Truth
Philosophers are interested in a constellation of issues involving the concept of truth. A preliminary issue, although somewhat subsidiary, is to decide what sorts of things can be true. Is truth a property of sentences (which are linguistic entities in some language or other), or is truth a property of propositions (nonlinguistic, abstract and timeless entities)? The principal issue is: What is truth? It is the problem of being clear about what you are saying when you say some claim or other is true. The most important theories of truth are the Correspondence Theory, the Semantic Theory, the Deflationary Theory, the Coherence Theory, and the Pragmatic Theory. They are explained and compared here. Whichever theory of truth is advanced to settle the principal issue, there are a number of additional issues to be addressed:
- Can claims about the future be true now?
- Can there be some algorithm for finding truth – some recipe or procedure for deciding, for any claim in the system of, say, arithmetic, whether the claim is true?
- Can the predicate “is true” be completely defined in other terms so that it can be eliminated, without loss of meaning, from any context in which it occurs?
- To what extent do theories of truth avoid paradox?
- Is the goal of scientific research to achieve truth?
Table of Contents
- The Principal Problem
- What Sorts of Things are True (or False)?
- Correspondence Theory
- Tarski’s Semantic Theory
- Coherence Theories
- Pragmatic Theories
- Deflationary Theories
- Related Issues
- References and Further Reading
1. The Principal Problem
The principal problem is to offer a viable theory as to what truth itself consists in, or, to put it another way, “What is the nature of truth?” To illustrate with an example – the problem is not: Is it true that there is extraterrestrial life? The problem is: What does it mean to say that it is true that there is extraterrestrial life? Astrobiologists study the former problem; philosophers, the latter.
This philosophical problem of truth has been with us for a long time. In the first century AD, Pontius Pilate (John 18:38) asked “What is truth?” but no answer was forthcoming. The problem has been studied more since the turn of the twentieth century than at any other previous time. In the last one hundred or so years, considerable progress has been made in solving the problem.
The three most widely accepted contemporary theories of truth are [i] the Correspondence Theory ; [ii] the Semantic Theory of Tarski and Davidson; and [iii] the Deflationary Theory of Frege and Ramsey. The competing theories are [iv] the Coherence Theory , and [v] the Pragmatic Theory . These five theories will be examined after addressing the following question.
2. What Sorts of Things are True (or False)?
Although we do speak of true friends and false identities, philosophers believe these are derivative uses of “true” and “false”. The central use of “true”, the more important one for philosophers, occurs when we say, for example, it’s true that Montreal is north of Pittsburgh. Here,”true” is contrasted with “false”, not with “fake” or “insincere”. When we say that Montreal is north of Pittsburgh, what sort of thing is it that is true? Is it a statement or a sentence or something else, a “fact”, perhaps? More generally, philosophers want to know what sorts of things are true and what sorts of things are false. This same question is expressed by asking: What sorts of things have (or bear) truth-values?
The term “truth-value” has been coined by logicians as a generic term for “truth or falsehood”. To ask for the truth-value of P, is to ask whether P is true or whether P is false. “Value” in “truth-value” does not mean “valuable”. It is being used in a similar fashion to “numerical value” as when we say that the value of “x” in “x + 3 = 7″ is 4. To ask “What is the truth-value of the statement that Montreal is north of Pittsburgh?” is to ask whether the statement that Montreal is north of Pittsburgh is true or whether it is false. (The truth-value of that specific statement is true.)
There are many candidates for the sorts of things that can bear truth-values:
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a. Ontological Issues
What sorts of things are these candidates? In particular, should the bearers of truth-values be regarded as being linguistic items (and, as a consequence, items within specific languages), or are they non-linguisticitems, or are they both? In addition, should they be regarded as being concrete entities, i.e., things which have a determinate position in space and time, or should they be regarded as abstract entities, i.e., as being neither temporal nor spatial entities?
