theories of truthOverview

Not so much an introduction as a switch-back tour of Anglo-American approaches to philosophical truth. Most are treated more fully in other pages. But note the power of logic when sentences can be reduced to statements in a literal and unambiguous language.


What do we mean by calling something true? Most obviously we mean according with or corresponding to "the facts" — whatever those facts might be, or how we arrive at them. Logicians, however, would insist on being more specific, and in two ways. Given a sentence, they would first strip out the context, and then ensure that the remaining propositions could be simply true or false. Two simplifications, therefore. First the context is set aside: the who, when, how, why that every journalist covers is removed. Then the proposition itself is made to conform to a simple assertion of fact: expressions of belief, hope, wish, intention, etc. are ruled out of court. Such an approach may be remorselessly simplistic, reducing sentences to their simplest components, but the sentences then rest on assured foundations and can be built upon in logically sound ways.

The matter is often put in terms of two concepts: intension and extension. In a sentence They were marsupials. intension is whatever (anatomy, etc.) defines the set of marsupials, and extension is the set of entities referred to by the expression (what the sentence was talking about). The two concepts are clearly not the same, and one set can be full and the other empty: The marsupials that walk on the moon. The distinction is a convenient way of avoiding paradoxes, of avoiding contradictory statements about the same thing — the famous morning and evening star problem — but its larger use is in tying together sentence and the outside world. The extension is the state of affairs to which the sentence refers, and the intension is that which allows us to pick out the extension of the sentence in all possible worlds (the propositions). The world can then be viewed in the articulation of language. {1}

The Building Blocks: Propositions

So runs the theory, entirely necessary if logic is to prevail. If sentences (rather than propositions {2}) are to be made the carriers of truth then a statement true today may not have been so a year ago, or if spoken by someone else. A sentence like: he believed her makes its appeal not to logic but the common understanding of the human heart, the novelist's province. But he believed p, where p is some proposition that is either true or false, does make itself amenable to treatment.

Logical Operators

What treatment? Take a sentence like: John exists. We recast that as : There is something that is John, and that something is identical to John. Expressed symbolically that becomes: (∃ x) (x = John). Everything is green becomes: (∀ x) (Green (x)). Using the negative ~ we can express: everything is green as: it is not the case that everything is not green: ~ (∃ x) ( ~ green (x)). Is this helpful? Immensely so. Numbers can be defined in this way. Perplexing sentences like: The present King of France is bald can be re-expressed as a conjunction of three propositions: 1. there is a King of France, 2. there is not more than one King of France, and 3. everything that is a King of France is bald. Put another way, this becomes: there is an x, such that x is a King of France, x is bald, and for every y, y is a King of France only if y is identical with x. In symbols: (∃ x) (K(x) & b(x) &(y)(K(y) ⊃ (y =x))). {3}

Using connectives like &, ~, ∃, ⊃, ∀ (and, not, some, supposing, all) very complex sentences can be built up where the truth value of the whole sentence is dependent only on the truth values of its components. And by that we arrive not only at secure judgements, but see clearly how the individual propositions systematically play their part in the overall truth or falsity of the sentence.


But how do we handle logical paradoxes like the following statement by a Cretan: All Cretans are liars. If asserted by a Cretan, all of whom are liars, the statement must be false — which must mean that Cretans tell the truth. How can we stop sentences making these problems? Alfred Tarski's solution was to consider the primary sentence as written in an object language, and a sentence which asserted truth or falsity of the preceding sentence as written in a metalanguage. The sentences in the two languages look the same — All Cretans are liars — but the metalanguage includes the first statement and naturalizes its self-destructing form. The languages are not operating on the same level, and the object language cannot refer to the metalanguage.{4}

But dealing with such paradoxes is only one aspect of Tarski's theory of truth. The theory deals with two matters: the materially adequate and the formally correct. For the first he proposed that any acceptable definition of truth should have as consequence all instances of the schema (called a T schema) that: S is true iff p (S is true if and only if p is true). By this Tarski meant that p can be replaced by any sentence for which truth is being defined, and S is to be replaced by the equivalent sentence in the metalanguage. For example:

'snow is white' is true iff snow is white

The essential point is this: the schema is extensional, is looking outward to the material conditions that satisfy it. And it rules out many (but not all, and not always as expected {5}) other definitions of truth.

Now the formal correctness, a much more demanding matter. Tarski was trying to avoid semantic circularities — words calling on other words ad infinitum — and also the notorious vagueness of natural language with its metaphoric equivalents and partial paraphrases. Both languages, object and metalanguage, therefore had to be logically formulated, but the metalanguage was further obliged to follow the usual rules of definitions.

Is the T schema the definition of truth? No. The languages of the two sides are separate. Moreover, we should avoid anything that involved the meanings of the constituent words, which are not primitive, i.e. do not rest on things self-evident. Tarski's approach is through "satisfaction", which is a relation between open sentences and ordered n-tuples of objects. Open sentences are those with free variables. In the open sentence: A is south of B, we can replace A by London, and satisfy the sentence by replacing B with any town in southern Europe. What we are looking for, in short, are pairs of locations: the n of n-tuples here is 2. True sentences are therefore those satisfied by all just such sequences, and false sentences are those satisfied by none. That is the end of the matter. And a very short matter it is. Though Tarski sets out formally the concepts of reference, satisfaction and truth, the method seems somewhat as a stratagem to evade what philosophers have generally expected of truth.

