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Truth

Truth is not amenable to any simple, widely-agreed upon definition. The notion is the subject of much theorizing by philosophers, logicians and thinkers. There are at least two broad senses in which the term is used, however, which is important to note at the outset:

On the one hand, there is truth as a broad, abstract concept that is applied to propositions, thoughts, beliefs, etc. On the other hand, there is truth as a body of important, profound, perhaps spiritual belief--Truth with a capital "T".

Looking at the two extremes, the question, "What is truth?" is apt to be given two completely different sort of answers by different professions. Analytic philosophers approach the question offering closely-reasoned defenses of precisely-worded definitions. By contrast, for religionists and some essayists, the question is simply another way of asking such broad religious questions as "Does the world have a creator and if so, what is its nature?" and "What is the meaning or purpose of life?" Giving an answer to the philosophers' question clearly does not entail giving an answer to the religionists' questions, and conversely.

A third class of question can be asked about truth, namely, whether it is absolute (roughly, it simply depends on the facts of reality) or relative to us (e.g., it depends upon our beliefs, culture, language, etc.). Philosophers generally discuss this not specifically under the heading of truth but instead moral absolutism, relativism, realism, anti-realism, and various other headings. Probably the reason for this is that philosophers do not so often speak about relativism about all truths, but about particular classes of truths (or "truths"): moral, epistemological, and aesthetic, just to name a few.

When focusing on the topic of truth itself, philosophers are mainly engaged in formulating philosophical theories of truth. There are, roughly speaking, four broad conceptions of truth that philosophers and logicians have discussed:

(A) The Correspondence Conception of Truth
(B) The Deflationary Conception of Truth
(C) The Semantic Conception of Truth
(D) The Epistemic Conception of Truth

Almost any attempt you will see which attempts to define or analyze the notion of truth will fall under one of the first four headings. Almost all of the most common attempts to define truth fall under The Epistemic Conception, which (paradoxically) is the one rejected by almost all contemporary philosophers and logicians (see below). We shall briefly describe each here:

Table of contents

(A) The Correspondence Conception of Truth

Consider first the correspondence theory, associated with Plato, Aristotle, G. E. Moore, Bertrand Russell, George Orwell, Karl Popper, Noam Chomsky] and others. We can define it as follows:

  • (1) The proposition that P is true iff P corresponds with the facts.

So "truth" means "correspondence with the facts." Thatís a traditional formulation of the theory. So let's try to explain what it says. For example, itís true that some dogs bark if the proposition, "Some dogs bark," corresponds with the facts. Which facts? Actually, just one: the fact that some dogs bark. So suppose that it is a fact that some dogs bark (thatís not hard to suppose). Then we can improve our example. We could say: itís true that some dogs bark if, and only if, the proposition, "Some dogs bark," corresponds with the fact that some dogs bark. Or we could say: itís true that God exists if, and only if, the proposition, "God exists," corresponds with the fact that God exists.

The most commonly cited problem for the correspondence theory is this question: what is correspondence? When does a proposition correspond with the facts? Well, you can think of correspondence as a sort of matching-up relation -- if a proposition can be matched up with a fact, then it corresponds to that fact. But thatís still puzzling, isnít it? I mean, when does a proposition "match up" with a fact? To say that "correspondence" means "matching up" doesnít really shed a whole lot of light on the subject. (Bertrand Russell and shortly after, Ludwig Wittgenstein, suggested that proposition and fact "correspond" when their structure is isomorphic.)

Well, one thing we might observe in any case is that, in order for a proposition to be true, according to the correspondence theory, there must be some fact to which it corresponds. So a fact has to exist in order to be matched up a proposition. And remember, weíve already decided which fact that a proposition has to correspond with: the proposition that P has to correspond with the fact that P, if the proposition that P is true.

So here is a suggestion that can help get us around the objection about correspondence. We can say that it is true that P if, and only if, there exists a fact that P. If we put it like that, then we donít have to talk about correspondence at all. We just say: itís true that some dogs bark if, and only if, there exists a fact, that some dogs bark. And we could put it even simpler than that:

  • (2) The proposition that P is true iff it is a fact that P.

