depends on what the rules are. The syntactic inference rules assume that the axioms are stated in some formal language that can be manipulated, but the axioms are not formal sentences; they are propositions. These propositions could be expressed by various formal languages that can be treated with various inference rules. But for the purposes of explanation, the rules shouldn't matter. It's important that the theorems follow from the axioms, but not important what the steps of the proof are.

If we abandon this syntactic notion of inference, we have no way of measuring fundamentality. The syntactic notion allowed us to count steps in a proof, counting a theorem as more fundamental the fewer the steps it took. Semantically, there is no way to measure the complexity of the inference. We can't instead count the number of inferences each proposition has (on the supposition that the more fundamental propositions entail more sub-theorems), because in a set closed under logical entailment, every proposition entails exactly infinitely many others. It also doesn't work to compare two propositions, and say that if one entails the other it is more central: Typically, a proposition is entailed not by a single proposition but a set, and often one of the propositions in the entailing set is entailed by a set that includes the entailed proposition (e.g., p entails p or q, but p or q and not-q entail p).

The other reason the axiomatic picture is too structured is that it relies only on logical implication. It may be that the world is structured this precisely, but it is not obviously so. It may be that the world is deterministic, so the conjunction of the laws of nature with the initial conditions suffice to entail every true proposition, and if it is, an axiomatic system may suffice. If it isn't, we may need to loosen the notion of implication.

But no alternative picture works better. To fix the second problem, we may allow other connections besides implication. One might think here of probability (p makes it more likely that q), or conversational implicature, or induction. None of these will work to explain the value of truth. First, consider probability. Since the structure is of true propositions, every proposition in the structure has a probability of 1 – whatever is true is perfectly probable. Of course, there are other senses of probability according to which something that's true is also improbable, but these are psychological senses. Something may well be both true and improbable, since the thing would have to be false or unlikely given certain beliefs I already have. In a case like that, a proposition may have a probability for me of 0.3, even if it is true. Conversational implicature, likewise, is obviously irrelevant to the structure of the true propositions. And so is induction. Induction allows us to go from what is better known to what is less well known, we are after the structure of the world – which propositions are in fact more fundamental, not which are better known to us.

So the hierarchy cannot be mortared with logical entailment. The other promising approach is to replace logical entailment with ontological entailment. This is the notion of grounding, as presented by Gideon Rosen.Footnote ⁸ The grounding relation is primitive, and hence not definable, but Rosen illustrates with synonymous idioms: a grounds b; b holds (obtains, is true) in virtue of a; b just because a. In one of his examples, Rosen explains naturalism as the thesis that intentional and normative truths are not fundamental. Every true proposition is a node in a tree, and the node's branches are the propositions that ground it. Naturalism is the thesis that the leaves of every tree are non-intensional and non-normative. If this relation is intelligible, grounding presents just the kind of property needed to solve the puzzle. There is a way to create a hierarchy of propositions: for all propositions p and q, if p explains q, then p is more central than q. The grounding relation does not have the same circularity problems as the inference relation, since if p grounds q, q cannot ground p. Each true proposition has a gradable property of fundamentality, with a proposition being less fundamental than the one that grounds it.Footnote ⁹

And this gives us what we need. Fundamentality is a gradable property. If quarks are the most basic particles, this is valuable to believe, and it is valuable to believe just because it is fundamental.

The concern I have with this solution, however, is that Rosen's version of grounding is conceptually confused. It turns on the difference between taking propositions to be what stands in need of explanation and taking facts or obtaining states of affairs as being what stands in need of explanation. It seems obvious to me that facts are what need to be explained. This is simply because I don't know what it means to explain a proposition, rather than the fact that the proposition is true. If I ask why, for instance, grass is green, I'm not asking for an explanation of a proposition, but of some fact about the world. Of course, when I request the explanation I will request it using a sentence expressing a proposition, and the explanation will come via sentences expressing propositions, but that doesn't mean that the thing that needed explanation was a sentence or a proposition. This is simply part of the concept of a fact: events have causes, propositions have logical implications, and facts have explanations.

