Truth

For the use of "true" and "false" in formal logic, see Logic.


The question, "what is truth?", is much debated by theologians, philosophers, and logicians.

One conventional way of approaching the subject, is to determine the sorts of things that can be true or false. Such truth bearers include statements, propositions, beliefs, sentences and thoughts.

The central problem concerning the notion of truth is to analyse what it means to say of a statement or proposition P that it is true. Intuitively, a statement or proposition P is true if it says of such-and-such a state of affairs, that it is the case. As Aristotle put it in his Metaphysics (Book 4),

To say of what is, that it is, or of what is not, that it is not, is true.

A special class of questions that can be asked about truth concern whether this property is objective (roughly, whether a truth bearer is true depends on the facts of reality) or relative to us (e.g., it depends only upon our beliefs, culture, language, point of view, etc.). Theories of truth which adopt the former view are called objectivist and those which adopt the latter view are called relativist. Philosophers generally discuss these questions as issues of epistemology, and ethics, for example; which are issues upon which the idea of truth has a crucial bearing. Accordingly, moral absolutism, relativism, realism, anti-realism, and so forth, are various approaches to the issues crucially impacted by the decision of the question, "what is truth?". We see below that the epistemic theories of truth involve questions concerning the subject ("me","we","they") and the state-of-affairs (concerning which "I", for example, may make statements which are either true or not true).

Table of contents
1 Four standard conceptions of truth
2 The Correspondence Conception of Truth
3 The Deflationary Conception of Truth
4 The Semantic Conception of Truth
5 The Epistemic Conception of Truth
6 Philosophy
7 Quote
8 See also
9 References

Four standard conceptions of truth

There are, roughly speaking, four broad conceptions of truth that philosophers and logicians have discussed:

  1. The Correspondence Conception of Truth
  2. The Deflationary Conception of Truth
  3. The Semantic Conception of Truth
  4. 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 these four headings. Many commonly-heard attempts to define the notion of 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 these conceptions here:

The Correspondence Conception of Truth

Consider first the correspondence theory, associated with Plato, Aristotle, G. E. Moore, Bertrand Russell, 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." That's a traditional formulation of the theory. So let's try to explain what it says. For example, it's 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 (that's not hard to suppose). Then we can improve our example. We could say: it's 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: it's 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 this relation of 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 that's still puzzling, isn't it? I mean, when does a proposition "match up" with a fact? To say that "correspondence" means "matching up" doesn't 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. See Richard Kirkham's book cited below for a discussion of this view.

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, we've 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 don't have to talk about correspondence at all. We just say: it's 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 it?s a fact that some dogs bark.

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

  • (4c) The proposition that snow is white is true if it?s 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 aren't we just letting this other word, fact, do all the work of the word we're confused about, 'true'? And then wouldn't 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: facts are basically combinations of objects together with their properties or relations; so the fact that Fido barks is the combination of an object (i.e., Fido) with one of Fido's 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 you've got an answer to the question, "What are facts?" You say: it's 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, it's for each part of a fact to exist. So if Fido exists, and Fido's barking exists, then the fact that Fido bark exists. And that's what makes it true to say that Fido barks. That's a very appealing way to answer the objection.

The Deflationary Conception of Truth

Another way, which has been perhaps even more popular, particularly in the last 30 years, is to offer an even further stripped-down theory. First, observe that if I say "It's a fact that P", I might as well have just said, "P". If I say, for example, that it's a fact that some dogs bark, then why don't I just say, "Some dogs bark"? Why do I have to declare that it's a fact? If I'm saying it, then I'm implying that it's 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 don?t we just say "P" in place of "it is a fact that P"? I mean, suppose I?m right, and when I say "It?s 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 don't talk about facts at all. So here's the new, even further stripped-down theory:

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

That's it! Statements of the form (T) are often called T-sentences. And some recent philosophers and logicians have argued that that's basically all there is to say about truth. To understand the notion of truth is to understand and accept all the T-sentences (and to reason in accordance with the equivalence of "P is true" and P).