Sentences are linguistic items: they exist in some language or other, either in a natural language such as English or in an artificial language such as a computer language. However, the term “sentence” has two senses: sentence-token and sentence-type. These three English sentence-tokens are all of the same sentence-type:
- Saturn is the sixth planet from the Sun.
- Saturn is the sixth planet from the Sun.
- Saturn is the sixth planet from the Sun.
Sentence-tokens are concrete objects. They are composed of ink marks on paper, or sequences of sounds, or patches of light on a computer monitor, etc. Sentence-tokens exist in space and time; they can be located in space and can be dated. Sentence-types cannot be. They are abstract objects. (Analogous distinctions can be made for letters, for words, for numerals, for musical notes on a stave, indeed for anysymbols whatsoever.)
Might sentence-tokens be the bearers of truth-values?
One reason to favor tokens over types is to solve the problems involving so-called “indexical” (or “token reflexive”) terms such as “I” and “here” and “now”. Is the claim expressed by the sentence-type “I like chocolate” true or false? Well, it depends on who “I” is referring to. If Jack, who likes chocolate, says “I like chocolate”, then what he has said is true; but if Jill, who dislikes chocolate, says “I like chocolate”, then what she has said is false. If it were sentence-types which were the bearers of truth-values, then the sentence-type “I like chocolate” would be both true and false – an unacceptable contradiction. The contradiction is avoided, however, if one argues that sentence-tokens are the bearers of truth-values, for in this case although there is only one sentence-type involved, there are two distinct sentence-tokens.
A second reason for arguing that sentence-tokens, rather than sentence-types, are the bearers of truth-values has been advanced by nominalist philosophers. Nominalists are intent to allow as few abstract objects as possible. Insofar as sentence-types are abstract objects and sentence-tokens are concrete objects, nominalists will argue that actually uttered or written sentence-tokens are the proper bearers of truth-values.
But the theory that sentence-tokens are the bearers of truth-values has its own problems. One objection to the nominalist theory is that had there never been any language-users, then there would be no truths. (And the same objection can be leveled against arguing that it is beliefs that are the bearers of truth-values: had there never been any conscious creatures then there would be no beliefs and, thus, no truths or falsehoods, not even the truth that there were no conscious creatures – an unacceptably paradoxical implication.)
And a second objection – to the theory that sentence-tokens are the bearers of truth-values – is that even though there are language-users, there are sentences that have never been uttered and never will be. (Consider, for example, the distinct number of different ways that a deck of playing cards can be arranged. The number, 8×1067 [the digit "8" followed by sixty-seven zeros], is so vast that there never will be enough sentence-tokens in the world’s past or future to describe each unique arrangement. And there are countless other examples as well.) Sentence-tokens, then, cannot be identified as the bearers of truth-values – there simply are too few sentence-tokens.
Thus both theories – (i) that sentence-tokens are the bearers of truth-values, and (ii) that sentence-types are the bearers of truth-values – encounter difficulties. Might propositions be the bearers of truth-values?
To escape the dilemma of choosing between tokens and types, propositions have been suggested as the primary bearers of truth-values.
The following five sentences are in different languages, but they all are typically used to express the same proposition or statement.
Saturn is the sixth planet from the Sun. [English] Saturn je šestá planeta od slunce. [Czech] Saturne est la sixième planète la plus éloignée du soleil. [French] [Hebrew] Saturn er den sjette planeten fra solen. [Norwegian]
The truth of the proposition that Saturn is the sixth planet from the Sun depends only on the physics of the solar system, and not in any obvious way on human convention. By contrast, what these five sentences say does depend partly on human convention. Had English speakers chosen to adopt the word “Saturn” as the name of a different particular planet, the first sentence would have expressed something false. By choosing propositions rather than sentences as the bearers of truth-values, this relativity to human conventions does not apply to truth, a point that many philosophers would consider to be a virtue in a theory of truth.