In his example of the tree of naturalism, Rosen says, ‘Every fact p, we may say, is associated with a tree that specifies the facts in virtue of which p obtains, the facts in virtue of which those facts obtain, and so on’.Footnote ¹⁰ Even though his official theory is a theory of propositional grounding, he usually talks instead about facts. He takes ‘fact’, officially, to mean ‘true proposition’, which is his way of preserving the intuition that facts are what are explained, what are grounded in each other. Because ‘fact’, for Rosen, officially means ‘true proposition’, ‘obtains’ must mean something like ‘is true’. Thus he is not really grounding one true proposition in another; he is grounding the fact that one proposition is true in the fact that another proposition is true.

Because of this, I take Rosen's version of grounding to be giving the wrong kind of explanation. Propositions are related to each other in entailment relations, not grounding relations. The fundamental truths, such as that God exists, or that quarks are not composed of smaller particles, are explanatorily fundamental, but I can't find a way to structure propositions in such a way that it answers this intuition, since neither logical nor ontological relations work. In the next section I argue that this intuition can be salvaged in a different way.

5. Degrees of truth

Denying 3 means claiming that some true propositions are truer than others. One way this has been claimed – usually in response to the liar or sorites paradox and their relatives – is that there is some kind of intermediate truth value, something between true and false. (Kripke, for example, uses the strong Kleene valuation system, which has an intermediate truth value.Footnote ¹¹) Whatever its merits are for dealing with the paradoxes, it is insufficient here. The intuitive differences in the value of truth are not reflected in the differences in truth on these theories. Consider an intermediate-truth-value response to the paradoxes of vagueness: pin the continuum of vague properties onto truth, so the proposition that Joe is bald, for example, will be true to just the degree that Joe is bald. This doesn't answer our intuitions about the value of truth, since we don't consider the proposition that Joe is bald (assuming Joe to be completely hairless, so the proposition that Joe is bald to be true without reservation) to be among the most valuable of truths. For a similar reason, intermediate-truth-value responses to the liar paradox won't work. On these responses, everything is equally true (and hence, on the assumption that it is truth that makes a proposition valuable, equally valuable), except the liar proposition and its relatives.

What these approaches have in common that suits them ill for addressing the puzzle of the value of truth is that they set an upper bound to truth. This is necessary for doing logic. Valid arguments preserve truth, and this is so even if the logic has more than two truth values. In this case we need to revise the truth tables for the standard operators, but this is easily done: conjunctions, for example, take the minimum of the truth values of the conjuncts, and disjunctions take the maximum. Negations need an upper bound: the truth of ~p is 1–p, where 1 is the highest truth value. But if there is no upper bound to the value of truth, a negation will invalidate any argument in which it's a premise.

But even though logic requires an upper bound to truth, neither beauty nor morality is like this: given any sculpture, there could be a sculpture that is more beautiful; given any action, there could be an action more heroic. These properties have no upper bound. So if truth comes in degrees, and these degrees are sufficient to explain its value, these degrees must go all the way up. Just as there is no upper bound to the amount of beauty or moral goodness something can have, so too, if truth is evaluative, there can be no intrinsic maximum to the amount of truth a proposition can have. This seems to be an unresolvable tension. If truth is adequate for logic, it must be binary, or at least have an upper bound. If truth is evaluative, it cannot have an upper bound. So it seems that a single concept cannot be preserved in logical inference and be evaluative.