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. It's 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 (see Horwich 1998, Truth). And a version called Disquotationalism, which has been developed by Hartry Field (see Field 2001 Truth and the Absence of Fact). 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 if 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 if 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 there's one simple objection to the theory that might occur to you. You might say: "Well, if I claim, 'Pigs fly', then the deflationary theory says that it's true that pigs fly! If I claim that philosophy is simple, then it's true that philosophy is simple!" This is a bad objection. It's bad because it has the deflationary theory wrong. The deflationary theory doesn't say: "It's true that P iff I claim that P." It says: "It's true that P if P." So, if pigs fly, if pigs do indeed fly, then it's true that pigs fly. Nothing wrong with saying that: that's correct. If pigs did fly, then it would be true that pigs fly. But that's quite different from saying that, if I claim that pigs fly, then it's true that pigs fly. So the deflationary theory doesn't say that whatever anyone says is true. What it does say is that, if I say something, then I'm 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, "It's true that God exists! It's true that there is a supreme being!" Have I added anything to my original claim when I say that it's true? I mean, have I added anything other than emphasis and a declaration that I really do believe what I'm 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 there's got to be some reason why we came up with this word "true". The redundancy version of deflationism says basically that it's only a term of emphasis. But is that really all it is? Isn't 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.

Here, we do not have a quotation of a specific sentence or an expression of the form "that P". Rather, we have a term "The last thing Plato said" and this indirectly refers to some statement or proposition. 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".

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. Part of Tarski's motivation in developing this conception of truth was to resolve the Liar paradox and this led Tarski to several interesting mathematical discoveries. In particular, Tarski's Indefinablity Theorem, which is similar to Goedel's Incompleteness Theorem. 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, in 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 introduced further ideas, such as the distinction between object language and meta-language (which is important in avoiding the semantic paradoxes such as the Liar Paradox).

For a language L containing ~ ("not"), & ("and"), v ("or") and quantifiers ("for all" and "there exists"), Tarski's inductive definition of truth looks like this:

  • (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)".

These explain how the truth conditions of complex sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their constituents. The simplest constituents are atomic sentences, and Tarski defined truth for these as follows:

  • (vi) An atomic sentence F(x1,...,xn) is true (relative to an assignment of values to the variables x1, ..., xn)) if the corresponding values of variables bear the relation denoted by the predicate F.

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. Tarski himself seems to have intended his account to be a refinement of the classical correspondence theory.

The Epistemic Conception of Truth

Coherence Theory

Another conception of truth that differs drastically from the previous conceptions (the correspondence theory, the deflationary theories and Tarski's semantic conception) is the Epistemic Conception of Truth. Our first example of this is called Coherence Theory. This conception of truth 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:

Roughly, P is true if it coheres with a system of propositions that it's part of. Typically a "system of propositions" is understood as a group of propositions that someone 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 doesn't 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 isn't 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. Conseqeuntly, the coherence theory is better regarded as a theory about when beliefs are justified than as a theory about when beliefs are true.

Consensus Theory

A related class of epistemic theories of truth, popular with sociologists and those who emphasize that all statements are social, interpersonal acts, is the Consensus Theory of Truth. In its most elementary form it says roughly that,

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

This account of truth seems obviously mistaken. For a proposition might be accepted by a community and yet be false (there are countlessly many examples). Similarly, a proposition might be true and yet rejected by the members of a community. According to this primitive version of Consensus Theory, which defines consensus in terms of actual beliefs that prevail in a group or society, when people believed that the Earth was flat, the proposition "The Earth is flat" was true, even though the Earth wasn't in fact flat. So, quite clearly, this analysis of truth is a non-starter.

Furthermore, a primitive version Consensus Theory based on factual consensus implies both relativism and anti-fallibilism. It says that whether a statement is true depends upon a perspective, and so a statement may be "true" for one community and yet "false" for another. Closely connected, the theory is also anti-fallibilist: it implies that mistakes and errors are impossible. According to primitive Consensus Theory, one simply cannot be mistaken about things, at least so long as one agrees with one's own community. (Note that the Correspondence, Deflationary and Semantic Conceptions are fallibilist, since they separate truth from belief.)

For these reasons (and others), no serious contemporary philosopher accepts a Consensus Theory of truth based on factual consensus.

Pragmatism

Two further epistemic theories of truth were introduced by the American philosophers, Charles Peirce (pronounced "purse") and William James in the late 19th and early 20th centuries. Peirce's theory is called long run pragmatism. William James's theory is more usually associated with the term "pragmatic theory of truth'. Both theories are, however, examples of the Epistemic Conception of Truth, since they closely relate the notion of truth to the notions of belief, acceptance and justification.

Peirce's version, roughly stated is:

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

So, Peirce's long-run pragmatist theory of truth is rather like the Consensus Theory mentioned above, but in order to avoid its problems, it is a long-run and idealized version of consensus. Truth is what consensus will be at 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 if human inquiry (truth-seeking) adopted the scientific method, then it would, at some point converge and reach a limit; there would be basically no questions left to be answered, and the resulting systems of beliefs would be both true and even complete. 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 that's 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.