Propositions are abstract entities; they do not exist in space and time. They are sometimes said to be “timeless”, “eternal”, or “omnitemporal” entities. Terminology aside, the essential point is that propositions are not concrete (or material) objects. Nor, for that matter, are they mental entities; they are not “thoughts” as Frege had suggested in the nineteenth century. The theory that propositions are the bearers of truth-values also has been criticized. Nominalists object to the abstract character of propositions. Another complaint is that it’s not sufficiently clear when we have a case of the same propositions as opposed to similar propositions. This is much like the complaint that we can’t determine when two sentences have exactly the same meaning. The relationship between sentences and propositions is a serious philosophical problem.
Because it is the more favored theory, and for the sake of expediency and consistency, the theory that propositions – and not sentences – are the bearers of truth-values will be adopted in this article. When we speak below of “truths”, we are referring to true propositions. But it should be pointed out that virtually all the claims made below have counterparts in nominalistic theories which reject propositions.
b. Constraints on Truth and Falsehood
There are two commonly accepted constraints on truth and falsehood:
Every proposition is true or false. [Law of the Excluded Middle.] No proposition is both true and false. [Law of Non-contradiction.]
These constraints require that every proposition has exactly one truth-value. Although the point is controversial, most philosophers add the further constraint that a proposition never changes its truth-value in space or time. Consequently, to say “The proposition that it’s raining was true yesterday but false today” is to equivocate and not actually refer to just one proposition. Similarly, when someone at noon on January 15, 2000 in Vancouver says that the proposition that it is raining is true in Vancouver while false in Sacramento, that person is really talking of two different propositions: (i) that it rains in Vancouver at noon on January 15, 2000 and (ii) that it rains in Sacramento at noon on January 15, 2000. The person is saying proposition (i) is true and (ii) is false.
c. Which Sentences Express Propositions?
Not all sentences express propositions. The interrogative sentence “Who won the World Series in 1951?” does not; neither does the imperative sentence “Please close the window.” Declarative (that is, indicative) sentences – rather than interrogative or imperative sentences – typically are used to express propositions.
d. Problem Cases
But do all declarative sentences express propositions? The following four kinds of declarative sentences have been suggested as not being typically used to express propositions, but all these suggestions are controversial.
1. Sentences containing non-referring expressions
In light of the fact that France has no king, Strawson argued that the sentence, “The present king of France is bald”, fails to express a proposition. In a famous dispute, Russell disagreed with Strawson, arguing that the sentence does express a proposition, and more exactly, a false one.
2. Predictions of future events
What about declarative sentences that refer to events in the future? For example, does the sentence “There will be a sea battle tomorrow” express a proposition? Presumably, today we do not know whether there will be such a battle. Because of this, some philosophers (including Aristotle who toyed with the idea) have argued that the sentence, at the present moment, does not express anything that is now either true or false. Another, perhaps more powerful, motivation for adopting this view is the belief that if sentences involving future human actions were to express propositions, i.e., were to express something that is now true or false, then humans would be determined to perform those actions and so humans would have no free will. To defend free will, these philosophers have argued, we must deny truth-values to predictions.
This complicating restriction – that sentences about the future do not now express anything true or false – has been attacked by Quine and others. These critics argue that the restriction upsets the logic we use to reason with such predictions. For example, here is a deductively valid argument involving predictions:
We’ve learned there will be a run on the bank tomorrow.
If there will be a run on the bank tomorrow, then the CEO should be awakened.
So, the CEO should be awakened.
Without assertions in this argument having truth-values, regardless of whether we know those values, we could not assess the argument using the canons of deductive validity and invalidity. We would have to say – contrary to deeply-rooted philosophical intuitions – that it is not really an argument at all. (For another sort of rebuttal to the claim that propositions about the future cannot be true prior to the occurrence of the events described, see Logical Determinism.)
