Directory:Jon Awbrey/TRUTH

Truth (10 May 2006)

Overview

The subjects of meaning and truth are commonly treated together, the common notion being that only meaningful things can be true or false. This association is found in ancient times, and has become standard in modern times under the heading of semantics, especially formal semantics. Another association of longstanding interest is the relation between truth and logical validity, "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale & Kneale, 16). Though not the main subjects of this article, meaning and validity are truth's neighbors, and incidental inquiries of them can serve to cast light on truth's character.

In an ancient fragment of text called the Dissoi Logoi, the writer is evidently trying to prove the impossibility of speaking consistently about truth and falsehood. One of the conundrums put forward to confound the reader cites the case of the verbal form, "I am an initiate", which is true when A says it but false when B says it. Escape from befuddlement seems easy enough if one observes that it is not the verbal expression, the sentence, to which the predicates of truth and falsity apply but what the sentence expresses, the proposition that it states. (Cf. Kneale & Kneale, 16). This same tension between strings of characters and their meanings remains with us to this day.

Philosophy of truth

It is conventional to refer to a distinctive philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory in the strictest logical sense. Most of the discussion to follow bows to that convention.

Theories of truth can be classified according to the following features:

• Primary subjects. What kinds of things are potentially meaningful enough to be asserted or not, believed or not, or considered true or false?
• Relevant objects. What kinds of things, in addition to primary subjects, are pertinent to deciding whether to assert them or not, believe them or not, or consider them true or false?
• Value predicates. What kinds of things are legitimate to say about primary subjects, either in themselves, or in relation to relevant objects?

In some discussions of meaning and truth that consider forms of expression well beyond the limits of literally-interpreted linguistic forms, potentially meaningful elements are called representations, or signs for short, taking these words in the broadest conceivable senses.

Most treatments of truth make an important distinction at this point, though the language in which they make it may vary. On the one hand there is a type of incomplete sign that is nevertheless said to be true or false of various objects. For example, in logic there are terms such as "man" or "woman" that are true of some things and false of others, and there are predicates such as "__is a man" or "__is a woman" that are true or false in the same way. On the other hand there is a type of complete sign that expresses what grammarians traditionally call a complete thought. Here one speaks of sentences and propositions. Some considerations of truth admit both types of signs, terms and sentences, while others admit only the bearers of complete thoughts into the arena of judgment. In a number of recent discussions that focus on linguistic analysis, the vehicles of complete thoughts are described as truthbearers, with no intention of prejudging whether they bear truth or falsehood. The things that can be said about any of these representations, signs, or truthbearers are expressed in what most truth theorists describe as truth predicates.

Truthbearers

In some branches of philosophy and fields of science the domain of potentially meaningful entities may include almost any kind of informative or significant element — the generic terms sign or representation will continue to serve for these — but the linguistic turn in analytic philosophy begins with a focus on the syntactic character of the sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Truthbearer is used by a number of writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is not applied to a person or group of persons; instead, the term is applied to entities that are specific enough that they can reasonably be subjected to analysis of whether or not they are true.

Truthbearers typically have two possible values, true or false. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

As predicate terms, most discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. A truth predicate that is used to ascribe truth to something, in and of itself, in effect treating truth as an intrinsic property of the thing, is called a one-place or monadic truth predicate. Other forms of truth predicates may be used to say that something is true in relation to specified numbers and types of other things. These are called many-place or polyadic truth predicates.

In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says that a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence? This question serves as useful touchstone for sorting out various accounts of truth.

Propositional attitudes

What sort of name shall we give to verbs like 'believe' and 'wish' and so forth? I should be inclined to call them 'propositional verbs'. This is merely a suggested name for convenience, because they are verbs which have the form of relating an object to a proposition. As I have been explaining, that is not what they really do, but it is convenient to call them propositional verbs. Of course you might call them 'attitudes', but I should not like that because it is a psychological term, and although all the instances in our experience are psychological, there is no reason to suppose that all the verbs I am talking of are psychological. There is never any reason to suppose that sort of thing. (Russell 1918, 227).

In linguistics and logic, the formal properties of verbs like assert, believe, command, consider, deny, doubt, hunt, imagine, judge, know, want, wish, and a host of others, are treated under the headings of intentionality, modality, and propositional attitude. (Cf. Quine 1956).

What a proposition is, is one thing. How we feel about it, or how we regard it, is another. We can accept it, assert it, believe it, command it, contest it, declare it, deny it, doubt it, enjoin it, exclaim it, expect it, imagine it, intend it, know it, observe it, prove it, question it, suggest it, or wish it were so. Different attitudes toward propositions are called propositional attitudes, and they are also discussed under the headings of intentionality and linguistic modality.

Many problems in human communication, and even personal integrity, arise from the circumstance that the same proposition may be affected by various propositional attitudes and expressed in sundry linguistic modes at one and the same time. In order to compare propositions of different colors and flavors, as it were, we have no basis for comparison but to examine the underlying propositions themselves. Thus we are brought back to matters of language and logic. Despite the name, propositional attitudes are not regarded as psychological attitudes proper, since the formal disciplines of linguistics and logic are concerned with nothing more concrete than what can be said in general about their formal properties and their patterns of interrelation.

The variety of attitudes that a proposer can bear toward a single proposition is a critical factor in evaluating its truth. One topic of central concern is the relation between the modes of assertion and belief, especially when viewed in light of the proposer's intentions. For example, we frequently find ourselves faced with the question of whether a person's assertions conform to his or her beliefs. Discrepancies here can occur for many reasons, but when the departure of assertion from belief is intentional, we usually call that a lie.

Other key comparisons of multiple modalities involve the relationship between belief and knowledge, and the discrepancies that occur among observations, expectations, and intentions. Deviations of observations from expectations are commonly perceived as surprises, phenomena that call for explanations to reduce the shock of amazement. Deviations of observations from intentions are commonly experienced as problems, situations that call for plans of action to reduce the drive of dissatisfaction. Either type of discrepancy forms an impulse to inquiry (Awbrey & Awbrey 1995).

Reflection and quotation

The study of propositional attitudes is no sooner begun than it leads to the all-important philosophical distinction between (1) using a meaning-bearer to bear its meaning in an active manner and (2) mentioning a meaning-bearer in a form that keeps its meaning in a more inert or inhibited state. The reasons for doing the latter are various, but involve the need to reflect on a potential meaning, to compare and contrast it with others, to criticize and evaluate both its logical implications and its practical consequences, all before deciding whether to put its meaning into action or not.

Propositional attitudes (8 May 2006)

What a proposition is, is one thing. How we feel about it, or how we regard it, is another. We can accept it, assert it, believe it, command it, contest it, declare it, deny it, doubt it, enjoin it, exclaim it, expect it, imagine it, intend it, know it, observe it, prove it, question it, suggest it, or wish it were so. Different attitudes toward propositions are called propositional attitudes, and they are also discussed under the headings of intentionality and linguistic modality.

Many problematic situations in real life arise from the circumstance that many different propositions in many different modalities are in the air at once. In order to compare propositions of different colors and flavors, as it were, we have no basis for comparison but to examine the underlying propositions themselves. Thus we are brought back to matters of language and logic. Despite the name, propositional attitudes are not regarded as psychological attitudes proper, since the formal disciplines of linguistics and logic are concerned with nothing more concrete than what can be said in general about their formal properties and their patterns of interaction.

One topic of central concern is the relation between the modalities of assertion and belief, perhaps with intention thrown in for good measure. For example, we frequently find ourselves faced with the question of whether a person's assertions conform to his or her beliefs. Discrepancies here can occur for many reasons, but when the departure of assertion from belief is intentional, we usually call that a lie.

Other comparisons of multiple modalities that frequently arise are the relationships between belief and knowledge and the discrepancies that occur among observations, expectations, and intentions. Deviations of observations from expectations are commonly perceived as surprises, phenomena that call for explanations to reduce the shock of amazement. Deviations of observations from intentions are commonly experienced as problems, situations that call for plans of action to reduce the drive of dissatisfaction. Either type of discrepancy forms an impulse to inquiry (Awbrey & Awbrey 1995).

Theories of truth

As always with classification schemes, a caution against cut-and-dried categories needs to be observed. There are perspectives on truth that combine selected elements from one or more of the identified types. For example, Susan Haack (1993) proposes a theory of foundherentism that seeks a middle ground between the perspectives on knowledge known as foundationalism and coherentism, closely related to the correspondence and coherence theories of truth, respectively.

Truth and the conduct of life

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? (Plato, Alcibiades, 135A).

In classical formulations, truth is defined as the good of logic, where logic is seen as a normative science, that is, an inquiry into a good that seeks descriptive knowledge of this value and procedural knowledge of the means to achieve it as a goal (Peirce, CP 5.39). In this view, truth cannot be discussed to much effect outside the context of inquiry, knowledge, and logic, all very broadly considered.

Truth (6 Jun 2006)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Philosophy of truth

Since only meaningful things can be true or false, the association of the subjects of meaning and truth is standard. Both are studied as part of semantics, especially formal semantics. Truth is also related to logical validity, because the latter concept is defined in terms of truth and falsehood. For these reasons, meaning and validity are touched upon frequently both in this article and in published discussions of truth. It is conventional to refer to a philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory by strictly empirical or logical criteria. Most of the discussion below follows this convention.

Signs, sentences, and propositions

In some branches of philosophy and fields of science the domain of potentially meaningful entities may include almost any kind of informative or significant element, described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of signs. Analytic philosophy, by contrast, begins with a focus on the words and syntax of a sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Sentences with demonstrative terms and indexical pronouns, words such as "I", "it", "now", "here", "this", "that", and so forth, can be true when uttered by one person but false when uttered by another, or even by the same person in a different place and time. For example, "I am a football fan", is true for some persons in some contexts and false for others. This suggests that it is not the sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Difficulties in human communication often arise from the fact that persons are capable of taking up different attitudes, called propositional attitudes, toward what they think, say, or write, and may express their different stances in widely different linguistic modalities. Propositions can, for example, be accepted, asserted, believed, commanded, contested, declared, denied, doubted, enjoined, exclaimed, expected, imagined, intended, observed, proven, questioned, suggested, or wished to be true. Differentiating among the various attitudes and modalities that persons are capable of taking toward a proposition can be critical in evaluating truth. Due to the many factors involved, the analyses can be quite complex, and the philosophical discussions generally reflect this complexity.

Truthbearers

Truthbearer is used by a number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Major theories of truth

Questions about what is a proper basis upon which to decide whether, and to what extent, belief is in accordance with fact, and to what extent statements and the ideas they convey are in accord with real things, whether for a single person or an entire community or society, are among the many important questions dealt with by the theories introduced in this section.

Traditional theories of truth share the claim that truth is a property that certain types of things may have, perhaps in relation to other things, and so the assertion that something is true makes a substantive, significant claim about it. There have more recently arisen so-called deflationary or minimalist theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Realist (substantive) theories of truth

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this variety of perspectives, then, the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A definable relation among meaning-bearing elements.
3. An identifiable relation among meaningful elements and other types of objects in reality.
4. A specifiable relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth.

Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not to be obtained by throwing out all relative data, or seeking data that has no tincture of subjectivity, but only by using this data, the only kind that we ever really have, as the ore from which laws and truths are mined.

Extracting the bearing of the analogy for the current context, one can see that merely including interpretive agents as participants in the transactions among meaning elements and objective relatives does not in itself obviate the possibility of truths having objective reference to mind-independent realities.

Truth (7 Jun 2006)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Philosophy of truth

Since only meaningful things can be true or false, the association of the subjects of meaning and truth is standard. Both are studied as part of semantics, especially formal semantics. Truth is also related to logical validity, because the latter concept is defined in terms of truth and falsehood. For these reasons, meaning and validity are touched upon frequently both in this article and in published discussions of truth. It is conventional to refer to a philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory by strictly empirical or logical criteria. Most of the discussion below follows this convention.