Correspondence Theory of Truth

Let's turn to easier matters. We would agree with Ramsey and Russell {6} that nothing is gained by adding It is true that.... to some proposition. The phrase is transparent, adds nothing. If we call 'b' the sentence It is true that 'a' , and 'c' the sentence It is true that 'b', and so on round the alphabet, the original proposition 'a' will not be one iota different. Sentence 'z' will be equivalent to sentence 'a', would it not? But suppose each It is true that is added by a different person, with different expertise and/or motivations, would we not be a little less confident? And, even if assured on this point, would we not feel that truth does not apply in equal force to all judgements, that it is not a property common to all true sentences, i.e. external to them and independent of the route taken to arrive at propositions?

Such doubts introduce the notion of judgement. Many philosophers dislike the correspondence theory — that truth is something that corresponds to the facts — precisely because of this naive acceptance of "the facts." Even at its basic level, things in the world are not directly given to us: we make interpretations and intelligent integrations of our sensory experience, as Kant claimed and extensive studies of the physiology of perception show all too plainly.{7} Scientists make observations in ways guided by contemporary practice and the nature of the task in hand.

Other Theories of Truth: Coherence

What does this mean? That truth and meaning are mere words, brief stopping places on an endless web of references? No. If we want a truth and meaning underwritten entirely by logic — completely, each step of the way, with no possible exceptions — then that goal has not been reached. The match is close enough to refute the extravagant claims of Postmodernism, but not complete.

But perhaps the enterprise was always overambitious. After all, Russell and Whitehead's monumental attempt to base mathematics on logic also failed, and even mathematics can have gaps in its own procedures, as Gödel indicated.

So what other approaches are there? Two: the theory of coherence and that of pragmatism. The first calls something true when it fits neatly into a well-integrated body of beliefs. The second is judged by its results, the practical "cash value" of its contribution. Theories of coherence were embraced by very different philosophies, and pragmatism is currently enjoying a modest revival in the States.

Stated more formally, {8} the coherence theory holds that truth consists in a relation of coherence between beliefs or propositions in a set, such that a belief is false when it fails to fit with other mutually coherent members of a set. Though this concept of truth may seem more applicable to aesthetics or sociology, even a scientific theory is commonly preferred on the grounds of simplicity, experimental accessibility, utility, theoretical elegance and strength, fertility and association with models rendering such processes intelligible, on the very attributes of the coherence theory.{9}

But if the set of beliefs needs to be as comprehensive as possible, what is to stop us inflating the system with beliefs whose only merit is that they fit the system, to make a larger but still consistent fairy-tale? Appeal to the outside world — that these new beliefs are indeed "facts" — is invalid, as our measure of truth is coherence within the set of beliefs, not correspondence with matters outside.{10}

Given that there will be more than one way of choosing a set of beliefs from the available data, and no external criteria help us decide, Rescher {11} suggested using plausibility filters. We select those beliefs which seem in themselves most plausible, reducing the short-list by further selection if necessary. But how is this plausibility to be decided? If beliefs resembles Euclid's geometry, we might indeed accept some of them — that parallel lines never meet, for example — by an appeal to sturdy common sense, but most beliefs are not of this nature, and even Euclidean geometry has its limits. How can we be sure — a further problem — that our set of beliefs is the most comprehensive possible if new investigations may yet turn up data that is better incorporated in another set of beliefs?

Idealists like Bradley {12} argued that reality was a unified and coherent whole, which he called the Absolute. Parts of the whole could only be partly true, and even those parts were doubtfully true given the uncertain nature of our sense perceptions. Better base truth in our rational faculties, he thought, and look for consistency and interdependence in what our thoughts tell us. But again there are difficulties. How much interdependence? If everything in a set of beliefs is entirely interdependent, then each one belief is entailed by each other belief, which leads to absurdities. If the interdependence is loosened, then the requirements for inclusion become less clear.{13}

Some Logical Positivists tried to get the best of both worlds. Incorrigible reports on experience, which they called protocol sentences, were based on correspondence of knowledge and reality, but the assemblage of protocol sentences as a whole depended on their consistency and interdependence, i.e. on coherence theory. But even this happy compromise was dashed by Neurath who pointed out that protocol sentences were not then the product of unbiased observation as required, but of investigations controlled by the need for coherence in the set of protocol sentences. What controls what? We are like sailors, he said, who must completely rebuild their boat on the open sea. {14}

Other Theories of Truth: Pragmatism

What then of the third theory of truth: pragmatism? In its crudest form, that something is true simply because it yields good works or congenial beliefs, the theory has few adherents. But its proponents — Pierce, James, Dewey and latterly Quine — put matters more subtly. Reality, said C.S. Pierce, constrains us to the truth: we find by enquiry and experiment what the world is really like. Truth is the consensus of beliefs surviving that investigation, a view that includes some correspondence theory and foreshadows Quine's web of beliefs. William James was not so committed a realist, and saw truth as sometimes manufactured by the verification process itself, a view that links him to relativists like Feyerband. John Dewey stressed the context of application, that we need to judge ideas by how they work in specific practices. But that makes truth into a property acquired in the individual circumstances of verification, perhaps even individual-dependent, which has obvious drawbacks. {15}