3. Liar Sentences
“This very sentence expresses a false proposition” and “I’m lying” are examples of so-called liar sentences. A liar sentence can be used to generate a paradox when we consider what truth-value to assign it. As a way out of paradox, Kripke suggests that a liar sentence is one of those rare declarative sentences that does not express a proposition. The sentence falls into the truth-value gap. See the article Liar Paradox.
4. Sentences that state moral, ethical, or aesthetic values
Finally, we mention the so-called “fact/value distinction.” Throughout history, moral philosophers have wrestled with the issue of moral realism. Do sentences such as “Torturing children is wrong” – which assert moral principles – assert something true (or false), or do they merely express (in a disguised fashion) the speaker’s opinions, or feelings or values? Making the latter choice, some philosophers argue that these declarative sentences do not express propositions.
3. Correspondence Theory
We return to the principal question, “What is truth?” Truth is presumably what valid reasoning preserves. It is the goal of scientific inquiry, historical research, and business audits. We understand much of what a sentence means by understanding the conditions under which what it expresses is true. Yet the exact nature of truth itself is not wholly revealed by these remarks.
Historically, the most popular theory of truth was the Correspondence Theory. First proposed in a vague form by Plato and by Aristotle in his Metaphysics, this realist theory says truth is what propositions have by corresponding to a way the world is. The theory says that a proposition is true provided there exists a fact corresponding to it. In other words, for any proposition p,
p is true if and only if p corresponds to a fact.
The theory’s answer to the question, “What is truth?” is that truth is a certain relationship—the relationship that holds between a proposition and its corresponding fact. Perhaps an analysis of the relationship will reveal what all the truths have in common.
Consider the proposition that snow is white. Remarking that the proposition’s truth is its corresponding to the fact that snow is white leads critics to request an acceptable analysis of this notion of correspondence. Surely the correspondence is not a word by word connecting of a sentence to its reference. It is some sort of exotic relationship between, say, whole propositions and facts. In presenting his theory of logical atomism early in the twentieth century, Russell tried to show how a true proposition and its corresponding fact share the same structure. Inspired by the notion that Egyptian hieroglyphs are stylized pictures, his student Wittgenstein said the relationship is that of a “picturing” of facts by propositions, but his development of this suggestive remark in his Tractatus Logico-Philosophicus did not satisfy many other philosophers, nor after awhile, even Wittgenstein himself.
And what are facts? The notion of a fact as some sort of ontological entity was first stated explicitly in the second half of the nineteenth century. The Correspondence Theory does permit facts to be mind-dependent entities. McTaggart, and perhaps Kant, held such Correspondence Theories. The Correspondence theories of Russell, Wittgenstein and Austin all consider facts to be mind-independent. But regardless of their mind-dependence or mind-independence, the theory must provide answers to questions of the following sort. “Canada is north of the U.S.” can’t be a fact. A true proposition can’t be a fact if it also states a fact, so what is the ontological standing of a fact? Is the fact that corresponds to “Brutus stabbed Caesar” the same fact that corresponds to “Caesar was stabbed by Brutus”, or is it a different fact? It might be argued that they must be different facts because one expresses the relationship of stabbing but the other expresses the relationship of being stabbed, which is different. In addition to the specific fact that ball 1 is on the pool table and the specific fact that ball 2 is on the pool table, and so forth, is there the specific fact that there are fewer than 1,006,455 balls on the table? Is there the generalfact that many balls are on the table? Does the existence of general facts require there to be the Forms of Plato or Aristotle? What about the negative proposition that there are no pink elephants on the table? Does it correspond to the same situation in the world that makes there be no green elephants on the table? The same pool table must involve a great many different facts. These questions illustrate the difficulty in counting facts and distinguishing them. The difficulty is well recognized by advocates of the Correspondence Theory, but critics complain that characterizations of facts too often circle back ultimately to saying facts are whatever true propositions must correspond to in order to be true. Davidson has criticized the notion of fact, arguing that “if true statements correspond to anything, they all correspond to the same thing” (in “True to the Facts”, Davidson [1984]). Davidson also has argued that facts really are the true statements themselves; facts are not named by them, as the Correspondence Theory mistakenly supposes.