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of potentially meaningful entities may include almost any kind of informative or significant element, described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of signs. Analytic philosophy, by contrast, begins with a focus on the words and syntax of a sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Sentences with demonstrative terms and indexical pronouns, words such as "I", "it", "now", "here", "this", "that", and so forth, can be true when uttered by one person but false when uttered by another, or even by the same person in a different place and time. For example, "I am a football fan", is true for some persons in some contexts and false for others. This suggests that it is not the sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Difficulties in human communication often arise from the fact that persons are capable of taking up different attitudes, called propositional attitudes, toward what they think, say, or write, and may express their different stances in widely different linguistic modalities. Propositions can, for example, be accepted, asserted, believed, commanded, contested, declared, denied, doubted, enjoined, exclaimed, expected, imagined, intended, observed, proven, questioned, suggested, or wished to be true. Differentiating among the various attitudes and modalities that persons are capable of taking toward a proposition can be critical in evaluating truth. Due to the many factors involved, the analyses can be quite complex, and the philosophical discussions generally reflect this complexity.

Truthbearers

Truthbearer is used by a number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Major theories of truth

Questions about what is a proper basis upon which to decide whether, and to what extent, belief is in accordance with fact, and to what extent statements and the ideas they convey are in accord with real things, whether for a single person or an entire community or society, are among the many important questions dealt with by the theories introduced in this section.

Traditional theories of truth share the claim that truth is a property that certain types of things may have, perhaps in relation to other things, and so the assertion that something is true makes a substantive, significant claim about it. There have more recently arisen so-called deflationary or minimalist theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Realist (substantive) theories of truth

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The terms "objectively" and "in reality" imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this variety of perspectives, the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A definable relation among meaning-bearing elements.
3. An identifiable relation among meaningful elements and other types of objects in reality.
4. A specifiable relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Truth (8 Jun 2006 a)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Overview

Any attempt to address a subject so deeply entangled with all human forms of expression and inquiry and so wide-ranging in the complexities of its issues must begin by identifying a few points of focus for the initial setting out and a few lines of likely direction for organizing the account.

As a practical matter, academic studies and everyday discussions of truth always begin by acknowledging, either tacitly or expressly, a particular horizon for their activity. That is, they accept a number of limitations on the subject matter and a variety of restrictions on the methods and styles that are considered in bounds of sensible proceedings. The alternative, an attempt to proceed without bounds of any kind, typically results in discursive chaos and intellectual paralysis. Different horizons may of course be adopted at different times, and this is the way that fallible and finite human beings normally extend the range of their understanding beyond the transcience of the moment.

These considerations lead to the following pair of questions to ask about any discussion or investigation of truth:

• Aspects. What sorts of subjects and predicates are considered within bounds? Is the discussion concerned with a broader or a narrower domain of subject matters and a deeper or a shallower spectrum of things that can be said about these subjects?

• Approaches. What attitudes, methods, and styles of discussion are characteristic of a given approach to the aspects of truth that are acknowledged by the approach in question? All human approaches to absolutes are just that, approximations to desired levels of accuracy and completeness that are yet to be achieved. Depending on the application, an approach to a subject may be nothing more than a hazy impression of the area, or it may be so advanced as to admit of an axiomatic theory.

Aspects of meaning and truth

Since only meaningful things can be true or false, the association of the subjects of meaning and truth is standard. Both are studied as part of semantics, especially formal semantics. Truth is also related to logical validity, because the latter concept is defined in terms of truth and falsehood. For these reasons, meaning and validity are touched upon frequently both in this article and in published discussions of truth. It is conventional to refer to a philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory by strictly empirical or logical criteria. Most of the discussion below follows this convention.

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of potentially meaningful entities may include almost any kind of informative or significant element, described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of signs. Analytic philosophy, by contrast, begins with a focus on the words and syntax of a sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Sentences with demonstrative terms and indexical pronouns, words such as "I", "it", "now", "here", "this", "that", and so forth, can be true when uttered by one person but false when uttered by another, or even by the same person in a different place and time. For example, "I am a football fan", is true for some persons in some contexts and false for others. This suggests that it is not the sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Difficulties in human communication often arise from the fact that persons are capable of taking up different attitudes, called propositional attitudes, toward what they think, say, or write, and may express their different stances in widely different linguistic modalities. Propositions can, for example, be accepted, asserted, believed, commanded, contested, declared, denied, doubted, enjoined, exclaimed, expected, imagined, intended, observed, proven, questioned, suggested, or wished to be true. Differentiating among the various attitudes and modalities that persons are capable of taking toward a proposition can be critical in evaluating truth. Due to the many factors involved, the analyses can be quite complex, and the philosophical discussions generally reflect this complexity.

Truthbearers

Truthbearer is used by a number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Approaches to meaning and truth

Questions about what is a proper basis upon which to decide whether, and to what extent, belief is in accordance with fact, and to what extent statements and the ideas they convey are in accord with real things, whether for a single person or an entire community or society, are among the many important questions dealt with by the theories introduced in this section.

Traditional theories of truth share the claim that truth is a property that certain types of things may have, perhaps in relation to other things, and so the assertion that something is true makes a substantive, significant claim about it. There have more recently arisen so-called deflationary or minimalist theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Linguistic-analytic approaches

Language is commonly taken up as a mirror or a window for looking on the subject of truth. The assumption here, whether tacitly assumed or uttered for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought before this most facile of human glasses.

Systems-theoretic approaches

Physical properties of symbol systems

In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Realist (substantive) theories of truth

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The terms "objectively" and "in reality" imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this variety of perspectives, the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A definable relation among meaning-bearing elements.
3. An identifiable relation among meaningful elements and other types of objects in reality.
4. A specifiable relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Truth (8 Jun 2006 b)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Overview

Any attempt to address a subject so deeply entangled with all human forms of expression and inquiry and so wide-ranging in the complexities of its issues must begin by identifying a few points of focus for the initial setting out and a few lines of likely direction for organizing the account.

As a practical matter, academic studies and everyday discussions of truth always begin by acknowledging, either tacitly or expressly, a particular horizon for their activity. That is, they accept a number of limitations on the subject matter and a variety of restrictions on the methods and styles that are considered in bounds of sensible proceedings. The alternative, an attempt to proceed without bounds of any kind, typically results in discursive chaos and intellectual paralysis. Though practical methods depend on observing the practical limits of a given horizon, it is still possible under the right conditions to integrate the bits of data from localized frames of reference into more comprehensive and consensual views of the subject matter. This strategy of integration has been given a number of different names in different fields, notably by Michael Polanyi, who called it the principle of mutual control, referring to the way that domains of personal and disciplinary expertise form "chains of overlapping neighborhoods" (Polanyi 1966, p. 72).

These considerations lead to the following pair of questions to ask about any discussion or investigation of truth:

• Aspects. What sorts of subjects and predicates are considered within bounds? Is the discussion concerned with a broader or a narrower domain of subject matters and a deeper or a shallower spectrum of things that can be said about these subjects?

• Approaches. What attitudes, methods, and styles of discussion are characteristic of a given approach to the aspects of truth that are acknowledged by the approach in question? All human approaches to absolutes are just that, approximations to desired levels of accuracy and completeness that are yet to be achieved. Depending on the application, an approach to a subject may be nothing more than a hazy impression of the area, or it may be so advanced as to admit of an axiomatic theory.

Aspects of meaning and truth

Since only meaningful things can be true or false, the association of the subjects of meaning and truth is standard. Both are studied as part of semantics, especially formal semantics. Truth is also related to logical validity, because the latter concept is defined in terms of truth and falsehood. For these reasons, meaning and validity are touched upon frequently both in this article and in published discussions of truth. It is conventional to refer to a philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory by strictly empirical or logical criteria. Most of the discussion below follows this convention.

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of potentially meaningful entities may include almost any kind of informative or significant element, described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of signs. Analytic philosophy, by contrast, begins with a focus on the words and syntax of a sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Sentences with demonstrative terms and indexical pronouns, words such as "I", "it", "now", "here", "this", "that", and so forth, can be true when uttered by one person but false when uttered by another, or even by the same person in a different place and time. For example, "I am a football fan", is true for some persons in some contexts and false for others. This suggests that it is not the sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Difficulties in human communication often arise from the fact that persons are capable of taking up different attitudes, called propositional attitudes, toward what they think, say, or write, and may express their different stances in widely different linguistic modalities. Propositions can, for example, be accepted, asserted, believed, commanded, contested, declared, denied, doubted, enjoined, exclaimed, expected, imagined, intended, observed, proven, questioned, suggested, or wished to be true. Differentiating among the various attitudes and modalities that persons are capable of taking toward a proposition can be critical in evaluating truth. Due to the many factors involved, the analyses can be quite complex, and the philosophical discussions generally reflect this complexity.

Truthbearers

Truthbearer is used by a number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Approaches to meaning and truth

Questions about what is a proper basis upon which to decide whether, and to what extent, belief is in accordance with fact, and to what extent statements and the ideas they convey are in accord with real things, whether for a single person or an entire community or society, are among the many important questions dealt with by the theories introduced in this section.

Traditional theories of truth share the claim that truth is a property that certain types of things may have, perhaps in relation to other things, and so the assertion that something is true makes a substantive, significant claim about it. There have more recently arisen so-called deflationary or minimalist theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Linguistic-analytic approaches

Language is commonly taken up as a mirror or a window for looking on the subject of truth. The assumption here, whether tacitly assumed or uttered for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought before this most facile of human glasses.

Systems-theoretic approaches

Physical properties of symbol systems

In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Realist (substantive) theories of truth

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The terms "objectively" and "in reality" imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this variety of perspectives, the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A definable relation among meaning-bearing elements.
3. An identifiable relation among meaningful elements and other types of objects in reality.
4. A specifiable relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Truth (8 Jun 2006 c)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Overview

Overview of linguistic approaches to truth

Since only meaningful things can be true or false, the association of the subjects of meaning and truth is standard. Both are studied as part of semantics, especially formal semantics. Truth is also related to logical validity, because the latter concept is defined in terms of truth and falsehood. For these reasons, meaning and validity are touched upon frequently both in this article and in published discussions of truth. It is conventional to refer to a philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory by strictly empirical or logical criteria. Most of the discussion below follows this convention.

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of potentially meaningful entities may include almost any kind of informative or significant element, described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of signs. Analytic philosophy, by contrast, begins with a focus on the words and syntax of a sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Sentences with demonstrative terms and indexical pronouns, words such as "I", "it", "now", "here", "this", "that", and so forth, can be true when uttered by one person but false when uttered by another, or even by the same person in a different place and time. For example, "I am a football fan", is true for some persons in some contexts and false for others. This suggests that it is not the sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Difficulties in human communication often arise from the fact that persons are capable of taking up different attitudes, called propositional attitudes, toward what they think, say, or write, and may express their different stances in widely different linguistic modalities. Propositions can, for example, be accepted, asserted, believed, commanded, contested, declared, denied, doubted, enjoined, exclaimed, expected, imagined, intended, observed, proven, questioned, suggested, or wished to be true. Differentiating among the various attitudes and modalities that persons are capable of taking toward a proposition can be critical in evaluating truth. Due to the many factors involved, the analyses can be quite complex, and the philosophical discussions generally reflect this complexity.

Truthbearers

Truthbearer is used by a number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Linguistic analytic views of truth

Questions about what is a proper basis upon which to decide whether, and to what extent, belief is in accordance with fact, and to what extent statements and the ideas they convey are in accord with real things, whether for a single person or an entire community or society, are among the many important questions dealt with by the theories introduced in this section.

"Substantive" theories of truth share the claim that truth is a property that certain types of things may have, perhaps in relation to other things, and so the assertion that something is true makes a substantive, significant claim about it. There have more recently arisen so-called deflationary or minimalist theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Substantive theories of truth

Coherence theory

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There is no single coherence theory of truth but rather an assortment of perspectives that are commonly collected under this title. A pervasive tenet is the idea that truth is primarily a property of whole systems of propositions and can be ascribed to individual propositions only derivatively according to their coherence with the whole. Where theorists differ is mainly on the question of whether coherence entails many possible true systems of thought or only a single absolute system. For coherence theories in general, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple logical consistency. For example, the completeness and comprehensiveness of the underlying set of concepts is a critical factor in judging the utility and validity of a coherent system.