So consider that the revised version of the correspondence theory:

  • (3) P is true when it is a fact that P.

Examples of this might be:

  • (4a) The proposition that dogs bark is true if itís a fact that some dogs bark.

  • (4b) The proposition that God exists is true if itís a fact that God exists.

  • (4c) The proposition that snow is white is true if itís a fact that snow is white.

And so on. We can regard that as explaining what it means for a proposition to correspond with a fact: basically, if there is a fact that P, then that fact corresponds with the proposition that P.

But this reformulation of the theory faces now a different problem. Namely what are facts, and what does it mean to say that facts exist, or that there is some alleged fact? Look at the problem like this. Our reformulation basically says that "true proposition" means "factual proposition." So then we have to ask ourselves: "Have we really explained anything about truth, about true propositions, if we merely said that they are factual? Because then arenít we just letting this other word, Ďfactí, do all the work of the word weíre confused about, Ďtrueí? And then wouldnít we have to give some account of what facts are?"

There are at least two different ways to reply to this objection. The first way to reply is to actually offer a theory of what facts are. This is something that philosophers, this century, have actually tried to do. They say things like this: some facts are basically combinations of objects together with their properties or relations; so the fact that Fido barks is the combination of an object, Fido, with one of Fidoís properties, that he barks. But of course that is only one kind of fact; there would be other kinds of facts, about all dogs; or about the relation between dogs and cats; and so on. But the idea is that it is possible, anyway, to specify and categorize all those different kinds of facts. And then youíve got an answer to the question, "What are facts?" You say: itís one of these sorts of things (pointing to your theory of facts). And when it is asked, "What does it mean for a fact to exist?" you can answer: well, itís for each part of a fact to exist. So if Fido exists, and Fidoís barking exists, then the fact that Fido bark exists. And thatís what makes it true to say that Fido barks. That's a very appealing way to answer the objection.

(B) The Deflationary Conception of Truth

But there is another way, which has been perhaps even more popular, particularly in the last 30 years. And this is to offer an even further stripped-down theory. First, observe that if I say that itís a fact that P, I might as well have just said, "P". If I say, for example, that itís a fact that some dogs bark, then why donít I just say, "Some dogs bark"? Why do I have to declare that itís a fact? If Iím saying it, then Iím implying that itís a fact, am I not? Sure. Well notice that, in the previous theory of truth, these words occur: "it is a fact that P". So then why donít we just say "P" in place of "it is a fact that P"? I mean, suppose Iím right, and when I say "Itís a fact that P," I really mean nothing more than when I say "P." Then why not just substitute "P" in for "it is a fact that P" in our previous, revised correspondence theory? Then we donít talk about facts at all. So hereís the new, even further stripped-down theory:

  • (T) The proposition that P is true iff P.

Thatís it! Statements of the form (T) are often called T-sentences. And some people say that thatís basically all there is to say about truth. To understand the notion of truth is to understand and accept all the T-sentences.

The original version of this bare-bones theory was called "the redundancy theory of truth", and it is due to F. P. Ramsey and Alfred Ayer, English philosophers who wrote their works in the 1920s and 1930s. Itís called "the redundancy theory" because it basically implies that saying that something is true is always redundant. (This has loose connections with the "performative theory of truth", associated with Peter Strawson.)

The redundancy theory of truth is really a special version of what is now called The Deflationary Conception of Truth, or deflationism for short. Deflationism has two major versions. A version called Minimalism, which has been developed by Paul Horwich. And a version called Disquotationalism, which has been developed by Hartry Field. The minimalist theory takes truth bearers to be propositions and takes, as constituting the notion of truth, statements of the following form:

  • (T*) The proposition that P is true iff P.

The disquotational theory in contrast takes sentences as the central truth bearers, and its basic principles take the following form:

  • (T**) The sentence "P" is true iff P.

Roughly, statements of any of the forms (T), (T*) or (T**) are called "T-sentences", and deflationists take T-sentences to be central in characterizing the notion of truth.