But The truth of an idea is not a stagnant property inherent in it, wrote James.{16} Truth happens to an idea. It becomes true, is made true by events. Its verity is in fact an event, a process, the process namely of its verifying itself, its verification...Any idea that helps us to deal, whether practically or intellectually, with reality, that doesn't entangle our progress in frustrations, that fits, in fact, and adapts our life to the reality's whole setting, will agree sufficiently to meet the requirement. The true, to put it briefly, is only the expedient in our way of thinking, just as the right is only the expedient in our way of behaving. Expedient in almost any fashion, and expedient in the long run and on the whole, of course. But what of inexpedient truths, don't they exist? And what of truths as yet unverified, but nonetheless truths for all that? Truth as something active, that helps us deal with life, is an important consideration, but pragmatism ultimately affords no more complete a theory of truth than those of correspondence or coherence.


Firstly we see the Anglo-American approach to philosophy in action, very broadly and simply in these notes. And we appreciate something of the power and the limitations of modern logic. But could we not have been barking up the wrong tree? Language is not a matter of logic but of codes and social customs. Certainly the large though now somewhat defunct school of linguistic philosophy thought so. And perhaps life and literature is not to be grounded in logic at all, as the continental schools of philosophy have contended all along?

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1. pp.190-5 and 197-201 in F.R. Palmer's Semantics (1976).
2. See any elementary philosophy text book, e.g. Chapter 2 of A.C. Grayling's An Introduction to Philosophical Logic (1982).
3. Particularly useful are Logic, modern in Ted Honderich's The Oxford Companion to Philosophy (1995), Chapters 4-6 of Susan Haack's Philosophy of Logics (1980), Stephen Barker's The Elements of Logic (1980), Chapters 5 and 6 of Roger Scruton's Modern Philosophy (1996). Also Chapters 4 and 7 of Anders Wedberg's A History of Philosophy: Volume 3: From Bolzano to Wittgenstein (1984), Chapter 2 of Sybil Wolfram's Philosophical Logic: An Introduction (1989).
4. pp. 157-160 of Grayling 1982.
5. p. 101 in Haack 1980.
6. pp. 226-35 of Simon Blackburn's Spreading the Word: Groundings in Philosophy of Language (1984).
7. Illusion entry in David Cooper's A Companion to Aesthetics (1995). Also Ernst Gombridge's Art and Illusion (1960).
8. p. 126 of Grayling 1982.
9. p. 237 of Blackburn 1984.
10. p. 239-41 of Blackburn 1984.
11. N. Rescher's The Coherence Value of Truth (1970).
12. F.H. Bradley's Essays on Truth and Reality (1914).
13. p.134 in Grayling 1982.
14. p.136 in Grayling 1982.
15. pp 126- 32 in Grayling, 1982, and Cornel West's The American Evasion of Philosophy: A Genealogy of Pragmatism (1989).
16. William James's Pragmatism (1970).  

Internet Resources

1. Rationality. Truth in context: brief introduction.
2. The Revision Theory of Truth. Eric Hammer. Jan. 2003. Various ways of getting at the meaning of truth.
3. The Identity Theory of Truth. Stewart Candlish. Aug. 2002. Theory that truth is identical to its means of expression: difficulties.
4. Truth. Excellent introduction to four conceptions of truth.
5. Logic. Overview of its types and formulation.
6. Liar Paradox. Alternative views of the paradox.
7. Insolubles. Paul Vincent Spade. Aug. 2001. Pre-modern history of the Liar and other paradoxes.
8. Alfred Tarski. Introduction, but more detailed than summary in page above.
9. The Lvov-Warsaw School. Jan Wolenski. May 2003.
. Aims and achievements of the school, which included Tarski.
10. Tarski's Truth Definitions. Wilfrid Hodges. Nov. 2001. Technical, and much more rigorous than the simple presentation above.
11. Alfred Tarski. Philosophers.aspx?PhilCode=Tars. Short listing.
12. Correspondence Theory of Truth. Short entry, with links.
13. The Correspondence Theory of Truth. Marian David. May 2002. Readable account of the theory and its assumptions.
14. The Coherence Theory of Truth. James O. Young. May 2001. Versions of the theory and their difficulties.
15. The Deflationary Theory of Truth. Daniel Stoljar. Aug. 1997. Moore, Ramsey and others.
16. Pragmatism. Note and links to key thinkers.
17. William James. Russell Goodman. Jan. 2003. Very readable account, with extensive bibliography.
18. Richard Rorty. Bjørn Ramberg. Feb. 2001. Balanced account of Rorty's brand of pragmatism.
19. Feminist Approaches to the Intersection of Pragmatism and Continental Philosophy. Shannon Sullivan. Dec. 2002. femapproach-prag-cont/. Survey of contemporary concerns.

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