Some variants of coherence theory are claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics. However, formal reasoners are content to contemplate axiomatically independent but mutually contradictory systems side by side, for example, the various alternative geometries. On the whole, coherence theories have been criticized as lacking justification in their application to other areas of truth, especially with respect to assertions about the natural world, empirical data in general, assertions about practical matters of psychology and society, especially when used without support from the other major theories of truth.

Coherence theories distinguish the thought of continental rationalist philosophers, particularly of Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley. They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel.

Correspondence theory

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Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory, in essence, attempts to posit a relationship (a "truth relation") between thoughts or statements on the one hand, and things or objects on the other, as it might theoretically exist independently of the persons involved in the exchange and independently of other issues. It is a traditional model which goes back at least to some of the classical Greek philosophers. This class of theory holds that the truth or the falsity of a representation is determined in principle solely by how it relates to objective reality, by whether it accurately describes (that is, corresponds with) that reality.

Correspondence theory has traditionally operated on the assumption that there is an objective truth relation with which it is the human task to become properly aligned. In practice, however, more recent theorists have articulated that this ideal cannot be achieved independently of some analysis of additional factors. For example, analyses of correspondence that are cast within particular languages are forced to admit the particular language in question as an additional parameter at the outset of theoretical work, and only gradually construct a language-independent truth predicate by means of a careful theory of translation among different languages. There are strong theoretical limitations on the extent to which this can be done. Commentators and proponents of several of the theories introduced below also have widely asserted that the correspondence theory neglects the role of the persons involved in the "truth relation."

Constructivist theory

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Social constructivism holds that truth is constructed by social processes, is historically and culturally specific, and that it is in part shaped through the power struggles within a community. Constructivism views all of our knowledge as "constructed," because it does not reflect any external "transcendent" realities (as a pure correspondence theory might hold). Rather, perceptions of truth are viewed as contingent on convention, human perception, and social experience. It is believed by constructivists that representations of physical and biological reality, including race, sexuality, and gender are socially constructed. Giambattista Vico, Hegel, Garns, and Marx were among the first to suggest such an ambitious expansion of social determinism.

Consensus theory

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The consensus theory holds that truth is whatever is agreed upon, or in some versions, might come to be agreed upon, by some specified group. The label "consensus theory" of is variously attached to a number of otherwise very diverse philosophical perspectives. Some variants of "pragmatic theory of truth" have been included as consensus theory, though the range of "pragmatic theories" is sufficiently broad that it merits its own classification. Among the current advocates of consensus theory as a useful accounting of the concept of "truth" is Jürgen Habermas. Among its current strong critics is the philosopher Nicholas Rescher.

Minimalist (deflationary) theories of truth

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Other philosophers reject the thesis that the concept or term truth refers to a real property of sentences or propositions. From this point of view, to assert the proposition ““2 + 2 = 4” is true” is logically equivalent to asserting the proposition “2 + 2 = 4”, and the phrase “is true” is completely dispensable in this and every other context. These positions are broadly described (1) as deflationary theories of truth, since they purport to deflate the presumptive importance of the concept truth, (2) as disquotational theories, to draw attention to the disappearance of the quotation marks in cases like the above example, or (3) as minimalist theories of truth. Whichever term is used, deflationary theories can be said to hold in common that "[t]he predicate 'true' is an expressive convenience, not the name of a property requiring deep analysis."

In addition to highlighting this formal feature of the predicate "is true", some deflationists point out that the concept enables us to express things that might otherwise require infinitely long sentences. For example, one cannot express confidence in Michael's accuracy by asserting the endless sentence:

Michael says, 'snow is white' and snow is white, or he says 'roses are red' and roses are red or he says ... etc.

But it can be expressed succinctly by saying:

Whatever Michael says is true.

Once we have identified the truth predicate's formal features and utility, deflationists argue, we have said all there is to be said about truth. The primary theoretical concern of these views is to explain away those special cases where it appears that the concept of truth does have peculiar and interesting properties. (See Semantic paradoxes, and below.)

Performative theory of truth

Attributed to P. F. Strawson is the performative theory of truth which holds that to say "'Snow is white' is true" is to perform the speech act of signalling one's agreement with the claim that snow is white (much like nodding one's head in agreement). The idea that some statements are more actions than communicative statements is not as odd as it may seem. Consider, for example, that when the bride says "I do" at the appropriate time in a wedding, she is performing the act of taking this man to be her lawful wedded husband. She is not describing herself as taking this man. In a similar way, Strawson holds: "To say a statement is true is not to make a statement about a statement, but rather to perform the act of agreeing with, accepting, or endorsing a statement. When one says 'It's true that it's raining,' one asserts no more than 'It's raining.' The function of [the statement] 'It's true that...' is to agree with, accept, or endorse the statement that 'it's raining.'"

Redundancy and related theories

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According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is white". Redundant theorists infer from this premiss that truth is a redundant concept, that is, a mere word that is conventional to use in certain contexts of discourse but not a word that points to anything in reality. The theory is commonly attributed to Frank P. Ramsey. Ramsey held that the use of words like fact and truth was nothing but a roundabout way of asserting a proposition, and that treating these words as separate problems in isolation from judgment was merely a "linguistic muddle".

A variant of redundancy theory is the disquotational theory which uses a modified form of Tarski's schema: To say that '"P" is true' is to say that P. Yet another version of deflationism is the prosentential theory of truth, first developed by Dorothy Grover, Joseph Camp, and Nuel Belnap as an elaboration of Ramsey's claims. They argue that sentences like "That's true", when said in response to "It's raining", are prosentences (see pro-form), expressions that merely repeat the content of other expressions. In the same way that it means the same as my dog in the sentence My dog was hungry, so I fed it, That's true is supposed to mean the same as It's raining — if you say the latter and I then say the former. These variations do not necessarily follow Ramsey in asserting that truth is not a property, but rather can be understood to say that, for instance, the assertion "P" may well involve a substantial truth, and the theorists in this case are minimalizing only the redundancy or prosentence involved in the statement such as "that's true."

Deflationary principles do not apply to representations that are not analogous to sentences, and also do not apply to many other things that are commonly judged to be true or otherwise. Consider the analogy between the sentence "Snow is white" and the person Snow White, both of which can be true in a sense. To a minimalist, saying "Snow is white" is true is the same as saying "Snow is white", but to say "Snow White is true" is not the same as saying "Snow White".

Linguistic-analytic approaches

Language is commonly taken up as a mirror or a window for looking on the subject of truth. The assumption here, whether tacitly assumed or uttered for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought before this most facile of human glasses.

Semiotic approaches

Pragmatic theory of truth

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Three influential versions of the pragmatic theory of truth are due to Charles Peirce, William James, and John Dewey.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). James's pragmatic theory is in part a synthesis of correspondence and coherence theory, with an added dimension. Truth is verifiable to the extent that thoughts and statements correspond with actual things, as well as "hang together", or cohere, and these are in turn verified by the observed results of the application of proposed truths to actual practice James extended his pragmatic theory well beyond the scope of scientific verifiability, and even into the realm of the mystical: "On pragmatic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, then it is 'true'". John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

Physical symbol systems

In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Truth (9 Jun 2006 a)

Approaches independent of analytic philosophy

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The terms "objectively" and "in reality" imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this variety of perspectives, the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A definable relation among meaning-bearing elements.
3. An identifiable relation among meaningful elements and other types of objects in reality.
4. A specifiable relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

Language is commonly taken up as a mirror or a window for looking on the subject of truth. The assumption here, whether tacitly assumed or uttered for the sake of critical reflection, is that an examination of its verbal expressions can tell us something of signficance about any subject that is brought before this most facile of human glasses.

Hermeneutics

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Semiotics

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Pragmatic theory of truth

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Three influential versions of the pragmatic theory of truth, introduced mainly in the late 19th and very early 20th century, are due to Charles Peirce, William James, and John Dewey.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). James's pragmatic theory is in part a synthesis of correspondence and coherence theory, with an added dimension. Truth is verifiable to the extent that thoughts and statements correspond with actual things, as well as "hang together", or cohere, and these are in turn verified by the observed results of the application of proposed truths to actual practice James extended his pragmatic theory well beyond the scope of scientific verifiability, and even into the realm of the mystical: "On pragmatic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, then it is 'true'". John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

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Physical symbol systems

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Truth (9 Jun 2006 b)

Approaches independent of analytic philosophy

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this context the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A relation among meaning-bearing elements in a system of signs.
3. A relation among meaningful elements and other types of objects in reality.
4. A relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

Language is ready to hand as a metaphorical mirror for reflecting on the subject of truth. The natural assumption that motivates this approach to truth is the more general idea that examining the forms of verbal expressions that are used to talk about any given subject matter can tell us something of significance, beyond their surface demeanors, about the subject in view.

Semiotics differs from linguistics in that it generalizes the definition of a sign to encompass signs in any medium or sensory modality. Thus it broadens the range of sign systems and sign relations, and extends the definition of language in what amounts to its widest analogical or metaphorical sense.

Hermeneutics

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Semiotics

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Pragmatic theory of truth

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Three influential versions of the pragmatic theory of truth, introduced mainly in the late 19th and very early 20th century, are due to Charles Peirce, William James, and John Dewey.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Physical symbol systems

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Truth (10 Jun 2006)

Approaches independent of analytic philosophy

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this context the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A relation among meaning-bearing elements in a system of signs.
3. A relation among meaningful elements and other types of objects in reality.
4. A relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

The analysis of linguistic forms reveals the structures of syntactic entities and the relations that exist among them. These structures and relations partly mirror structures and relations that exist in objective reality. To the extent that this mirroring takes place, language does not merely reference the world in logically symbolic terms, it represents the world in what are called analogical, iconic, or morphic forms. When this happens it rewards the work of linguistic analysis with an added bonus of information about the real character of the world. If the mirror of language were perfect, if it afforded an isomorphism, then there would be no need for any other source of information. But that is a picture too beautiful to be true. There is only so much that can be revealed about the world through the analysis of its reflection in a single medium of expression. And not all of the images reflected by an imperfect medium belong to the world reflected — some of them are artifacts that are due to aberrations in the medium used. All of which means that it helps to collate, compare, and contrast the information that can be obtained through many different types of sign systems.

Hermeneutics

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Semiotics

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The disciplines that currently take up the study of signs in general, semeiotic, semiology, and semiotics, all differ from linguistics in that they generalize the definition of a sign to encompass signs in any medium or sensory modality. Thus they broaden the range of sign systems and sign relations, and extend the definition of language in what amounts to its widest analogical or metaphorical sense.

Pragmatic theory of truth

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Three influential versions of the pragmatic theory of truth, introduced mainly in the late 19th and very early 20th century, are due to Charles Peirce, William James, and John Dewey.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Physical symbol systems

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Truth (11 Jun 2006)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Overview of the philosophy of truth

Since only meaningful things can be true or false, the association of the subjects of meaning and truth is standard. Both are studied as part of semantics, especially formal semantics. Truth is also related to logical validity, because the latter concept is defined in terms of truth and falsehood. For these reasons, meaning and validity are touched upon frequently both in this article and in published discussions of truth. It is conventional to refer to a philosophical treatment of a particular subject matter as a theory, whether or not it qualifies as a theory by strictly empirical or logical criteria. Most of the discussion below follows this convention. Most of the modern terms introduced immediately below are characteristic of what may be termed the "linguistic-analytic" school that is predominant in modern philosophical discussion.

Basic linguistic-analytic philosophy

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of potentially meaningful entities may include almost any kind of informative or significant element, described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of signs. Analytic philosophy, by contrast, begins with a focus on the words and syntax of a sentence, from which is abstracted its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment.