The idea is that, instead of saying, "It is true that some dogs bark," you could, without loss of meaning, say simply, "Some dogs bark". In principle, we could always eliminate talk of truth, in favor of simply forthrightly asserting whatever it is that we say is true.

Now thereís one simple objection to the theory that might occur to you. You might say: "Well, if I claim, ĎPigs fly,í then the deflationary theory says that itís true that pigs fly! If I claim that philosophy is simple, then itís true that philosophy is simple!" This is a bad objection. Itís bad because it has the deflationary theory wrong. The deflationary theory doesnít say: "Itís true that P iff I claim that P." It says: "Itís true that P iff P." So, if pigs fly, if pigs do indeed fly, then itís true that pigs fly. Nothing wrong with saying that: thatís correct. If pigs did fly, then it would be true that pigs fly. But thatís quite different from saying that, if I claim that pigs fly, then itís true that pigs fly. So the deflationary theory doesnít say that whatever anyone says is true. What it does say is that, if I say something, then Iím committed to saying that what I said is true.

And this makes some sense. Suppose, on the one hand, I say, "God exists! There is a supreme being!" Then suppose on the other hand that I say, "Itís true that God exists! Itís true that there is a supreme being!" Have I added anything to my original claim when I say that itís true? I mean, have I added anything other than emphasis and a declaration that I really do believe what Iím saying? The redundancy version of deflationism thinks not; saying that something is true is only adding emphasis.

But some people disagree. They think that there is something that the redundancy theory is missing. They think thereís got to be some reason why we came up with this word "true." The redundancy version of deflationism says basically that itís only a term of emphasis. But is that really all it is? Isnít the idea, rather, that one specifically wishes to point to the fact that a proposition bears some relation to reality -- correspondence, describing the facts, something like that?

There is a second, and important, objection to the redundancy version of deflationism. We can eliminate "true" from a statement like,

  • (5) "Snow is white" is true.

to obtain just,

  • (6) Snow is white.

But we cannot do likewise when we attribute truth to a statement by some kind of indirect reference. For example,

  • (7) The last thing Plato said was true.

The redundancy view of truth provides no guidance for eliminating "true" from this statement. Ramsey himself was aware of this, and suggested something along the lines of the following

  • (8) (If the last thing Plato said was "Snow is white", then snow is white) and (If the last thing Plato said was "Penguins waddle", then penguins waddle) and (If the last thing Plato said was "Grass is pink", then grass is pink) and ... etc.

So, the idea is that we can eliminate "true" from (7) by using an infinitely long conjunction of statements of the form

  • (9) If the last thing Plato said was "P", then P.

Similarly, contemporary deflationists such as Horwich and Field do not in general advocate the older redundancy view, and do think that "true" is not merely a method of emphasis. First, both minimalists and disquotationalists argue that truth just is a property which satisfies the "equivalence condition" that P and "P is true" are equivalent. Second, disquotationalists have further argued that a property (or predicate) satisfying this condition has an important logical use, which permits one to express infinitely many statements all in one go. For example, if we wish to assert each statement that a mathematical theory T proves, we should have to list them all, and then say, one by one:

  • (10) S1, S2, S2, ...

The modern deflationists (following W.V. Quine) have pointed out that instead of asserting all of these particular statements, one can instead say simply:

  • (11) All theorems of T are true.

So, instead of asserting all the theorems of T one by one, you can simply say a single statement (6), "All theorems of T are true". Well, weíre not going to resolve that dispute now. The dispute quickly becomes very technical and draws a lot on results and problems in logic.

(C) The Semantic Conception of Truth

In some ways related to both the Correspondence Conception and the Deflationary Conception is the Semantic Conception of Truth, due to Alfred Tarski, a Polish logician who published his work on truth in the 1930s. Tarski took the T-sentences not to give the theory of truth itself, but to be a constraint on defining the notion of truth. That is, on Tarski's view, any adequate definition or theory of truth must imply all of the T-sentences (this constraint is known as Convention T). Tarski developed a rather complicated theory, involving what is known as an inductive definition of truth and further ideas, such as the distinction between object language and meta-language (which is important in avoiding the semantic paradoxes).

