NECESSARY TRUTH

The philosophical problem of truth is actually a nest of problems. There is, first, the question “What is truth? And that is different from the question “What are the criteria (or tests) of truth?” A further question is how we justify truth claims. And closely related to all these is the problem of truth-bearers, that is, “What types of entity can properly be said to be true or false?” The problem of necessary truth is similarly manifold. The question “What is necessary truth?” is a different one from the question “What are the criteria of necessary truth?” And both of these are different from the question “How is necessary truth to be justified?” Finally, there is the difficult problem of what types of thing can properly be said to be necessarily true. It seems plausible to say here, however, that whatever we come up with to fulfill the role of truth-bearer will also qualify as a vehicle for necessary truth.

The close relations between the problems of truth and the problems of necessary truth have been generally overlooked in the literature on both subjects. Let me comment briefly on these relations. First, one of the main objections to the correspondence theory of truth is that it seems not to leave room for necessary truth. Necessary truths do not seem to correspond to experienceable situations in the physical world as do contingent truths. For example, although we know what it would be to observe that John is taller than Bill, we do not understand what it would be to observe that if John is taller than Bill then Bill is shorter than John. This latter proposition seems not to square with the correspondence theory, for its truth seems not to be a matter of correspondence with reality. This shows, I think, that it is incumbent on theorists of truth to deal in some way with the problem of necessary truth.

A second relation between the two topics is that one’s list of criteria of truth must include at least one criterion of necessary truth. If necessary truth is a kind of truth, then obviously our test(s) for necessary truth need to be included among out tests for truth. Similarly for justifications of truth-claims. Whatever we list as ways to justify truth-claims needs to include ways to justify claims of necessary truth.

Finally, there is this point. Theoreticians seeking to define and account for necessary truth must always bear in mind that it is a kind of truth. They must not come up with a theory of necessary truth that makes it impossible to give a general account of truth. For example, if they were to claim that necessary truth is truth by convention, then it is incumbent upon them to explain what truth is in such a way as to allow for the possibility of truth by convention. Some theories of truth, such as the correspondence theory, may not qualify for this role. The upshot of all this is that every account of truth needs to include an account of necessary truth, and vice versa: everyone who claims that there is such a thing as necessary truth is obliged to tell us what truth in general might be. I hope to have covered the latter topic in my essay, entitled “Correspondence with Reality.” So I turn, then, to the other issue, the nature of necessary truth.

Some theories reject the very existence of necessarily true propositions. One of those theories is possibilism, the claim that everything is possible and nothing is impossible. Obviously this entails that there is no such thing as necessary truth. I find possibilism to be incoherent and will not try to make sense of it here. There are clear examples of necessary truth, such as “1+1=2,” “All bachelors are unmarried,” “Triangles have three sides,” etc., so any theory which denies that has got to be wrong.

Another theory which rejects the idea of necessary truth is that form of conventionalism which classifies the statements of logic and mathematics as mere formal rules, and hence not to be spoken of as “true” or “false” at all. My objection to this theory is that we do speak of mathematical truth and logical truth, and it seems intuitively plausible to do so. Ask the average man whether it is true that 7+5=12. If he is not a philosopher, he will say yes. Any theory that runs counter to our ordinary usage on this matter should certainly be regarded as implausible. Of course, this is not enough to refute the view in question, but we would certainly prefer a theory that allows for the existence of necessary truth to a theory that doesn’t. Let us turn, then, to such theories. If all of them are found deficient, then (and only then) would we wish to reconsider the idea that our commonplace belief in necessary truth is erroneous and mistaken.

Of the various theories that allow for necessary truth, there are three that are of particular importance and need close attention. I shall call these the “truth by convention” approach, the “a prioricity” approach, and the “unthinkability” approach.

According to the “truth by convention” approach, a necessarily true statement is one that is true in virtue of the rules or conventions of the language or system in which it is expressed. Thus, to say of the English sentence “All fathers are males” that it is necessarily true is to say of it that it is the rules of English, especially the definition of the word “father,” that make it true. And to say that the arithmetical formula “7+5=12” is necessarily true is to say that that formula is a consequence of the rules and conventions of our system of arithmetic.

I have three main objections to this view. The first is that it is not sentences that are necessarily true, but rather propositions. And these are not linguistic entities; they are not part of (nor determined by) any language or system of symbols. We say, for example, “Otto believes that snow is white (or all fathers are male)” even if Otto speaks no English. The object of his belief (a proposition) is not some item in Otto’s native language. Therefore, rules or conventions of language could not be what makes any proposition true.