Defenders of the Correspondence Theory have responded to these criticisms in a variety of ways. Sense can be made of the term “correspondence”, some say, because speaking of propositions corresponding to facts is merely making the general claim that summarizes the remark that
(i) The sentence, “Snow is white”, means that snow is white, and (ii) snow actually is white,
and so on for all the other propositions. Therefore, the Correspondence theory must contain a theory of “means that” but otherwise is not at fault. Other defenders of the Correspondence Theory attack Davidson’s identification of facts with true propositions. Snow is a constituent of the fact that snow is white, but snow is not a constituent of a linguistic entity, so facts and true statements are different kinds of entities.
Recent work in possible world semantics has identified facts with sets of possible worlds. The fact that the cat is on the mat contains the possible world in which the cat is on the mat and Adolf Hitler converted to Judaism while Chancellor of Germany. The motive for this identification is that, if sets of possible worlds are metaphysically legitimate and precisely describable, then so are facts.
4. Tarski’s Semantic Theory
For an illustration of the theory, consider the German sentence “Schnee ist weiss” which means that snow is white. Tarski asks for the truth-conditions of the proposition expressed by that sentence: “Under what conditions is that proposition true?” Put another way: “How shall we complete the following in English: ‘The proposition expressed by the German sentence “Schnee ist weiss” is true …’?” His answer:
| T: | The proposition expressed by the German sentence “Schnee ist weiss” is true if and only if snow is white. |
We can rewrite Tarski’s T-condition on three lines:
- The proposition expressed by the German sentence “Schnee ist weiss” is true
- if and only if
- snow is white
Line 1 is about truth. Line 3 is not about truth – it asserts a claim about the nature of the world. Thus T makes a substantive claim. Moreover, it avoids the main problems of the earlier Correspondence Theories in that the terms “fact” and “correspondence” play no role whatever.
A theory is a Tarskian truth theory for language L if and only if, for each sentence S of L, if S expresses the proposition that p, then the theory entails a true “T-proposition” of the bi-conditional form:
| (T) | The proposition expressed by S-in-L is true, if and only if p. |
In the example we have been using, namely, “Schnee ist weiss”, it is quite clear that the T-proposition consists of a containing (or “outer”) sentence in English, and a contained (or “inner” or quoted) sentence in German:
| T: | The proposition expressed by the German sentence “Schnee ist weiss” is true if and only if snow is white. |
There are, we see, sentences in two distinct languages involved in this T-proposition. If, however, we switch the inner, or quoted sentence, to an English sentence, e.g. to “Snow is white”, we would then have:
| T: | The proposition expressed by the English sentence “Snow is white” is true if and only if snow is white. |
In this latter case, it looks as if only one language (English), not two, is involved in expressing the T-proposition. But, according to Tarski’s theory, there are still two languages involved: (i) the language one of whose sentences is being quoted and (ii) the language which attributes truth to the proposition expressed by that quoted sentence. The quoted sentence is said to be an element of the object language, and the outer (or containing) sentence which uses the predicate “true” is in the metalanguage.
Tarski discovered that in order to avoid contradiction in his semantic theory of truth, he had to restrictthe object language to a limited portion of the metalanguage. Among other restrictions, it is the metalanguage alone that contains the truth-predicates, “true” and “false”; the object language does not contain truth-predicates.
It is essential to see that Tarski’s T-proposition is not saying:
| X: | Snow is white if and only if snow is white. |
This latter claim is certainly true (it is a tautology), but it is no significant part of the analysis of the concept of truth – indeed it does not even use the words “true” or “truth”, nor does it involve an object language and a metalanguage. Tarski’s T-condition does both.