Tarski's inductive definition of truth included the following important principles:

  • (i) A negation ~A is true iff A is not true.

  • (ii) A conjunction A&B is true iff A is true and B is true

  • (iii) A disjunction A v B is true iff A is true or B is true.

  • (iv) A universal statement "for all x A(x)" is true iff each object satisfies "A(x)".

  • (v) An existential statement "there exists x A(x)" is true iff there is an object which satisfies "A(x)".

Tarski's semantic conception of truth plays an important role in modern logic and also in much contemporary philosophy of language. It is rather controversial matter whether Tarski's semantic theory should be counted as either a correspondence theory or as a deflationary theory.

(D) The Epistemic Conception of Truth

Letís take a quick look at another conception of truth, that differs quite a bit from the correspondence theory, the deflationary theories and Tarski's semantic conception. This is an example of the Epistemic Conception of Truth and is called the coherence theory, and is associated with the Idealist school of philosophers, such as Hegel and so on. The coherence theory offers another definition of "truth". It says that truth depends on coherence, as follows:

  • (12) The proposition that P is true iff P is part of a coherent system of propositions.

Roughly, P is true if it coheres with a system of propositions that itís part of. Typically a "system of propositions" is understood as a group of propositions that some one person believes. So if you like, you can think of "system of propositions" as meaning a belief system. It is because of this reference to beliefs and their justification that it is called an epistemic theory of truth. Then the idea is that if your belief system is coherent, then your beliefs are true. And if you come across a belief that doesnít cohere with the others, then you can toss it out as incoherent and thus false.

We shall not try and give an example of a coherent system or a belief that is true because it is part of the system. The reason isnít that the coherence theory is obviously wrong, but because the coherence theory is better regarded as a theory about justified belief, that is, when beliefs are justified or rational. The coherence theory is better regarded as a theory about when beliefs are justified than as a theory about when beliefs are true. Thatís my claim, anyway -- Iím telling you this only so you can understand why weíre not examining the theory in any depth right now. But when we look at the coherence theory of justification, I will give examples and criticisms that apply to coherence theories generally -- whether of truth or of justification.

A related epistemic theory of truth, popular with sociologists is the Consensus Theory of Truth, which roughly says that,

  • (13) The proposition that P is true relative to a community C iff all members of the community accept P.

Despite the popularity of this theory of truth, it is easy to see that it is very confused and false. For obviously a statement may be accepted and yet be false, and there are countless examples of this from history and current affairs. For example, if there is a consensus for some statement, say, "The USA is peaceful nation", then the consensus theory implies that this statement is true. And thus, it implies that the USA is a peaceful nation. This is a most counter-intuitive consequence of the consensus theory. Whether "The USA is a peaceful nation" is true or false depends upon the relevant facts, and not upon whether there is consensus concerning those facts. (Similar points were made by Russell and Orwell).

Pragmatism

Another epistemic theory was introduced by American philosophers, Charles Peirce (pronounced "purse") and William James, in the late 19th and early 20th centuries. Their theory is called pragmatism, or the pragmatic theory[?] of truth. Pragmatism is another example of the Epistemic Conception of Truth, since it closely relates the notion of truth to the notions of belief and justification.

"Pragmatism" is one of those neat words that philosophers like so much that they want to appropriate it for themselves, without regard to how it has been used before. As a result, the term "pragmatism" means a lot of different things to a lot of different people; there are lots of versions of pragmatism. One very important, influential version, is due to Peirce, and has received some renewed interest from some philosophers today, like Richard Rorty and Hilary Putnam. Peirceís version, roughly stated is:

  • (14) The proposition that P is true iff P is agreed upon in the consensus achieved at the ideal limit of inquiry.