My second objection is that conventions are relative. What is in accord with one set of conventions may not be in accord with another set. Furthermore, conventions can be changed and are thus time-dependent. It would therefore follow from the “truth by convention” approach that necessary truth is relative and time-dependent, which, of course, is an intolerable consequence. No one who believes that there is such a thing as necessary truth could allow that it is something which is relative and time-dependent.

Finally, the very idea of “truth by convention” is incoherent. I see no way to reconcile it with the correspondence theory of truth. Roderick Chisholm is right: truth is correspondence with reality. But one cannot determine or alter reality by stipulating conventions. So the very notion of “correspondence with reality by convention” is a bogus idea from the start. So much, then, for conventionalism as a theory of necessary truth.

I turn now to the “a prioricity” approach, which identifies necessary truth with a priori truth. A statement is said to be true a priori if and only if it can be known to be true by human beings independently of any confirmatory sensory experience. I have two main objections to this theory.

First, to define “necessary truth” as “truth which can be known by humans independently of experience” is to give a circular definition. It is circular because of the word “can” which appears in it. That is just another modal operator, like the term “necessary.” To say “X can be known” is equivalent to saying “it is not necessary for X to be unknown.” Thus, the definition of “necessary truth” in question implicitly uses the very concept of necessity in its formulation. Hence, the definition needs to be rejected as circular.

My second objection to the “a prioricity” approach is that there are counter-examples to it. Not all necessary truths need be a priori truths. Consider, for example, the unproven Goldbach conjecture, that every even number is the sum of two prime numbers. Either this proposition or its negation is a necessary truth. Yet it may be that neither of them is an a priori truth, for it may be that neither of them will ever be known to be true by any human. In other words, we can be quite sure that one of the two propositions is a necessary truth but we cannot be sure that either of them is an a priori truth, for we have no reason to believe that either of them will ever come to be known by anyone.

Another type of counter-example is one which shows that not all a priori truths need be necessary truths. Suppose, for example, that humans in the future develop the ability to transmit contingent knowledge by the use of drugs or diet or brain operations. Then such knowledge would be a priori, yet contingent. For example, suppose a brain operation is performed on Mr. X who did not previously know anything about astronomy. As a result of the operation, he comes to know, say, that the sun is 93 million miles away. He did not acquire that contingent fact by any sort of sensory experience. Hence, it is something which can be known independently of sensory experience, which makes it a priori. So it would be both a priori and contingent. The mere possibility of this sort of counter-example is enough to refute the a prioricity approach.

I come, finally, to what I call the “unthinkability” approach. According to this view, a necessary truth is simply one the negation of which is unthinkable. Here, too, circularity seems to be a fatal flaw. What can “unthinkable” mean except “necessarily unthought”? To say of a proposition that it is impossible to think it is only to say that it is necessary that no one think it. Therefore, to define “necessary truth” in terms of “unthinkability” is to give a circular definition, one that already contains the idea of necessity implicitly within it.

There would be no problem here if we were only called upon to define the “truth component” of necessary truth, for we already have the correspondence theory to help us with that. We could say that a necessary truth is a proposition that corresponds with a necessary state of affairs. But our present problem is not with the “truth component” but with the concept of necessity. How are we to define that? If we say that a necessary truth is a proposition that corresponds with a necessary state of affairs, then we are still left with the problem of defining “necessary state of affairs.” Some define a “necessary state of affairs” as one that obtains in all possible worlds. But that won’t do because of circularity. A possible world is nothing more than a world the nonexistence of which is not necessary, so we would end up defining “necessary” in terms of “possible” and “possible” in terms of “necessary.” It is clear that if we are to define “necessary” then it must be done in nonmodal terms, but I see no way whatever for that to be done. As the philosopher G. E. Moore might have said, the concept of necessity is simple and unanalyzable and therefore verbally indefinable.

An analogy with the way an intuitionist construes ethical properties may be helpful here. Just as the term “good” is indefinable, so also the term “necessary” is indefinable. Just as we need to appeal in some way to intuition to ascertain that an action or state is good, so also we need to appeal to some sort of intuition to ascertain that a state of affairs in necessary. In answer to the question “What makes an action good?” the intuitionist replies, “It just is, that’s all.” Similarly, in answer to the question “What makes a state of affairs necessary?” I am constrained to reply, “It just is, that’s all.” The point here is that it is not humans and their apprehension of a state of affairs that makes the state of affairs necessary. It bears its necessity within itself, independently of all thought. The state of affairs of 1+1 equaling 2 would still be necessary even if there were no minds. Similarly, it is not our apprehension of an act that makes it morally right or wrong, according to the intuitionist. Rather, rightness and wrongness are properties that acts have in and of themselves, independently of all thought or apprehension. (I do not mean here to agree with ethical intuitionism, only to use it as an analogy.) Finally, just as an intuitionist might appeal to the concept of an ideal observer to get around the prima facie subjectivity of moral intuition, so also I could appeal to the concept of an ideal observer to defend the objectivity of our intuitions about the necessity of various states of affairs. In fact, this is essentially what I do in my book on type crossings (Type Crossings, Mouton & Co., 1966).

