COHERENCE THEORY OF TRUTH

The coherence theory is one of the two traditional theories of truth, the other being the correspondence theory. The coherence theory is characteristic of the great rationalist system-building metaphysicians Gottfried Wilhelm Leibniz, Benedict (Baruch) de Spinoza, G. W. F. Hegel, and Francis Herbert Bradley; but it has also had a vogue with several members of the logical positivist school, notably Otto Neurath and Carl Gustav Hempel, who were much influenced by the systems of pure mathematics and theoretical physics. According to the coherence theory, to say that a statement (usually called a judgment) is true or false is to say that it coheres or fails to cohere with a system of other statements; that it is a member of a system whose elements are related to each other by ties of logical implication as the elements in a system of pure mathematics are related. Many proponents of the theory hold, indeed, that each member of the system implies every other member. To test whether a statement is true is to test it for coherence with a system of statements. The system with which all true statements must cohere is said by its logical positivist supporters to be that accepted by the scientists of the contemporary culture. The metaphysical supporters of coherence, on the other hand, insist that a statement cannot properly be called true unless it fits into the one comprehensive account of the universe or reality, which itself forms a coherent system. In either case, no statement can be known to be true until it is known to cohere with every other statement of the system; where the system consists of all true statements, such knowledge is unattainable.

It is not altogether possible to give a plausible exposition of the theory independently of its close historical links with rationalist and idealist metaphysics, but the account might go something like this.

In practice, we sometimes reject as false an ordinary person's assertions—for instance, that he saw a ghost—or even a scientist's results—for instance, in experiments on extrasensory perception—on the ground that they do not cohere with the other commonsense or scientific views that we also hold as true.

Meaning of Truth

In the exact and reputable science of pure mathematics, the logical test for the truth or acceptability of any proposition is whether it coheres with some of the other propositions, and ultimately with the axioms, of its system. In this test, which is not merely a practical one, for a proposition to cohere with other propositions is for it to be logically deducible from them. Further, this coherence is what we mean by calling such a proposition true.

internal relations

It is characteristic of the parts of a logical system like that of pure mathematics that no part would be what it is if its relations to the other parts were different from what they are. Thus, 2 would not be the number we associate with the numeral 2 if it were the third of 4 instead of the half of 4 or the cube root of 27 instead of the cube root of 8. Hence, it is said, the meaning and the truth of, for instance, "2 + 2 = 4" are bound up with the meaning and the truth of all the other statements in the arithmetical system; and our knowledge of its meaning and its truth is bound up with our knowledge of their meaning and their truth. This principle that nothing would be what it is if its relations to other things were different—which is called the doctrine of internal relations—holds, say the metaphysical supporters of coherence, for every element, whether in thought or in reality. For example, they argue that we would not even understand, much less know the truth or falsity of, a statement about something blue if blue were "divorced in our thought from all the colours in the spectrum to which it is related by likeness and difference, all the shades within its own range, and all the definition it possesses in virtue of being thought as a quality rather than as a substance or a relation" (Brand Blanshard, The Nature of Thought, Vol. II, p. 316). Further, not only would we not know the meaning or truth of such a statement, but it also cannot properly be said to have its meaning or truth-value independently of its relations to other statements. The statement "Caesar crossed the Rubicon in 49 BCE" is said to be pregnant with a meaning "owing to the concrete political situation within which it took place" that it would not otherwise have.

degrees of truth

A corollary of the principle of internal relations and of the coherence theory in general is the doctrine of degrees of truth. If the truth of any given statement is bound up with, and can only be seen with, the truth of all the statements of the system and thus is bound up with the whole system, it is argued that individual statements as such are only partly true—and, therefore, partly false—while only the whole system is wholly true. "Truth," said Bradley, "must exhibit the mark of expansion and all-inclusiveness."