Sentences with demonstrative terms and indexical pronouns, words such as "I", "it", "now", "here", "this", "that", and so forth, can be true when uttered by one person but false when uttered by another, or even by the same person in a different place and time. For example, "I am a football fan", is true for some persons in some contexts and false for others. This suggests that it is not the sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Difficulties in human communication often arise from the fact that persons are capable of taking up different attitudes, called propositional attitudes, toward what they think, say, or write, and may express their different stances in widely different linguistic modalities. Propositions can, to give a few examples, be accepted, asserted, believed, commanded, contested, declared, denied, doubted, enjoined, exclaimed, expected, imagined, intended, observed, proven, questioned, suggested, speculated, said with sarcasm, or wished to be true. Differentiating among the many attitudes and modalities that persons are capable of taking toward a proposition can be critical in evaluating truth. Due to the many factors involved, the analyses can be quite complex, and the philosophical discussions generally reflect this complexity.

Truthbearers

Truthbearer is used by a number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Analytic and post-analytic philosophy

The treatment of meaning and truth in analytic philosophy, along with the post-analytic perspectives for which it sets the agenda, begins with a focus on meaning and truth as expressed in formal languages and formal systems, in some of its branches continuing through a series of ordinary language movements that attempt to expand the use of logical analysis to natural languages.

"Substantive" theories of truth share the claim that truth is a property that certain types of things may have, perhaps in relation to other things, and so the assertion that something is true makes a substantive, significant claim about it. There have more recently arisen so-called deflationary or minimalist theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Substantive theories of truth

Coherence theory

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There is no single coherence theory of truth but rather an assortment of perspectives that are commonly collected under this title. A pervasive tenet is the idea that truth is primarily a property of whole systems of propositions and can be ascribed to individual propositions only derivatively according to their coherence with the whole. Where theorists differ is mainly on the question of whether coherence entails many possible true systems of thought or only a single absolute system. For coherence theories in general, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple logical consistency. For example, the completeness and comprehensiveness of the underlying set of concepts is a critical factor in judging the utility and validity of a coherent system.

Some variants of coherence theory are claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics. However, formal reasoners are content to contemplate axiomatically independent but mutually contradictory systems side by side, for example, the various alternative geometries. On the whole, coherence theories have been criticized as lacking justification in their application to other areas of truth, especially with respect to assertions about the natural world, empirical data in general, assertions about practical matters of psychology and society, especially when used without support from the other major theories of truth.

Coherence theories distinguish the thought of continental rationalist philosophers, particularly of Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley. They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel.

Correspondence theory

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Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory, in essence, attempts to posit a relationship (a "truth relation") between thoughts or statements on the one hand, and things or objects on the other, as it might theoretically exist independently of the persons involved in the exchange and independently of other issues. It is a traditional model which goes back at least to some of the classical Greek philosophers. This class of theory holds that the truth or the falsity of a representation is determined in principle solely by how it relates to objective reality, by whether it accurately describes (that is, corresponds with) that reality.

Kant discussed the correspondence theory of truth in the following manner:

Truth is said to consist in the agreement of knowledge with the object. According to this mere verbal definition, then, my knowledge, in order to be true, must agree with the object. Now, I can only compare the object with my knowledge by this means, namely, by taking knowledge of it. My knowledge, then, is to be verified by itself, which is far from being sufficient for truth. For as the object is external to me, and the knowledge is in me, I can only judge whether my knowledge of the object agrees with my knowledge of the object. Such a circle in explanation was called by the ancients Diallelos. And the logicians were accused of this fallacy by the sceptics, who remarked that this account of truth was as if a man before a judicial tribunal should make a statement, and appeal in support of it to a witness whom no one knows, but who defends his own credibility by saying that the man who had called him as a witness is an honourable man. (Kant, 45).

Correspondence theory has traditionally operated on the assumption that there is an objective truth relation with which it is the human task to become properly aligned. In practice, however, more recent theorists have articulated that this ideal cannot be achieved independently of some analysis of additional factors. For example, analyses of correspondence that are cast within particular languages are forced to admit the particular language in question as an additional parameter at the outset of theoretical work, and only gradually construct a language-independent truth predicate by means of a careful theory of translation among different languages. There are strong theoretical limitations on the extent to which this can be done. Commentators and proponents of several of the theories introduced below also have widely asserted that the correspondence theory neglects the role of the persons involved in the "truth relation."

Minimalist (deflationary) theories of truth

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A number of philosophers reject the thesis that the concept or term truth refers to a real property of sentences or propositions. These philosophers are responding, at least in significant part, to the common use of truth predicates ("...is true" or its equivalent) that was particularly prevalent in philosophical discourse on truth in the first half of the 20th century. From this point of view, to assert the proposition ““2 + 2 = 4” is true” is logically equivalent to asserting the proposition “2 + 2 = 4”, and the phrase “is true” is completely dispensable in this and every other context. These positions are broadly described (1) as deflationary theories of truth, since they purport to deflate the presumptive importance of the concept truth, (2) as disquotational theories, to draw attention to the disappearance of the quotation marks in cases like the above example, or (3) as minimalist theories of truth. Whichever term is used, deflationary theories can be said to hold in common that "[t]he predicate 'true' is an expressive convenience, not the name of a property requiring deep analysis."

In addition to highlighting this formal feature of the predicate "is true", some deflationists point out that the concept enables us to express things that might otherwise require infinitely long sentences. For example, one cannot express confidence in Michael's accuracy by asserting the endless sentence:

Michael says, 'snow is white' and snow is white, or he says 'roses are red' and roses are red or he says ... etc.

But it can be expressed succinctly by saying:

Whatever Michael says is true.

Once we have identified the truth predicate's formal features and utility, deflationists argue, we have said all there is to be said about truth. The primary theoretical concern of these views is to explain away those special cases where it appears that the concept of truth does have peculiar and interesting properties. (See Semantic paradoxes, and below.)

Performative theory of truth

Attributed to P. F. Strawson is the performative theory of truth which holds that to say "'Snow is white' is true" is to perform the speech act of signalling one's agreement with the claim that snow is white (much like nodding one's head in agreement). The idea that some statements are more actions than communicative statements is not as odd as it may seem. Consider, for example, that when the bride says "I do" at the appropriate time in a wedding, she is performing the act of taking this man to be her lawful wedded husband. She is not describing herself as taking this man. In a similar way, Strawson holds: "To say a statement is true is not to make a statement about a statement, but rather to perform the act of agreeing with, accepting, or endorsing a statement. When one says 'It's true that it's raining,' one asserts no more than 'It's raining.' The function of [the statement] 'It's true that...' is to agree with, accept, or endorse the statement that 'it's raining.'"

Redundancy and related theories

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According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is white". Redundant theorists infer from this premiss that truth is a redundant concept, that is, a mere word that is conventional to use in certain contexts of discourse but not a word that points to anything in reality. The theory is commonly attributed to Frank P. Ramsey. Ramsey held that the use of words like fact and truth was nothing but a roundabout way of asserting a proposition, and that treating these words as separate problems in isolation from judgment was merely a "linguistic muddle".

A variant of redundancy theory is the disquotational theory which uses a modified form of Tarski's schema: To say that '"P" is true' is to say that P. Yet another version of deflationism is the prosentential theory of truth, first developed by Dorothy Grover, Joseph Camp, and Nuel Belnap as an elaboration of Ramsey's claims. They argue that sentences like "That's true", when said in response to "It's raining", are prosentences (see pro-form), expressions that merely repeat the content of other expressions. In the same way that it means the same as my dog in the sentence My dog was hungry, so I fed it, That's true is supposed to mean the same as It's raining — if you say the latter and I then say the former. These variations do not necessarily follow Ramsey in asserting that truth is not a property, but rather can be understood to say that, for instance, the assertion "P" may well involve a substantial truth, and the theorists in this case are minimalizing only the redundancy or prosentence involved in the statement such as "that's true."

Deflationary principles do not apply to representations that are not analogous to sentences, and also do not apply to many other things that are commonly judged to be true or otherwise. Consider the analogy between the sentence "Snow is white" and the person Snow White, both of which can be true in a sense. To a minimalist, saying "Snow is white" is true is the same as saying "Snow is white", but to say "Snow White is true" is not the same as saying "Snow White".

Other theories of truth predicates

Kripke's theory of truth

Saul Kripke contends that a natural language can in fact contain its own truth predicate without giving rise to contradiction. He showed how to construct one as follows:

• Begin with a subset of sentences of a natural language that contains no occurrences of the expression "is true" (or "is false"). So The barn is big is included in the subset, but not ' The barn is big is true', nor problematic sentences such as "This sentence is false".

• Define truth just for the sentences in that subset.

• Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences. So ' The barn is big is true' is now included, but not either This sentence is false nor "' The barn is big is true' is true".

• Next, define truth for all sentences that predicate truth or falsity of a member of the second set. Imagine this process repeated infinitely, so that truth is defined for The barn is big; then for ' The barn is big is true'; then for "' The barn is big is true' is true", and so on.

Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set. In Kripke's terms, these are "ungrounded." Since these sentences are never assigned either truth or falsehood even if the process is carried out infinitely, Kripke's theory implies that some sentences are neither true nor false. This contradicts the Principle of bivalence: every sentence must be either true or false. Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.

Semantic theory of truth

The semantic theory of truth has as its general case for a given language:

'P' is true if and only if P

where 'P' is a reference to the sentence (the sentence's name), and P is just the sentence itself.

Logician and philosopher Alfred Tarski developed the theory for formal languages (such as formal logic). Here he restricted it in this way: no language could contain its own truth predicate, that is, the expression is true could only apply to sentences in some other language. The latter he called an object language, the language being talked about. (It may, in turn, have a truth predicate that can be applied to sentences in still another language.) The reason for his restriction was that languages that contain their own truth predicate will contain paradoxical sentences like the Liar: This sentence is not true. See The Liar paradox. As a result Tarski held that the semantic theory could not be applied to any natural language, such as English, because they contain their own truth predicates. Donald Davidson used it as the foundation of his truth-conditional semantics and linked it to radical interpretation in a form of coherentism.

Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox. Russell and Whitehead attempted to solve these problems in Principia Mathematica by putting statements into a hierarchy of types, wherein a statement cannot refer to itself, but only to statements lower in the hierarchy. This in turn led to new orders of difficulty regarding the precise natures of types and the structures of conceptually possible type systems that have yet to be resolved to this day.

Theories of truth as socially constructed

Constructivist theory

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Social constructivism holds that truth is constructed by social processes, is historically and culturally specific, and that it is in part shaped through the power struggles within a community. Constructivism views all of our knowledge as "constructed," because it does not reflect any external "transcendent" realities (as a pure correspondence theory might hold). Rather, perceptions of truth are viewed as contingent on convention, human perception, and social experience. It is believed by constructivists that representations of physical and biological reality, including race, sexuality, and gender are socially constructed. Giambattista Vico, Hegel, Garns, and Marx were among the first to suggest such an ambitious expansion of social determinism.

Consensus theory

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The consensus theory holds that truth is whatever is agreed upon, or in some versions, might come to be agreed upon, by some specified group. The label "consensus theory" of is variously attached to a number of otherwise very diverse philosophical perspectives. Some variants of "pragmatic theory of truth" have been included as consensus theory, though the range of "pragmatic theories" is sufficiently broad that it merits its own classification. Among the current advocates of consensus theory as a useful accounting of the concept of "truth" is Jürgen Habermas. Among its current strong critics is the philosopher Nicholas Rescher.

Approaches independent of analytic philosophy

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this context the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A relation among meaning-bearing elements in a system of signs.
3. A relation among meaningful elements and other types of objects in reality.
4. A relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

The analysis of linguistic forms reveals the structures of syntactic entities and the relations that exist among them. These structures and relations partly mirror structures and relations that exist in objective reality. To the extent that this mirroring takes place, language does not merely reference the world in logically symbolic terms, it represents the world in what are called analogical, iconic, or morphic forms. When this happens it rewards the work of linguistic analysis with an added bonus of information about the real character of the world. If the mirror of language were perfect, if it afforded an isomorphism, then there would be no need for any other source of information. But that is a picture too beautiful to be true. There is only so much that can be revealed about the world through the analysis of its reflection in a single medium of expression. And not all of the images reflected by an imperfect medium belong to the world reflected — some of them are artifacts that are due to aberrations in the medium used. All of which means that it helps to collate, compare, and contrast the information that can be obtained through many different types of sign systems.