Let me elaborate slightly on that. In order for intuition to be an effective test of conceptual necessity, certain conditions must obtain. First, people who are to do the intuiting must understand exactly what they are doing. When confronted by the question “Is such-and-such state of affairs necessary?” they must thoroughly understand what is being asked. Among other things, they must be able to distinguish the relevant sense of “necessity” from other senses of “necessity” (such as “empirical necessity”). Second, they must know exactly what state of affairs is being asked about. If one person is talking about “1+1” in an arithmetical system of base 10 and another is talking about “1+1” in a binary system, then obviously they are talking about different things. In that case, suppose one were to say, “The state of affairs of 1+1 equaling 2 is necessary,” and the other were to reply, “Not so.” I would say that they are not really disagreeing with each other, for they are not talking about the same state of affairs. The position that I shall defend, then, is that when the conditions are right (i.e., the same state of affairs being talked about, the same concept of necessity being employed, etc.), then there would never be any disagreements about which states of affairs are necessary and which ones aren’t. That is, we all share the same intuitions about such matters.

So what are we to make of the concept of necessary truth? It seems to me to be indefinable. We simply intuit the necessity of necessary truths in somewhat like the way we are supposed (by the ethical intuitionist) to intuit the rightness or wrongness of actions. Perhaps unthinkability could be appealed to as a criterion or test of necessary truth, even if it cannot be used as a definition (because of the resulting circularity). Suppose you know what a certain proposition is in the sense that you know what combination of concepts it contains. Then you try to think that proposition (i.e., put together in thought its combination of concepts), but you fail. In that case, you could legitimately declare that the negation of the given proposition is a necessary truth. There is much here that needs to be clarified and made more precise, but it does not as yet seem hopeless to try to do that. (See the book Type Crossings for further discussion of the “unthinkability” approach.)

There is still the objection: how can the truth of mathematical formulas and other necessary truths be a matter of correspondence with reality? We do not experience such things in reality. As pointed out earlier, we know what it would be to observe that John is taller than Bill, but we do not know what it could be to observe that if John is taller than Bill then Bill is shorter than John. This latter relationship (which is a relation between propositions, not a relation between John and Bill) is too abstract to locate anywhere in the physical world. How, then, can it be a state of affairs that obtains out there?

One reply is perhaps dogmatic: let us just allow that some states of affairs obtain even though they are not observable by sense perception. Then we can include necessary states of affairs in that group. [Also included would be such non-observable states of affairs as the fact that it did not snow in Cuba in July of 1842, the fact that it will not snow in Cuba tomorrow, and the fact that if it had snowed here last night then I would not now be going outside with short sleeves.]

It might be objected that the idea of a necessary state of affairs, for example 1+1 equaling 2, is a very obscure idea. What is accomplished by clinging to such a difficult notion? It seems to me that two things are accomplished. First, some coherent way of treating the problems of necessary truth is provided without going to such lengths as to deny the very existence of necessary truth. And second, truth can then be defined by some version of the correspondence theory. Both of these results are intuitively satisfying. It is plausible to maintain that there definitely are necessary truths, and it is also in accord with our intuitions about truth to define it as some sort of correspondence with reality. After all, what is truth? Truth is when you tell it like it is; everyone knows that!

There is another reply that might be made. Near the end of the essay “Correspondence with Reality” (which is immediately prior to this one on the website), I formulated a version of the correspondence theory referred to as “definition (D).” The problems that have to do with states of affairs and the relation of correspondence do not arise in connection with (D) since it does not make any appeal to those notions. As was pointed out, the main difficulty with definition (D) seems to lie in its application to complex propositions. It could be a bit difficult to sort all that out, but it does not seem impossible. There always seem to be certain properties or relations ascribed to some thing or things and the truth of the proposition could be said to lie in whether or not the thing(s) do indeed have the properties or relations in question, complex as the matter might be. Assuming, as suggested in the given essay, that all those problems can be adequately solved, we can say that (D) provides us not only with an answer to the question “What is truth?” but also with an answer that is applicable to necessary truths as well.