So, the pragmatist theory of truth is rather like the Consensus Theory mentioned above, but it is a long-run and idealized version of consensus. Truth is what consensus will be the ideal limit of scientific inquiry. Peirce invites us to imagine what science will be like a few hundred, or perhaps a few thousand years from now. He predicted that human inquiry and truth-seeking would, or at the very least could, at some point come to an end, a limit; there would, he thought, be basically no questions left to be answered, and the state of human knowledge could not be improved upon. At that point there would be, he thought, some very general consensus, firmly agreed-upon, by all inquirers. And if some proposition now being considered would be something that everyone would agree on, in that ideal limit of inquiry, then that proposition is true. And thatís what it means to say that a proposition is true: that it is part of the consensus that would exist in the ideal limit of inquiry.

The appeal of this theory may be that the truth is knowable: if something is true, then it can be known to be true. Then what, really, is knowability? Well, something would be knowable if it could be known -- if not now, then by someone, somewhere down the road. So something is knowable if we could, after long hard careful inquiry, discover it.

Now, suppose you thought that all truth is knowable in this sense. In that case, everything that could be known, would be known in the ideal limit of inquiry. In the perfect science all truths would be known. There wouldnít be any truths left over. So then why not say that there is no more to truth than that what that perfect science would tell us? That would simplify matters. There would be no need to look for any sort of correspondence between propositions and the world, or between propositions and a coherent system of propositions. Truth, since it is knowable, is whatever the perfect science would tell us in the ideal limit of inquiry[?]. In that way pragmatism is very optimistic.

Two basic objections are commonly made to pragmatism. First, the standard objection of skeptics and realists: maybe there are some truths that arenít knowable. Why think that every proposition must be knowable? Why not say there are some true propositions that we canít ever know, not even in some ideal limit of inquiry? Let me give you an example. There are probably complex processes going on inside of black holes; but black holes are so gravitationally powerful that not even light can escape from them. So we could not possibly get knowledge of some specific events going on, right now, inside some black hole. Nonetheless there would seem to be some facts there; scientists might even know enough to be able to describe what might be going on; the point, though, is that they canít confirm that it is going on, even if they can describe, in generalities, what might be going on. So the first problem for pragmatism is that it certainly appears that there are some truths that would not appear in the perfected science in the ideal limit of inquiry -- because they cannot be known at all. You can probably think of more examples yourself; maybe truths about what went on in the minds of people long dead, or facts about very distant events. (This is called the "Problem of Buried Secrets".) Perhaps there are facts about subatomic particles which we cannot, in principle, ever know.

A second objection, due originally to Bertrand Russell, is that pragmatism describes an indicator or a sign of truth. It really cannot be regarded as a theory of the meaning of the word "true." Do you see the difference? Thereís a difference between stating an indicator and giving the meaning. For example, when the streetlights turn at the end of a day, thatís an indicator, a sign, that evening is coming on. It would be an obvious mistake to say that the word "evening" just means "the time that the streetlights turn on." In the same way, while it might be an indicator of truth, that a proposition is part of that perfect science at the ideal limit of inquiry, that just isnít what "truth" means.

Russell's objection isnít so much an argument against pragmatism, so much as it is a request -- that we make sure that we arenít confusing an indicator of truth with the meaning of the concept truth. There is a difference between the two and pragmatism confuses them.

Philosophy

After this very brief discussion of theories of truth, we note that contemporary philosophers tend to favor either some revised correspondence theory, some deflationary theory or the semantic theory; but we just havenít discussed them in enough depth to be able to say that with any certainty. But this survey introduces you to the terrain: among different conceptions of truth there are the correspondence conception, the deflationary conception (including the redundancy theory, minimalism and disquotationalism), Tarski's semantic conception and the epistemic conception (including the coherence theory and pragmatism).

With such a variety to choose from at the very least you should be convinced that you donít have to rest content with any sort of relativism that says that truth is just the same as belief.

Quote

  • "Truth - Something somehow discreditable to someone." - H.L. Mencken

References

[1] Kirkham, Richard 1992: Theories of Truth. Bradford Books. A very good reference book.

[2] http://www.ditext.com/tarski/tarski Tarski's classic 1944 paper on the Semantic Conception of Truth online.

[3] Blackburn, S and Simmons K. 1999. Truth. Oxford University Press. A good anthology of classic articles, including papers by James, Russell, Ramsey, Tarski and more recent work.

See also Truth-value.



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