Criterion of Truth

Coherence theorists might admit that their arguments hitherto have been drawn from the nature of the a priori reasoning typical of mathematics and metaphysics; but some have also claimed that an examination of the a posteriori reasoning of the empirical sciences and ordinary life also supports the theory, not only as giving the meaning of "truth" but also as giving the test of truth (ibid., pp. 226–237). In testing for truth it is obvious, runs the claim, that coherence is our only criterion when dealing with statements about the past. No one can now compare the statement that the battle of Hastings was fought in 1066 with anything else than other statements, such as those that occur in documents, history books, or works of art. However, we can contrast with this a statement about something present, such as "There is a cat on the mat." If asked how you would test this, your reply might be "I would look and see. If what I saw corresponded to what was asserted, I would call the judgment true." However, you are assuming that "there is some solid chunk of fact, directly presented to sense and beyond all question, to which thought must adjust itself" (ibid., p. 228). What you take and use as a fact is really "another judgement or set of judgements, and what provides the verification is the coherence between the initial judgement and these" (ibid.). Consider how much of your previous experience and education, how great an exercise of your powers of conceptualization, has gone into your perception of the cat on the mat; how much, in a word, your supposed perception of fact is really a judgment, since, without a stock of judgments, what is seen could never be identified as a cat and a mat, respectively. Your test of the truth of the judgment that there is a cat on the mat or your comparison with what was there turns out to be a comparison of the original judgment with another judgment. This example, in addition, shows not only that coherence is the test or criterion of truth, but also that it gives the meaning of "truth," for it shows that the truth of the tested judgment consists in its coherence with other judgments and not with something other than a judgment.

Assumptions of the Theory

The arguments used by supporters of the coherence theory rest on various assumptions about meaning, fact, thought, and judgment that are linked partly with the impression made on them by the a priori reasoning of mathematics and logic and partly with their theory of knowledge.

a priori as paradigm of truth

Metaphysics is traditionally nonempirical; its conclusions are a priori deductions from certain tenets, such as George Berkeley's "To be is to be perceived" or Zeno's analysis of infinity. The conceptual statements typical of philosophy—such as that no one can know what is false, that no one can know what has not yet been proved, or that no one can know what is going to be—are true or false because of logical relations between such concepts as knowledge, truth, proof, and the future. Further, ever since Plato, mathematics has been the metaphysician's ideal; Leibniz's system was based on certain principles that he held to characterize logic and mathematics, and Spinoza's famous book on ethics is subtitled "proved in geometrical order." Some of the logical positivists, because of their training in mathematics and theoretical physics, sought to establish all knowledge as a vast system of logically interrelated statements expressed in the language of physics. In such systems, the criterion of truth is indeed the coherence of the statement under consideration with at least some other members of the system.

Criticism

Coherence of a statement with other members of the system is not sufficient to prove the coherence theory of truth. First, the a priori statements typical of pure mathematics, unlike the empirical statements of science and everyday life, serve not to give information about characteristics of objects in the world but to show the various conclusions that can be derived from a given set of axioms and a given set of rules for operating on them. It is no objection to the truth of a given mathematical statement that there are or may be other systems with whose members it does not cohere or that it is a member of a system with no application to the world.

However, it is an objection to coherence as the meaning of "truth" or as the only criterion of truth that it is logically possible to have two different but equally comprehensive sets of coherent statements between which there would be, in the coherence theory, no way to decide which was the set of true statements. To reject a particular empirical statement like "He saw a ghost" because it conflicts with the body of our beliefs is not to assimilate the judgments of everyday life to those of mathematics, since this rejection, unlike the analogous one in mathematics, is made only because we think the body of our everyday beliefs has already been shown to be true of the world. Coherence of one judgment with another is accepted as a practical test of truth only because the second judgment is independently accepted as true.

Metaphysical supporters of the coherence theory distinguish their comprehensive system from particular systems such as those of mathematics by linking it to experience by means of their theory of knowledge, which assimilates what is thought, what is experienced, and what is. This appeal to experience and reality is indeed an inconsistency in the metaphysical version of the coherence theory, but it is more sensible than the position of the logical positivist supporters of the theory, who, in the name of consistency, allow that mutually incompatible but internally coherent systems of statements differ not in truth but only in the historical fact that our contemporaries have adopted one of the systems.

Second, there is in the a priori statements typical of mathematics and philosophy a close connection between meaning and truth. Such statements as "Twice two is half of eight" or "What is known cannot be false" are true in virtue of the meanings of the words that express them; it is because the meanings of the words are internally related as they are that these statements are true. It is not because of the relations between the meanings of "knowledge" and "breakfast," however, that it is true that no one knows what Pompey had for breakfast on the day he was murdered, nor is it because of the relations between the meanings of "two" and "four" that it is true that I made two mistakes on page four of my typescript.