Hermeneutics

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Semiotics

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The disciplines that currently take up the study of signs in general, semeiotic, semiology, and semiotics, all differ from linguistics in that they generalize the definition of a sign to encompass signs in any medium or sensory modality. Thus they broaden the range of sign systems and sign relations, and extend the definition of language in what amounts to its widest analogical or metaphorical sense.

Pragmatic theory of truth

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Three influential versions of the pragmatic theory of truth, introduced mainly in the late 19th and very early 20th century, are due to Charles Peirce, William James, and John Dewey.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Physical symbol systems

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Types of truth

Metaphysical subjectivism holds that the truth or falsity of all propositions depends, at least partly, on what we believe. In contrast, metaphysical objectivism holds that truths are independent of our subjective beliefs. Except for propositions that are actually about our beliefs or sensations, what is true or false is independent of what we think is true or false.

Relative truths are statements or propositions that are true only relative to some standard, convention, or point-of-view, such as that of one's own culture. Many would agree that the truth or falsity of some statements are relative: That the fork is to the left of the spoon depends on where one stands. Relativism is the doctrine that all truths within a particular domain (say, morality or aesthetics) are of this form, and entails that what is true varies across cultures and eras. For example, moral relativism is the view that moral expectations are socially determined.

Relative truths can be contrasted with absolute truths. The latter are statements or propositions that are taken to be true for all cultures and all eras. For example, for the microeconomist, that the laws of supply and demand determine the value of any consumable in a market economy is true in all situations; for the Kantian, "act only according to that maxim by which you can at the same time will that it should become a universal law" forms an absolute moral truth. They are statements that are often claimed to emanate from the very nature of the universe, God, human nature, or some other ultimate essence or transcendental signifier.

The concept of absolute truth, as understood in philosophy, should not be confused with the concept of absolute truth as it is used in religious traditions.

Absolutism in a particular domain of thought is the view that all statements in that domain are either absolutely true or absolutely false: none is true for some cultures or eras while false for other cultures or eras.

Truth in specialized contexts

Truth in jurisprudence

Truth, as a concept, is a central issue in law, though the actual use of the word "truth" in legal practice tends to be limited to certain very specific contexts. Witnesses who swear under oath to testify truthfully in courts of law are not expected to make infallibly true statements, but to make a good faith attempt to accurately recount prior events from memory, or provide expert testimony. Triers-of-fact are then charged with the responsibility to determine the credibility or veracity of a witness's testimony. Differing accounts from separate witnesses testifying in good-faith are commonplace. Errors are not attributed to perjury unless a very stringent standard of proof is met when charging a witness with lying under oath.

Beyond the standard oath taken by witnesses, the word "truth" is seldom officially used. Courts, judges and juries are never referred to, for instance, as "finders of truth." In addition to procedural and substantive legal rulings, courts designate a finder of fact (jury or judge) to decide what the facts are in a case given often conflicting sets of information. In a very specific and limited context, "truth" is also a legal term of art referring to a standard affirmative defense to a charge of defamation, this use of the term in this specific manner deriving from common law dating back at least seven centuries. William J. Shields summarizes the weight which the law gives to the word "truth" by noting that Black’s Law Dictionary devotes just a few lines to it: "1. A fully accurate account of events, factuality. 2. Defamation. An affirmative defense by which the defendant asserts that the alleged defamatory statement is substantially accurate." Shields goes on to say:

By contrast, the definition of “fact” covers about two full pages, with three principal meanings and 42 definitions of specific types of fact. “Evidence” covers five full pages with four principal meanings and 93 definitions of specific types. Even the definition of the crime of perjury avoids the use of “truth”: “the act or an instance of a person’s deliberately making material false or misleading statements while under oath.” Perusal of other legal references (treatises, dictionaries, periodicals, etc.) will yield the same results. Where “truth” or “true” is defined, it will be to the effect of “that which is a fact” or “that which is verifiable,” leading back to the legal concepts of evidence and proof.

Truth in mathematics

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There are two main truth theories in mathematics. They are the model theory of truth and the proof theory of truth.

Historically, with the 19th century development of Boolean algebra mathematical models of logic began to treat "truth", also represented as "T" or "1", as an arbitrary constant. "Falsity" is also an arbitrary constant, which can be represented as "F" or "0". In propositional logic, these symbols can be manipulated according to a set of axioms and rules of inference, often given in the form of truth tables.

In addition, from at least the time of Hilbert's program at the turn of the 20th century to the proof of Gödel's theorem and the development of the Church-Turing thesis in the early part of that century, true statements in mathematics were generally assumed to be those statements which are provable in a formal axiomatic system.

The works of Kurt Gödel, Alan Turing, and others shook this assumption, with the development of statements that are true but cannot be proven, and of statements whose truth or falsity is undecidable. Two examples of the latter can be found in Hilbert's problems. Work on Hilbert's 10th problem led in the late 20th century to the construction of specific Diophantine equations for which it is undecidable whether they have a solution , or even if they do, whether they have a finite or infinite number of solutions. More fundamentally, Hilbert's first problem was on the continuum hypothesis. Gödel and Paul Cohen showed that this hypothesis cannot be proved or disproved using the standard axioms of set theory. In the view of some, then, it is equally reasonable to take either the continuum hypothesis or its negation as a new axiom.

Truth in science

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Truth (22 Jun 2006)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Overview of the philosophy of truth

Basic concepts

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of entities which potentially convey truth may include almost any kind of meaningful, informative or significant element, commonly described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of words or representations. Analytic philosophy, which exerted a dominant influence on philosophical discussion of truth throughout the 20th century, commonly begins with a focus on the words and syntax of a sentence, from which an attempt is made to determine its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment. Thus it is not necessarily the literally interpreted sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Truthbearers

Truthbearer is used by a significant number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Theories of truth as expressed in language

Questions about what is a proper basis on which to decide whether and to what extent words, symbols, ideas and beliefs may be said to be true, whether for a single person or an entire community or society, are among the many important questions addressed by the theories introduced below.

The major "substantive" or "robust" theories each deal with truth as something with a nature, a phenomenon, or thing, or type of human experience about which significant things can be said. These theories each present perspectives that are widely agreed by philosophers to apply in some way to a broad set of occurrences that can be observed in human interaction, or which offer significant, stable explanations for issues related to the idea of truth in human experience (thus the word "robust"). There also have more recently arisen so-called "deflationary" or "minimalist" theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Substantive ("robust") theories of truth

Coherence theory

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For coherence theories in general, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple logical consistency. For example, the completeness and comprehensiveness of the underlying set of concepts is a critical factor in judging the utility and validity of a coherent system. A pervasive tenet of coherence theories is the idea that truth is primarily a property of whole systems of propositions and can be ascribed to individual propositions only derivatively according to their coherence with the whole. Among the assortment of perspectives commonly regarded as coherence theory, theorists differ on the question of whether coherence entails many possible true systems of thought or only a single absolute system.

Some variants of coherence theory are claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics. However, formal reasoners are content to contemplate axiomatically independent but mutually contradictory systems side by side, for example, the various alternative geometries. On the whole, coherence theories have been criticized as lacking justification in their application to other areas of truth, especially with respect to assertions about the natural world, empirical data in general, assertions about practical matters of psychology and society, especially when used without support from the other major theories of truth.

Coherence theories distinguish the thought of continental rationalist philosophers, particularly of Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley. They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel.

Correspondence theory

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Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory, in essence, attempts to posit a relationship (a "truth relation") between thoughts or statements on the one hand, and things or objects on the other, as it might theoretically exist independently of the persons involved in the exchange and independently of other issues. It is a traditional model which goes back at least to some of the classical Greek philosophers. This class of theory holds that the truth or the falsity of a representation is determined in principle solely by how it relates to objective reality, by whether it accurately describes (that is, corresponds with) that reality.

Immanuel Kant discussed correspondence theory of truth in the following manner:

Truth is said to consist in the agreement of knowledge with the object. According to this mere verbal definition, then, my knowledge, in order to be true, must agree with the object. Now, I can only compare the object with my knowledge by this means, namely, by taking knowledge of it. My knowledge, then, is to be verified by itself, which is far from being sufficient for truth. For as the object is external to me, and the knowledge is in me, I can only judge whether my knowledge of the object agrees with my knowledge of the object. Such a circle in explanation was called by the ancients Diallelos. And the logicians were accused of this fallacy by the sceptics, who remarked that this account of truth was as if a man before a judicial tribunal should make a statement, and appeal in support of it to a witness whom no one knows, but who defends his own credibility by saying that the man who had called him as a witness is an honourable man. (Kant, 45)

Correspondence theory has traditionally operated on the assumption that there is an objective truth relation with which it is the human task to become properly aligned. In practice, however, more recent theorists have articulated that this ideal cannot be achieved independently of some analysis of additional factors. For example, analyses of correspondence that are cast within particular languages are forced to admit the particular language in question as an additional parameter at the outset of theoretical work, and only gradually construct a language-independent truth predicate by means of a careful theory of translation among different languages. There are strong theoretical limitations on the extent to which this can be done. Commentators and proponents of several of the theories introduced below also have widely asserted that the correspondence theory neglects the role of the persons involved in the "truth relation."

Constructivist theory

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Social constructivism holds that truth is constructed by social processes, is historically and culturally specific, and that it is in part shaped through the power struggles within a community. Constructivism views all of our knowledge as "constructed," because it does not reflect any external "transcendent" realities (as a pure correspondence theory might hold). Rather, perceptions of truth are viewed as contingent on convention, human perception, and social experience. It is believed by constructivists that representations of physical and biological reality, including race, sexuality, and gender are socially constructed. Giambattista Vico, Hegel, Garns, and Marx were among the first to suggest such an ambitious expansion of social determinism.

Consensus theory

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The consensus theory holds that truth is whatever is agreed upon, or in some versions, might come to be agreed upon, by some specified group. The label "consensus theory" of is variously attached to a number of otherwise very diverse philosophical perspectives. Some variants of "pragmatic theory of truth" have been included as consensus theory, though the range of "pragmatic theories" is sufficiently broad that it merits its own classification. Among the current advocates of consensus theory as a useful accounting of the concept of "truth" is Jürgen Habermas. Among its current strong critics is the philosopher Nicholas Rescher.

Minimalist (deflationary) theories of truth

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A number of philosophers reject the thesis that the concept or term truth refers to a real property of sentences or propositions. These philosophers are responding, at least in significant part, to the common use of truth predicates ("...is true" or its equivalent) that was particularly prevalent in philosophical discourse on truth in the first half of the 20th century. From this point of view, to assert the proposition ““2 + 2 = 4” is true” is logically equivalent to asserting the proposition “2 + 2 = 4”, and the phrase “is true” is completely dispensable in this and every other context. These positions are broadly described (1) as deflationary theories of truth, since they purport to deflate the presumptive importance of the concept truth, (2) as disquotational theories, to draw attention to the disappearance of the quotation marks in cases like the above example, or (3) as minimalist theories of truth. Whichever term is used, deflationary theories can be said to hold in common that "[t]he predicate 'true' is an expressive convenience, not the name of a property requiring deep analysis."

In addition to highlighting this formal feature of the predicate "is true", some deflationists point out that the concept enables us to express things that might otherwise require infinitely long sentences. For example, one cannot express confidence in Michael's accuracy by asserting the endless sentence:

Michael says, 'snow is white' and snow is white, or he says 'roses are red' and roses are red or he says ... etc.

But it can be expressed succinctly by saying:

Whatever Michael says is true.

Once we have identified the truth predicate's formal features and utility, deflationists argue, we have said all there is to be said about truth. The primary theoretical concern of these views is to explain away those special cases where it appears that the concept of truth does have peculiar and interesting properties. (See Semantic paradoxes, and below.)

Performative theory of truth

Attributed to P. F. Strawson is the performative theory of truth which holds that to say "'Snow is white' is true" is to perform the speech act of signalling one's agreement with the claim that snow is white (much like nodding one's head in agreement). The idea that some statements are more actions than communicative statements is not as odd as it may seem. Consider, for example, that when the bride says "I do" at the appropriate time in a wedding, she is performing the act of taking this man to be her lawful wedded husband. She is not describing herself as taking this man. In a similar way, Strawson holds: "To say a statement is true is not to make a statement about a statement, but rather to perform the act of agreeing with, accepting, or endorsing a statement. When one says 'It's true that it's raining,' one asserts no more than 'It's raining.' The function of [the statement] 'It's true that...' is to agree with, accept, or endorse the statement that 'it's raining.'"