What would a concept of limitless truth look like? It might look something like what we find in Plato. In the divided line section of the Republic, the sections of the line are arranged in proportion in terms of how much truth the objects possess (511e2–4), and thus Plato claims that some truths are truer than others. But he also makes clear that the highest level is not commonplace. Very little – only the Good – is true in this highest sense,Footnote ¹² and attaining knowledge of this highest level of truth is an extraordinary accomplishment. The Good is infinitely true, in the sense that everything else follows from it (511b, 516b, 517c), and, save this, there is no limit to the value of truth. We can summarize the Platonic position in two theses:

Degrees of Truth is the denial of thesis 3. Degrees of Truth and No Upper Bound, together with theses 1 and 2, are enough to explain the value of truth. (I don't claim that this is a historically accurate reading of Plato. It's not, at least in that the Good may be a counterexample to No Upper Bound. It is not Plato's theory, but it is a Platonic theory.Footnote ¹³)

A concept of truth that obeys these two theses, together with theses 1 and 2 from the original puzzle, may be evaluative, but cannot be the concept of truth used in logic. Indeed, such a concept of truth is counterintuitive, as it claims that the proposition that God exists (or its denial) or the proposition that quarks are not composed of smaller particles (or its denial) is more true than the proposition that the strawberries are on the table. Surely this is a gross violation of intuition. The one is more important, perhaps more valuable, but not more true.

But perhaps this is not a universal intuition. Sometimes people (not usually philosophers) distinguish Big-T-Truth from little-t-truth. One way to parse this distinction is to say that Truth is important and truth is not. We can use this distinction to explain how it is that truth can be binary and yet valuable: our concept of truth is a conflation of two different concepts. One of them, call it ‘Truth’, is variable, and behaves according to the Platonic theses above. The other, call it ‘truth’, is binary (or, perhaps, there is an intermediate truth value to avoid the paradoxes). (Or, if you like, you can call them ‘evaluative truth’ and ‘logical truth’, or truth_e' and ‘truth_l’, or ‘shmuth’ and ‘truth’.) These are two different concepts, and they obey different rules. But they are not completely unrelated. A proposition cannot be True without being true, even if two propositions that are equally true may have wildly different levels of Truth.

These two concepts are related in a way similar to moral goodness and moral permissibility. Permissibility is a binary property that supervenes on goodness, a variable property. Two actions with different levels of goodness may both be equally permissible – i.e., permissible simpliciter. So with truth. There one property – truth – that is binary, and another – Truth – that is variable. The two properties are intimately related, but are nevertheless distinct.

The difference between denying thesis 2 and denying thesis 3 turns on the difference between taking propositions to be what stands in need of explanation and taking facts or obtaining states of affairs as being what stands in need of explanation. (A fact, in this sense, is something other than a true proposition.) The grounding relation between propositions discussed in section 4 claims that it is propositions that are explained. If, however, facts are what stand in need of explanation, it is, in the first place, facts that are hierarchical – some facts are more fundamental than others; for all facts a and b, if a explains b, then a is more fundamental than b. We can establish a derivative hierarchy of propositions, of course: if proposition p correspondsFootnote ¹⁴ to fact a, and proposition q corresponds to fact b, and a is more fundamental than b, then p is more True than q. Assuming a realist conception of truth (whether correspondence or deflationist) it seems natural to use the word ‘truth’ to describe a property that involves correspondence to fact.

Prima facie there are three relationships that might be used to construct a hierarchy of propositions of the kind needed to explain the value of truth: the propositions' relation to the world, their relation to each other, and their relation to us. The second and third were rejected in section 4. I am arguing here for the first: a proposition is more valuable than another because of its connection to the world, and it seems natural to refer to this with the name ‘truth’, and it seems natural to see how this can be confused with ‘logical’ truth to give rise to the original puzzle.

This is a solution to the original puzzle. In fact, truth is not valuable – the property that logic studies is not valuable. Any intuition that truth is valuable comes from confusing it with a different concept, Truth. But, even though this solves the puzzle, it doesn't constitute a full theory of the value of truth, as I have only sketched what it is that makes one proposition Truer than another. But a full theory of the value of truth may not be the sort of thing that can be presented in less than a book. It is at least equal in difficulty to a full theory of the value of beauty. What is it that makes one object more beautiful than another? Until we have an account of Truth that specifies how to work out the Truth value of a given proposition, any theory of Truth will be partial.