Third, even within mathematics coherence gives the criterion, not the meaning, of truth. Mathematical statements are true in virtue of the criterion of coherence with each other, whereas it would seem that empirical statements are true in virtue of the criterion of correspondence with the nature of the world. However, to say that either kind of statement is true is to say that what it asserts is a fact. Whether "X is Y " is a mathematical or an empirical statement, if "X is Y " is true, then it is a fact that X is Y.

Fourth, even when confined to mathematics, the coherence doctrine of degrees of truth does not seem tenable. The fact that a given statement in mathematics is not true unless it coheres with some (or even all) other statements in the system does not imply that it is not itself wholly true; it could at most imply that it does not give the whole truth.

Ambiguities in degrees of truth

It is worth pointing out here how the theory of degrees of truth depends for its plausibility and its air of paradox on various ambiguities. There are at least three different ways in which we may qualify truth. First, we commonly ask how true something is, meaning how much truth is there in it, and commonly reply that it is partly, entirely, or perfectly true. For example, [in 1967] the report that African-Americans in the southern U.S. have been deprived of their right to vote might be said to be not quite true, either on the supposed grounds that they have been denied the opportunity to exercise their right rather than been deprived of it or that, although there has been a deprivation of the right, it is women who have been deprived.

Second, instead of asking how much truth there is in something, we may quite differently ask how much of the truth there is in it. To ask how much truth there is in something is to ask how much of what is not true is included; to ask how much of the truth there is in something is to ask how much of what is true is not included. A particular statement could be perfectly true without containing more than a minute proportion of the whole truth. Being wholly true is not the same as being the whole truth, nor is being partly true the same as being part of the truth. What is only partly true is necessarily partly false, but what is part of the truth may be entirely true.

Third, we can, in the case of general statements like "Water boils at 100° C," ask how far or under what conditions is it true. It may, for example, be true of water at sea level but not at high altitudes.

When coherence theorists say that every statement is only partly true, they usually seem to mean that every statement is only part of the truth, since nothing but the whole system of statements can give the whole of the truth. What they mean, therefore, is quite correct but wrongly expressed, because they have confused the first and the second of the above qualifications of truth. A typically ambiguous assertion is Blanshard's remark that "the trueness of a proposition is indistinguishable from the amount of truth it contains." At other times, as in their discussion of mathematical statements, by "degrees of truth" they mean "true in certain conditions." Thus, the statement "2 + 2 = 4" is said to be only partly true, as it is true in pure mathematics but not necessarily in all applied fields. Here again, what is meant is correct enough—not that such statements are not perfectly true, but that they are not universally true. The main reason, however, for the coherence theorists' belief in degrees of truth is based on a mistaken deduction from their doctrine of internal relations. Because each statement is, according to this doctrine, logically connected with other statements, it follows both that the truth of each statement is dependent on the truth of other statements and that our knowledge of its truth depends on our knowledge of the truth of these other statements. What appears to be true might turn out to be false when its further connections become known. Hence, it is said, "a given judgement is true in the degree to which its content could maintain itself in the light of a completed system of knowledge." This conclusion, however, is mistaken. A statement can be perfectly true in itself even though it would not have been true unless it had been connected in certain ways with other true statements; and it can be perfectly true whether we know this or not.

epistemological assumptions

The second main influence in the usual defense of the coherence theory—that of a particular theory of knowledge—can be seen most prominently in the argument for transforming the commonsense belief that a statement (or judgment) is true if and only if it corresponds to facts into the doctrine that the judgment is true if and only if it coheres with another judgment or set of judgments. The first move in this transformation is from (a ) "'There is a cat on the mat' is true if and only if it corresponds to the fact that there is a cat on the mat" to (b ) "'There is a cat on the mat' is true if and only if it corresponds to the situation described as 'There is a cat on the mat.'" This is an illegitimate move, however, since a fact is not a situation, an event, or an object; otherwise we would have to postulate negative and conditional situations, events, and objects, to be described by such statements as "It is a fact that no one has yet succeeded in doing this" and "It is a fact that anyone who did succeed would be munificently rewarded." Hence, even if the moves designed to show that the situations, events, and objects we discover are not independent of our method of discovering them were valid, they would not show that facts are not independent of our methods of discovering them.