Redundancy and related theories

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According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is white". Redundant theorists infer from this premiss that truth is a redundant concept, that is, a mere word that is conventional to use in certain contexts of discourse but not a word that points to anything in reality. The theory is commonly attributed to Frank P. Ramsey. Ramsey held that the use of words like fact and truth was nothing but a roundabout way of asserting a proposition, and that treating these words as separate problems in isolation from judgment was merely a "linguistic muddle".

A variant of redundancy theory is the disquotational theory which uses a modified form of Tarski's schema: To say that '"P" is true' is to say that P. Yet another version of deflationism is the prosentential theory of truth, first developed by Dorothy Grover, Joseph Camp, and Nuel Belnap as an elaboration of Ramsey's claims. They argue that sentences like "That's true", when said in response to "It's raining", are prosentences (see pro-form), expressions that merely repeat the content of other expressions. In the same way that it means the same as my dog in the sentence My dog was hungry, so I fed it, That's true is supposed to mean the same as It's raining — if you say the latter and I then say the former. These variations do not necessarily follow Ramsey in asserting that truth is not a property, but rather can be understood to say that, for instance, the assertion "P" may well involve a substantial truth, and the theorists in this case are minimalizing only the redundancy or prosentence involved in the statement such as "that's true."

Deflationary principles do not apply to representations that are not analogous to sentences, and also do not apply to many other things that are commonly judged to be true or otherwise. Consider the analogy between the sentence "Snow is white" and the person Snow White, both of which can be true in a sense. To a minimalist, saying "Snow is white" is true is the same as saying "Snow is white", but to say "Snow White is true" is not the same as saying "Snow White".

Other theories of truth predicates

Kripke's theory of truth

Saul Kripke contends that a natural language can in fact contain its own truth predicate without giving rise to contradiction. He showed how to construct one as follows:

• Begin with a subset of sentences of a natural language that contains no occurrences of the expression "is true" (or "is false"). So The barn is big is included in the subset, but not ' The barn is big is true', nor problematic sentences such as "This sentence is false".

• Define truth just for the sentences in that subset.

• Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences. So ' The barn is big is true' is now included, but not either This sentence is false nor "' The barn is big is true' is true".

• Next, define truth for all sentences that predicate truth or falsity of a member of the second set. Imagine this process repeated infinitely, so that truth is defined for The barn is big; then for ' The barn is big is true'; then for "' The barn is big is true' is true", and so on.

Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set. In Kripke's terms, these are "ungrounded." Since these sentences are never assigned either truth or falsehood even if the process is carried out infinitely, Kripke's theory implies that some sentences are neither true nor false. This contradicts the Principle of bivalence: every sentence must be either true or false. Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.

Semantic theory of truth

The semantic theory of truth has as its general case for a given language:

'P' is true if and only if P

where 'P' is a reference to the sentence (the sentence's name), and P is just the sentence itself.

Logician and philosopher Alfred Tarski developed the theory for formal languages (such as formal logic). Here he restricted it in this way: no language could contain its own truth predicate, that is, the expression is true could only apply to sentences in some other language. The latter he called an object language, the language being talked about. (It may, in turn, have a truth predicate that can be applied to sentences in still another language.) The reason for his restriction was that languages that contain their own truth predicate will contain paradoxical sentences like the Liar: This sentence is not true. See The Liar paradox. As a result Tarski held that the semantic theory could not be applied to any natural language, such as English, because they contain their own truth predicates. Donald Davidson used it as the foundation of his truth-conditional semantics and linked it to radical interpretation in a form of coherentism.

Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox. Russell and Whitehead attempted to solve these problems in Principia Mathematica by putting statements into a hierarchy of types, wherein a statement cannot refer to itself, but only to statements lower in the hierarchy. This in turn led to new orders of difficulty regarding the precise natures of types and the structures of conceptually possible type systems that have yet to be resolved to this day.

Theories of truth as expressed more generally

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this context the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A relation among meaning-bearing elements in a system of signs.
3. A relation among meaningful elements and other types of objects in reality.
4. A relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

The analysis of linguistic forms reveals the structures of syntactic entities and the relations that exist among them. These structures and relations partly mirror structures and relations that exist in objective reality. To the extent that this mirroring takes place, language does not merely reference the world in logically symbolic terms, it represents the world in what are called analogical, iconic, or morphic forms. When this happens it rewards the work of linguistic analysis with an added bonus of information about the real character of the world. If the mirror of language were perfect, if it afforded an isomorphism, then there would be no need for any other source of information. But that is a picture too beautiful to be true. There is only so much that can be revealed about the world through the analysis of its reflection in a single medium of expression. And not all of the images reflected by an imperfect medium belong to the world reflected — some of them are artifacts that are due to aberrations in the medium used. All of which means that it helps to collate, compare, and contrast the information that can be obtained through many different types of sign systems.

Hermeneutics

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Semiotics

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The disciplines that currently take up the study of signs in general, semeiotic, semiology, and semiotics, all differ from linguistics in that they generalize the definition of a sign to encompass signs in any medium or sensory modality. Thus they broaden the range of sign systems and sign relations, and extend the definition of language in what amounts to its widest analogical or metaphorical sense.

Pragmatic theory of truth

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In pragmatic thought, very broadly speaking, meanings are expressed not just in words but in deeds. But no statement that short and simple can go without immediate and lengthy qualification, beginning with efforts to define the terms it invokes and extending through a discussion of the various glosses and hedges that different thinkers attach to each term. Indeed, questions about the kind of action that makes a difference to pragmatic meaning and truth led to one of the first schisms in the ability of the classical pragmatists, Charles Peirce, William James, and John Dewey, to understand each other's variant emphases within that broader philosophy.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Physical symbol systems

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Truth (23 Jun 2006)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. There are many other issues about which scholars disagree. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Overview of the philosophy of truth

Basic concepts

Signs, sentences, and propositions

In some branches of philosophy and fields of science, the set of entities which potentially convey truth may include almost any kind of meaningful, informative or significant element, commonly described by the generic terms sign or representation. Such entities may include words, pictoral representations, logical or mathematical symbols, etc., and also may include a wide variety of meaningful combinations or clusters of words or representations. Analytic philosophy, which exerted a dominant influence on philosophical discussion of truth throughout the 20th century, commonly begins with a focus on the words and syntax of a sentence, from which an attempt is made to determine its meaningful content, referred to as the corresponding proposition. A proposition is the content expressed by a sentence, held in a belief, or affirmed in an assertion or judgment. Thus it is not necessarily the literally interpreted sentence to which truth and falsity apply but what the sentence expresses, the proposition that it states.

Truthbearers

Truthbearer is used by a significant number of modern writers to refer to any entity that can be judged true or false. The term truthbearer may be applied to propositions, sentences, statements, ideas, beliefs, and judgments. Some writers exclude one or more of these categories, or argue that some of them are true (or false) only in a derivative sense. Other writers may add additional entities to the list. Truthbearer, in the context of modern philosophical discussion, is never applied to a person or group of persons; rather, the term is applied to the kinds of entities above because they are deemed specific enough to reasonably be subjected to a close analysis of whether or not they are true. Fictional forms of expression are usually regarded as false if interpreted literally, but may be said to bear a species of truth if interpreted suitably. Still other truthbearers may be judged true or false to a greater or lesser degree.

Truth predicates

Many discussions of truth allow for a number of phrases that are used to say in what ways signs or sentences or their abstract senses are regarded as true, either by themselves or in relation to other things. Theorists who admit the term call these phrases truth predicates. In ordinary parlance, the things that one says about a subject are expressed in predicates. If one says a sentence is true, then one is predicating truth of that sentence. Is this the same thing as asserting the sentence without the additional qualification that the sentence "is true"? This question serves as an important touchstone for sorting out some of the major theories of truth.

Truth as expressed in language

Questions about what is a proper basis on which to decide whether and to what extent words, symbols, ideas and beliefs may be said to be true, whether for a single person or an entire community or society, are among the many important questions addressed by the theories introduced below.

The major "substantive" or "robust" theories each deal with truth as something with a nature, a phenomenon, or thing, or type of human experience about which significant things can be said. These theories each present perspectives that are widely agreed by philosophers to apply in some way to a broad set of occurrences that can be observed in human interaction, or which offer significant, stable explanations for issues related to the idea of truth in human experience (thus the word "robust"). There also have more recently arisen so-called "deflationary" or "minimalist" theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Substantive ("robust") theories of truth

Coherence theory

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For coherence theories in general, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple logical consistency. For example, the completeness and comprehensiveness of the underlying set of concepts is a critical factor in judging the utility and validity of a coherent system. A pervasive tenet of coherence theories is the idea that truth is primarily a property of whole systems of propositions and can be ascribed to individual propositions only derivatively according to their coherence with the whole. Among the assortment of perspectives commonly regarded as coherence theory, theorists differ on the question of whether coherence entails many possible true systems of thought or only a single absolute system.

Some variants of coherence theory are claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics. However, formal reasoners are content to contemplate axiomatically independent but mutually contradictory systems side by side, for example, the various alternative geometries. On the whole, coherence theories have been criticized as lacking justification in their application to other areas of truth, especially with respect to assertions about the natural world, empirical data in general, assertions about practical matters of psychology and society, especially when used without support from the other major theories of truth.

Coherence theories distinguish the thought of continental rationalist philosophers, particularly of Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley. They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel.

Correspondence theory

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Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory, in essence, attempts to posit a relationship (a "truth relation") between thoughts or statements on the one hand, and things or objects on the other, as it might theoretically exist independently of the persons involved in the exchange and independently of other issues. It is a traditional model which goes back at least to some of the classical Greek philosophers. This class of theory holds that the truth or the falsity of a representation is determined in principle solely by how it relates to objective reality, by whether it accurately describes (that is, corresponds with) that reality.

Immanuel Kant discussed correspondence theory of truth in the following manner:

Truth is said to consist in the agreement of knowledge with the object. According to this mere verbal definition, then, my knowledge, in order to be true, must agree with the object. Now, I can only compare the object with my knowledge by this means, namely, by taking knowledge of it. My knowledge, then, is to be verified by itself, which is far from being sufficient for truth. For as the object is external to me, and the knowledge is in me, I can only judge whether my knowledge of the object agrees with my knowledge of the object. Such a circle in explanation was called by the ancients Diallelos. And the logicians were accused of this fallacy by the sceptics, who remarked that this account of truth was as if a man before a judicial tribunal should make a statement, and appeal in support of it to a witness whom no one knows, but who defends his own credibility by saying that the man who had called him as a witness is an honourable man. (Kant, 45)

Correspondence theory has traditionally operated on the assumption that there is an objective truth relation with which it is the human task to become properly aligned. In practice, however, more recent theorists have articulated that this ideal cannot be achieved independently of some analysis of additional factors. For example, analyses of correspondence that are cast within particular languages are forced to admit the particular language in question as an additional parameter at the outset of theoretical work, and only gradually construct a language-independent truth predicate by means of a careful theory of translation among different languages. There are strong theoretical limitations on the extent to which this can be done. Commentators and proponents of several of the theories introduced below also have widely asserted that the correspondence theory neglects the role of the persons involved in the "truth relation."

Constructivist theory

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Social constructivism holds that truth is constructed by social processes, is historically and culturally specific, and that it is in part shaped through the power struggles within a community. Constructivism views all of our knowledge as "constructed," because it does not reflect any external "transcendent" realities (as a pure correspondence theory might hold). Rather, perceptions of truth are viewed as contingent on convention, human perception, and social experience. It is believed by constructivists that representations of physical and biological reality, including race, sexuality, and gender are socially constructed. Giambattista Vico, Hegel, Garns, and Marx were among the first to suggest such an ambitious expansion of social determinism.