One appeal of this theory is that it is anti-sceptical. It implies that the truth is knowable: it implies that if something is true, then it can be known to be true (in the ideal limit of scientific inquiry). Now, suppose you thought that all truth is knowable. In that case, all truths could be known in the ideal limit of inquiry. In the perfect science all truths would be known. There wouldn't 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.

William James's version of the pragmatic theory of truth is roughly,

  • (15) The proposition that P is true iff P is useful to believe (or: believing P "works").

James's version of pragmatism was been taken up by later philosophers such as John Dewey and, most controversially, Richard Rorty.

Several objections are commonly made to pragmatist account of truth, of either sort. First, a sceptical objection: maybe there are some truths that aren't knowable. What reason is there to think that every true proposition must be knowable? Is it not possible that there are some true propositions that we can't 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 can't 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 appears that there might be 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.

A second objection, due originally to Bertrand Russell (1907) in a discussion of James's theory, is that pragmatism mixes up the notion of truth with epistemology. 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? There's a difference between stating an indicator and giving the meaning. For example, when the streetlights turn at the end of a day, that's 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 isn't what "truth" means.

Russell's objection isn't so much an argument against pragmatism, so much as it is a request -- that we make sure that we aren't confusing an indicator of truth with the meaning of the concept truth. There is a difference between the two and pragmatism confuses them.

There are many other objections to pragmatism. For example, how do we define what it means to say a belief "works"? Or that it is "useful to believe"? Presumably, it is sometimes useful to tell lies. In this case, pragmatism implies that lies can be true. Presumably this is an absurd conclusion. Suppose that religion is useful to believe. Then, according to James's theory, it is true. But why should it follow that God exists merely because believing that God exists is useful? More worryingly, in the Soviet Union under Stalin, certain beliefs concerning biology were adopted because they were "useful to believe" and this led to what is called Lysenkoism.

Another objection---which can be applied to all of the epistemic theories---is that pragmatism appears to be incompatible with the T-scheme mentioned above (and Tarski's inductive definition, in relation to the connecitves ~, & and so on). According to the T-scheme, if ~A is true, then A is not true. But presumably both a proposition A and its negation ~A might be useful to believe, which contradicts the T-scheme. For any determinate proposition A, either A is true or ~A is true. But it might be that neither is useful to believe. And so on.

A final objection is that pragmatism of James's variety (and Rorty's) entails both relativism and infallibilism. What is useful for you to believe might not be useful for me to believe. It follows that "truth" for you is different from "truth" for me (and that the relevant facts don't matter). This is relativism. Furthermore, if I consistently believe what is useful (for me) to believe, then (according to James's pragmatism) I never makes mistakes: I am infallible, on James's account. Indeed, everyone is infallible, at least insofar as they believe what is useful to believe. This seems like an absurd consequence of (James's version of) pragmatism.

A viable, more sophisticated consensus theory of truth, a mixture of Peircean theory with speech-act theory and social theory, is that presented and defended by Jürgen Habermas, which sets out the universal pragmatic conditions of ideal consensus and responds to many objections to earlier versions of a pragmatic, consensus theory of truth. Habermas distinguishes explicitly between factual consensus, i.e. the beliefs that happen to hold in a particular community, and rational consensus, i.e. consensus attained in conditions approximating an "ideal speech situation", in which inquirers or members of a community suspend or bracket prevailing beliefs and engage in rational discourse aimed at truth and governed by the force of the better argument, under conditions in which all participants in discourse have equal opportunities to engage in constative (assertions of fact), normative, and expressive speech acts, and in which discourse is not distorted by the intervention of power or the internalization of systematic blocks to communication.

Philosophy

After this very brief discussion of theories of truth, we note that contemporary philosophers tend to favor either some revised correspondence theory, or the semantic conception of Tarski or some deflationary theory; but we just haven't 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 and consensus theories and pragmatism).

With such a variety to choose from at the very least you should be convinced that you don't have to rest content with any sort of relativism that says that truth is just the same as belief.

Quote

See also

References

[1] 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.

[2] Field, H. 2001. Truth and the Absence of Fact. Oxford.

[3] Horwich, P. Truth. Oxford.

[4] Habermas, Jürgen. 2003. Truth and Justification. MIT Press.

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

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

[7] Williams, Bernard. 2002. Truth & Truthfulness: an essay in genealogy. Princeton University Press




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