The second move in the transformation is from (b ) "'There is a cat on the mat' is true if and only if it corresponds to the situation, event, or object describable as 'There is a cat on the mat'" to (c ) "'There is a cat on the mat' is true if and only if it corresponds to what is verified to be a cat on the mat." This is illegitimate, however, since (b ) is an explanation, although a false one, of the meaning of "true," whereas (c ) contains the reason why someone might hold that there is a cat on the mat. Something can be true without anyone's knowing it to be true, although, of course, no one would sincerely say it was true unless he thought he knew it was. Idealist supporters of the coherence theory, like Bradley, move easily from (b ) to (c ) because they tend to identify reality with experience and knowledge, what is with what is experienced or with what is known. Further, they move distractingly to and fro between assertions about truth and assertions about the truth (the whole truth, the ultimate truth, a part of the truth), from assertions about the notion of truth to assertions about that which actually happens to be true. Thus, they speak of the identity of reality and truth when they mean the identity of reality and the truth, that is, what is true.

The third move in the transformation is from (c ) "'There is a cat on the mat' is true if and only if it corresponds to what is verified to be a cat on the mat" to (d ) "'There is a cat on the mat' is true if and only if it corresponds to a verification, or an experience, that would be expressed in the judgment (or, in logical positivist language, "the observation statement") 'I see (or there is) a cat on the mat.'" Because of this move they rule out the correspondence theory as a test of the truth of statements about the past, since there can be no verifying experience about what happened in the past. This move, too, is illegitimate because it assimilates what is verified, or experienced, to the verification, or experience, of it—the cat on the mat that I perceive to my perception of the cat on the mat. Such an assimilation is a standard part of the theory of knowledge of the Idealist metaphysicians, but an analogous assimilation is made by some logical positivists who, in their talk about observation statements, do not carefully distinguish between the report of what is discovered and that of which it is a report. Having reached (d ), the coherence theorist then emphasizes how much our previously acquired powers of judgment are exercised in this experience. He concludes that the second term with which our original judgment that there is a cat on the mat corresponds is not, as we thought, a fact; it is really another judgment or set of judgments.

Whether the whole argument is designed to show that correspondence is really coherence when the correspondence is put forward as giving the nature of truth or only when it is put forward as giving the criterion of truth, it seems equally invalid.

What the coherence theory really does is to give the criteria for the truth and falsity of a priori, or analytic, statements. Any attempt to change the meaning of "coherence" from coherence with other statements to coherence with fact (or reality of experience) is to abandon the theory. A merit of the theory is that it sees that the reasons for calling an analytic statement true or false are not those which some correspondence theorists, primarily thinking of empirical statements, try to fasten on all statements. When it sets itself up as the theory of truth, its mistake is twofold. First, it suggests that the criteria appropriate to a priori, or analytic, statements apply to every kind of statement; what the metaphysicians really did was to suppose all statements to be a priori.

Second, it confuses the reasons, or criteria, for calling a statement true or false with the meaning of "truth" or "falsity." As far as the criteria of truth are concerned, we can say only of a priori, or analytic, statements that they are true because they cohere with each other, and only of empirical statements that they are true because of what the world is like; however, as far as the meaning of truth is concerned, we can say of any kind of statement that it is true if it corresponds to the facts. Thus, as well as saying that a true a priori statement coheres with other statements in the system, we can also say that it corresponds to the a priori facts. It may be a fact that the sum of the angles of a Lobachevskian triangle is less than two right angles and also that the field of Waterloo is a mile square. What we must remember is that although both sorts of statements, if true, state the facts—tell us how things are—this amounts to something different in the two cases; the size of the angles of a Lobachevskian triangle is not something in the world in the way that the size of the field of Waterloo is.

See also Analytic and Synthetic Statements; Blanshard, Brand; Bradley, Francis Herbert; Coherentism; Correspondence Theory of Truth; Fallacies; Hegel, Georg Wilhelm Friedrich; Hempel, Carl Gustav; Idealism; Leibniz, Gottfried Wilhelm; Logical Positivism; Neurath, Otto; Rationalism; Spinoza, Benedict (Baruch) de; Truth.

Bibliography

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Bibliography updated by Benjamin Fiedor (2005)