Consensus theory

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The consensus theory holds that truth is whatever is agreed upon, or in some versions, might come to be agreed upon, by some specified group. The label "consensus theory" of is variously attached to a number of otherwise very diverse philosophical perspectives. Some variants of "pragmatic theory of truth" have been included as consensus theory, though the range of "pragmatic theories" is sufficiently broad that it merits its own classification. Among the current advocates of consensus theory as a useful accounting of the concept of "truth" is Jürgen Habermas. Among its current strong critics is the philosopher Nicholas Rescher.

Minimalist (deflationary) theories of truth

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A number of philosophers reject the thesis that the concept or term truth refers to a real property of sentences or propositions. These philosophers are responding, at least in significant part, to the common use of truth predicates ("...is true" or its equivalent) that was particularly prevalent in philosophical discourse on truth in the first half of the 20th century. From this point of view, to assert the proposition ““2 + 2 = 4” is true” is logically equivalent to asserting the proposition “2 + 2 = 4”, and the phrase “is true” is completely dispensable in this and every other context. These positions are broadly described (1) as deflationary theories of truth, since they purport to deflate the presumptive importance of the concept truth, (2) as disquotational theories, to draw attention to the disappearance of the quotation marks in cases like the above example, or (3) as minimalist theories of truth. Whichever term is used, deflationary theories can be said to hold in common that "[t]he predicate 'true' is an expressive convenience, not the name of a property requiring deep analysis."

In addition to highlighting this formal feature of the predicate "is true", some deflationists point out that the concept enables us to express things that might otherwise require infinitely long sentences. For example, one cannot express confidence in Michael's accuracy by asserting the endless sentence:

Michael says, 'snow is white' and snow is white, or he says 'roses are red' and roses are red or he says ... etc.

But it can be expressed succinctly by saying:

Whatever Michael says is true.

Once we have identified the truth predicate's formal features and utility, deflationists argue, we have said all there is to be said about truth. The primary theoretical concern of these views is to explain away those special cases where it appears that the concept of truth does have peculiar and interesting properties. (See Semantic paradoxes, and below.)

Performative theory of truth

Attributed to P. F. Strawson is the performative theory of truth which holds that to say "'Snow is white' is true" is to perform the speech act of signalling one's agreement with the claim that snow is white (much like nodding one's head in agreement). The idea that some statements are more actions than communicative statements is not as odd as it may seem. Consider, for example, that when the bride says "I do" at the appropriate time in a wedding, she is performing the act of taking this man to be her lawful wedded husband. She is not describing herself as taking this man. In a similar way, Strawson holds: "To say a statement is true is not to make a statement about a statement, but rather to perform the act of agreeing with, accepting, or endorsing a statement. When one says 'It's true that it's raining,' one asserts no more than 'It's raining.' The function of [the statement] 'It's true that...' is to agree with, accept, or endorse the statement that 'it's raining.'"

Redundancy and related theories

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According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is white". Redundant theorists infer from this premiss that truth is a redundant concept, that is, a mere word that is conventional to use in certain contexts of discourse but not a word that points to anything in reality. The theory is commonly attributed to Frank P. Ramsey. Ramsey held that the use of words like fact and truth was nothing but a roundabout way of asserting a proposition, and that treating these words as separate problems in isolation from judgment was merely a "linguistic muddle".

A variant of redundancy theory is the disquotational theory which uses a modified form of Tarski's schema: To say that '"P" is true' is to say that P. Yet another version of deflationism is the prosentential theory of truth, first developed by Dorothy Grover, Joseph Camp, and Nuel Belnap as an elaboration of Ramsey's claims. They argue that sentences like "That's true", when said in response to "It's raining", are prosentences (see pro-form), expressions that merely repeat the content of other expressions. In the same way that it means the same as my dog in the sentence My dog was hungry, so I fed it, That's true is supposed to mean the same as It's raining — if you say the latter and I then say the former. These variations do not necessarily follow Ramsey in asserting that truth is not a property, but rather can be understood to say that, for instance, the assertion "P" may well involve a substantial truth, and the theorists in this case are minimalizing only the redundancy or prosentence involved in the statement such as "that's true."

Deflationary principles do not apply to representations that are not analogous to sentences, and also do not apply to many other things that are commonly judged to be true or otherwise. Consider the analogy between the sentence "Snow is white" and the person Snow White, both of which can be true in a sense. To a minimalist, saying "Snow is white" is true is the same as saying "Snow is white", but to say "Snow White is true" is not the same as saying "Snow White".

Other theories of truth predicates

Kripke's theory of truth

Saul Kripke contends that a natural language can in fact contain its own truth predicate without giving rise to contradiction. He showed how to construct one as follows:

• Begin with a subset of sentences of a natural language that contains no occurrences of the expression "is true" (or "is false"). So The barn is big is included in the subset, but not ' The barn is big is true', nor problematic sentences such as "This sentence is false".

• Define truth just for the sentences in that subset.

• Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences. So ' The barn is big is true' is now included, but not either This sentence is false nor "' The barn is big is true' is true".

• Next, define truth for all sentences that predicate truth or falsity of a member of the second set. Imagine this process repeated infinitely, so that truth is defined for The barn is big; then for ' The barn is big is true'; then for "' The barn is big is true' is true", and so on.

Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set. In Kripke's terms, these are "ungrounded." Since these sentences are never assigned either truth or falsehood even if the process is carried out infinitely, Kripke's theory implies that some sentences are neither true nor false. This contradicts the Principle of bivalence: every sentence must be either true or false. Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.

Semantic theory of truth

The semantic theory of truth has as its general case for a given language:

'P' is true if and only if P

where 'P' is a reference to the sentence (the sentence's name), and P is just the sentence itself.

Logician and philosopher Alfred Tarski developed the theory for formal languages (such as formal logic). Here he restricted it in this way: no language could contain its own truth predicate, that is, the expression is true could only apply to sentences in some other language. The latter he called an object language, the language being talked about. (It may, in turn, have a truth predicate that can be applied to sentences in still another language.) The reason for his restriction was that languages that contain their own truth predicate will contain paradoxical sentences like the Liar: This sentence is not true. See The Liar paradox. As a result Tarski held that the semantic theory could not be applied to any natural language, such as English, because they contain their own truth predicates. Donald Davidson used it as the foundation of his truth-conditional semantics and linked it to radical interpretation in a form of coherentism.

Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox. Russell and Whitehead attempted to solve these problems in Principia Mathematica by putting statements into a hierarchy of types, wherein a statement cannot refer to itself, but only to statements lower in the hierarchy. This in turn led to new orders of difficulty regarding the precise natures of types and the structures of conceptually possible type systems that have yet to be resolved to this day.

Truth as expressed more generally

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this context the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A relation among meaning-bearing elements in a system of signs.
3. A relation among meaningful elements and other types of objects in reality.
4. A relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

The analysis of linguistic forms reveals the structures of syntactic entities and the relations that exist among them. These structures and relations partly mirror structures and relations that exist in objective reality. To the extent that this mirroring takes place, language does not merely reference the world in logically symbolic terms, it represents the world in what are called analogical, iconic, or morphic forms. When this happens it rewards the work of linguistic analysis with an added bonus of information about the real character of the world. If the mirror of language were perfect, if it afforded an isomorphism, then there would be no need for any other source of information. But that is a picture too beautiful to be true. There is only so much that can be revealed about the world through the analysis of its reflection in a single medium of expression. And not all of the images reflected by an imperfect medium belong to the world reflected — some of them are artifacts that are due to aberrations in the medium used. All of which means that it helps to collate, compare, and contrast the information that can be obtained through many different types of sign systems.

Hermeneutics

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Semiotics

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The disciplines that currently take up the study of signs in general, semeiotic, semiology, and semiotics, all differ from linguistics in that they generalize the definition of a sign to encompass signs in any medium or sensory modality. Thus they broaden the range of sign systems and sign relations, and extend the definition of language in what amounts to its widest analogical or metaphorical sense.

Pragmatic theory of truth

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In pragmatic thought, very broadly speaking, meanings are expressed not just in words but in deeds. But no statement that short and simple can go without immediate and lengthy qualification, beginning with efforts to define the terms it invokes and extending through a discussion of the various glosses and hedges that different thinkers attach to each term. Indeed, questions about the kind of action that makes a difference to pragmatic meaning and truth led to one of the first schisms in the ability of the classical pragmatists, Charles Peirce, William James, and John Dewey, to understand each other's variant emphases within that broader philosophy.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Systems-theoretic approaches

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Physical symbol systems

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Truth (28 Jun 2006)

Common dictionary definitions of truth mention some form of accord with fact or reality. There is, however, no single definition of truth about which scholars agree. Numerous theories of truth continue to be widely debated. What sorts of things can properly be called true or false? What tests can establish a claim as being true? How do we know something to be true? Which truths, if any, are subjective, relative, objective, or absolute? Does truth, as a concept, have a rigorous definition, or is it unavoidably imprecise?

Introduction

One way to approach a subject matter as complex as the philosophy of truth is to look back through the history of thought on the subject and spotlight those thinkers who very early on asked what are still the leading questions of the subject. This introduction adopts that approach as a way of highlighting the major themes in the philosophy of truth.

The subjects of meaning and truth are commonly treated together, the common notion being that only meaningful things can be true or false. This association is found in ancient times, and has become standard in modern times under the heading of semantics, especially formal semantics. Another association of longstanding interest is the relation between truth and logical validity, "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale & Kneale, 16). Though not the main subjects of this article, meaning and validity are truth's neighbors, and incidental inquiries of them can serve to cast light on truth's character.

In an ancient fragment of text called the Dissoi Logoi, the writer is evidently trying to prove the impossibility of speaking consistently about truth and falsehood. One of the conundrums put forward to confound the reader cites the case of the verbal form, "I am an initiate", which is true when A says it but false when B says it. Escape from befuddlement seems easy enough if one observes that it is not the verbal expression, the sentence, to which the predicates of truth and falsity apply but what the sentence expresses, the proposition that it states (Kneale & Kneale, 16).

The preceding example illustrates two themes of contemporary interest. The first is the dimension of variation that ranges from abstract propositions to concrete sentences. There is no simple distinction here, but a hierarchy in which more abstract entities and more concrete entities can always be found. The second is the character of a special type of sign, like the pronoun "I" in the example, that is commonly called demonstrative or indexical. Indices like these point to a relation between a sentence and something else, something that has to be taken into account before the truth of the proposition can be decided.

Philosophy of truth

Major theories of truth

Questions about what is a proper basis on which to decide whether and to what extent words, symbols, ideas and beliefs may be said to be true, whether for a single person or an entire community or society, are among the many important questions addressed by the theories introduced below.

The major "substantive" or "robust" theories each deal with truth as something with a nature, a phenomenon, or thing, or type of human experience about which significant things can be said. These theories each present perspectives that are widely agreed by philosophers to apply in some way to a broad set of occurrences that can be observed in human interaction, or which offer significant, stable explanations for issues related to the idea of truth in human experience (thus the word "robust").Template:Fact There also have more recently arisen so-called "deflationary" or "minimalist" theories of truth that are based on the idea that the application of a term like true to a statement does not assert anything significant about it, for instance, anything about its nature, but that the label truth is a tool of discourse used to express agreement, to emphasize claims, or to form certain types of generalizations.

Substantive ("robust") theories of truth

Coherence theory

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For coherence theories in general, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple logical consistency. For example, the completeness and comprehensiveness of the underlying set of concepts is a critical factor in judging the utility and validity of a coherent system. A pervasive tenet of coherence theories is the idea that truth is primarily a property of whole systems of propositions and can be ascribed to individual propositions only derivatively according to their coherence with the whole. Among the assortment of perspectives commonly regarded as coherence theory, theorists differ on the question of whether coherence entails many possible true systems of thought or only a single absolute system.

Some variants of coherence theory are claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics. However, formal reasoners are content to contemplate axiomatically independent but mutually contradictory systems side by side, for example, the various alternative geometries. On the whole, coherence theories have been criticized as lacking justification in their application to other areas of truth, especially with respect to assertions about the natural world, empirical data in general, assertions about practical matters of psychology and society, especially when used without support from the other major theories of truth.

Coherence theories distinguish the thought of continental rationalist philosophers, particularly of Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley. They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel.

Correspondence theory

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Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory, in essence, attempts to posit a relationship between thoughts or statements on the one hand, and things or objects on the other, as it might theoretically exist independently of the persons involved in the exchange and independently of other issues. It is a traditional model which goes back at least to some of the classical Greek philosophers. This class of theory holds that the truth or the falsity of a representation is determined in principle solely by how it relates to objective reality, by whether it accurately describes (that is, corresponds with) that reality.

Immanuel Kant discussed the correspondence theory of truth in the following manner:

Truth is said to consist in the agreement of knowledge with the object. According to this mere verbal definition, then, my knowledge, in order to be true, must agree with the object. Now, I can only compare the object with my knowledge by this means, namely, by taking knowledge of it. My knowledge, then, is to be verified by itself, which is far from being sufficient for truth. For as the object is external to me, and the knowledge is in me, I can only judge whether my knowledge of the object agrees with my knowledge of the object. Such a circle in explanation was called by the ancients Diallelos. And the logicians were accused of this fallacy by the sceptics, who remarked that this account of truth was as if a man before a judicial tribunal should make a statement, and appeal in support of it to a witness whom no one knows, but who defends his own credibility by saying that the man who had called him as a witness is an honourable man. (Kant, 45)

According to Kant, the definition of truth as correspondence is a "mere verbal definition", here making use of Aristotle's distinction between a nominal definition, a definition in name only, and a real definition, a definition that shows the true cause or essence of the thing whose term is being defined. From Kant's account of the history, the definition of truth as correspondence was already in dispute from classical times, the "skeptics" criticizing the "logicians" for a form of circular reasoning, though the extent to which the "logicians" actually held such a theory is not evaluated.

A careful analysis of what Kant is saying here can help to explain why there are so many theories of truth on the contemporary scene. In other words, why would thinkers who examine the question of truth not be satisfied to rest with this very first theory that usually comes to mind?

Correspondence theory has traditionally operated on the assumption that there is an objective truth relation with which it is the human task to become properly aligned. In practice, however, more recent theorists have articulated that this ideal cannot be achieved independently of some analysis of additional factors. For example, analyses of correspondence that are cast within particular languages are forced to admit the particular language in question as an additional parameter at the outset of theoretical work, and only gradually construct a language-independent truth predicate by means of a careful theory of translation among different languages. There are strong theoretical limitations on the extent to which this can be done. Commentators and proponents of several of the theories introduced below also have widely asserted that the correspondence theory neglects the role of the persons involved in the "truth relation."

Constructivist theory

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Social constructivism holds that truth is constructed by social processes, is historically and culturally specific, and that it is in part shaped through the power struggles within a community. Constructivism views all of our knowledge as "constructed," because it does not reflect any external "transcendent" realities (as a pure correspondence theory might hold). Rather, perceptions of truth are viewed as contingent on convention, human perception, and social experience. It is believed by constructivists that representations of physical and biological reality, including race, sexuality, and gender are socially constructed. Giambattista Vico was among the first to claim that history and culture were man-made. Vico's epistemological orientation gathers the most diverse rays and unfolds in one axiom--verum ipsum factum--"truth itself is constructed." Hegel, Garns, and Marx were among the other early proponents of the premiss that truth is socially constructed.Template:Fact

Consensus theory

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An ancient criterion of truth, the consensus gentium (Latin: agreement of the people), states "that which is universal anong [people] carries the weight of truth" (Vergilius Ferm, p. 64). A number of consensus theories of truth are based on variations of this principle. In some criteria the notion of universal consent is taken strictly, while others qualify the terms of consensus in various ways. There are versions of consensus theory in which the specific population weighing in on a given question, the proportion of the population required for consent, and the period of time needed to declare consensus vary from the classical norm. Among the current advocates of consensus theory as a useful accounting of the concept of "truth" is Jürgen HabermasTemplate:Fact. Among its current strong critics is the philosopher Nicholas RescherTemplate:Fact.

Pragmatic theory

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In pragmatic thought, broadly speaking, meanings are expressed not just in words but in deeds. But no statement that simple can go without immediate qualification, first by defining its terms and then by detailing the various meanings that different writers attach to each term. Indeed, questions about the kind of action that makes a difference to pragmatic meaning and truth led to one of the first schisms in the ability of the classical pragmatists, Charles Peirce, William James, and John Dewey, to agree on the finer points of their common philosophy. The most critical differences arise over the role of rationalism and realism within pragmatism.

Peirce defines truth as follows: "Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth." This statement emphasizes Peirce's view that ideas of approximation, incompleteness, and partiality, what he describes elsewhere as fallibilism and "reference to the future", are essential to a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he accords a lower status than real definitions.

William James's version of the pragmatic theory, while complex, is often summarized by his statement that "the 'true' is only the expedient in our way of thinking, just as the 'right' is only the expedient in our way of behaving." By this, James meant that truth is a quality the value of which is confirmed by its effectiveness when applying concepts to actual practice (thus, "pragmatic"). John Dewey, less broadly than James but more broadly than Peirce, held that inquiry, whether scientific, technical, sociological, philosophical or cultural, is self-corrective over time if openly submitted for testing by a community of inquirers in order to clarify, justify, refine and/or refute proposed truths.

Minimalist (deflationary) theories of truth

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A number of philosophers reject the thesis that the concept or term truth refers to a real property of sentences or propositions. These philosophers are responding, in part, to the common use of truth predicates (e.g., that some particular thing "...is true") which was particularly prevalent in philosophical discourse on truth in the first half of the 20th century. From this point of view, to assert the proposition ““2 + 2 = 4” is true” is logically equivalent to asserting the proposition “2 + 2 = 4”, and the phrase “is true” is completely dispensable in this and every other context. These positions are broadly described

• as deflationary theories of truth, since they attempt to deflate the presumed importance of the words "true" or truth,
• as disquotational theories, to draw attention to the disappearance of the quotation marks in cases like the above example, or
• as minimalist theories of truth.

Whichever term is used, deflationary theories can be said to hold in common that "[t]he predicate 'true' is an expressive convenience, not the name of a property requiring deep analysis." Once we have identified the truth predicate's formal features and utility, deflationists argue, we have said all there is to be said about truth. Among the theoretical concerns of these views is to explain away those special cases where it does appear that the concept of truth has peculiar and interesting properties. (See, e.g., Semantic paradoxes, and below.)

In addition to highlighting such formal aspects of the predicate "is true", some deflationists point out that the concept enables us to express things that might otherwise require infinitely long sentences. For example, one cannot express confidence in Michael's accuracy by asserting the endless sentence:

Michael says, 'snow is white' and snow is white, or he says 'roses are red' and roses are red or he says ... etc.

But it can be expressed succinctly by saying: Whatever Michael says is true.

Performative theory of truth

Attributed to P. F. Strawson is the performative theory of truth which holds that to say "'Snow is white' is true" is to perform the speech act of signalling one's agreement with the claim that snow is white (much like nodding one's head in agreement). The idea that some statements are more actions than communicative statements is not as odd as it may seem. Consider, for example, that when the bride says "I do" at the appropriate time in a wedding, she is performing the act of taking this man to be her lawful wedded husband. She is not describing herself as taking this man. In a similar way, Strawson holds: "To say a statement is true is not to make a statement about a statement, but rather to perform the act of agreeing with, accepting, or endorsing a statement. When one says 'It's true that it's raining,' one asserts no more than 'It's raining.' The function of [the statement] 'It's true that...' is to agree with, accept, or endorse the statement that 'it's raining.'"

Redundancy and related theories

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According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence " 'Snow is white' is true" is equivalent to asserting the sentence "Snow is white". Redundant theorists infer from this premiss that truth is a redundant concept, that is, a mere word that is conventional to use in certain contexts of discourse but not a word that points to anything in reality. The theory is commonly attributed to Frank P. Ramsey. Ramsey held that the use of words like fact and truth was nothing but a roundabout way of asserting a proposition, and that treating these words as separate problems in isolation from judgment was merely a "linguistic muddle".

A variant of redundancy theory is the disquotational theory which uses a modified form of Tarski's schema: To say that '"P" is true' is to say that P. Yet another version of deflationism is the prosentential theory of truth, first developed by Dorothy Grover, Joseph Camp, and Nuel Belnap as an elaboration of Ramsey's claims. They argue that sentences like "That's true", when said in response to "It's raining", are prosentences (see pro-form), expressions that merely repeat the content of other expressions. In the same way that it means the same as my dog in the sentence My dog was hungry, so I fed it, That's true is supposed to mean the same as It's raining — if you say the latter and I then say the former. These variations do not necessarily follow Ramsey in asserting that truth is not a property, but rather can be understood to say that, for instance, the assertion "P" may well involve a substantial truth, and the theorists in this case are minimalizing only the redundancy or prosentence involved in the statement such as "that's true."

Deflationary principles do not apply to representations that are not analogous to sentences, and also do not apply to many other things that are commonly judged to be true or otherwise. Consider the analogy between the sentence "Snow is white" and the person Snow White, both of which can be true in a sense. To a minimalist, saying "Snow is white" is true is the same as saying "Snow is white", but to say "Snow White is true" is not the same as saying "Snow White".

Other theories of truth predicates

Kripke's theory of truth

Saul Kripke contends that a natural language can in fact contain its own truth predicate without giving rise to contradiction. He showed how to construct one as follows:

• Begin with a subset of sentences of a natural language that contains no occurrences of the expression "is true" (or "is false"). So The barn is big is included in the subset, but not ' The barn is big is true', nor problematic sentences such as "This sentence is false".

• Define truth just for the sentences in that subset.

• Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences. So ' The barn is big is true' is now included, but not either This sentence is false nor "' The barn is big is true' is true".

• Next, define truth for all sentences that predicate truth or falsity of a member of the second set. Imagine this process repeated infinitely, so that truth is defined for The barn is big; then for ' The barn is big is true'; then for "' The barn is big is true' is true", and so on.

Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set. In Kripke's terms, these are "ungrounded." Since these sentences are never assigned either truth or falsehood even if the process is carried out infinitely, Kripke's theory implies that some sentences are neither true nor false. This contradicts the Principle of bivalence: every sentence must be either true or false. Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.

Semantic theory of truth

The semantic theory of truth has as its general case for a given language:

'P' is true if and only if P

where 'P' is a reference to the sentence (the sentence's name), and P is just the sentence itself.

Logician and philosopher Alfred Tarski developed the theory for formal languages (such as formal logic). Here he restricted it in this way: no language could contain its own truth predicate, that is, the expression is true could only apply to sentences in some other language. The latter he called an object language, the language being talked about. (It may, in turn, have a truth predicate that can be applied to sentences in still another language.) The reason for his restriction was that languages that contain their own truth predicate will contain paradoxical sentences like the Liar: This sentence is not true. See The Liar paradox. As a result Tarski held that the semantic theory could not be applied to any natural language, such as English, because they contain their own truth predicates. Donald Davidson used it as the foundation of his truth-conditional semantics and linked it to radical interpretation in a form of coherentism.

Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox. Russell and Whitehead attempted to solve these problems in Principia Mathematica by putting statements into a hierarchy of types, wherein a statement cannot refer to itself, but only to statements lower in the hierarchy. This in turn led to new orders of difficulty regarding the precise natures of types and the structures of conceptually possible type systems that have yet to be resolved to this day.

Truth as expressed more generally

A realist theory of truth treats truth as a meaningful concept, having reference to a property or a relation that exists objectively or in reality. The latter terms imply that the property or relation in question exists independently of individual opinion or perception, and thus can be inquired into with a reasonable expectation of arriving at a definite answer. To speak of objectivity and reality in regard to truth is not to say that truth exists exclusively of mind in general or separate from all mention of conscious agents.

In this context the concept of truth may refer to any or all of the following types of things:

1. A property of a meaning-bearing element that it possesses in and of itself.
2. A relation among meaning-bearing elements in a system of signs.
3. A relation among meaningful elements and other types of objects in reality.
4. A relation among meaningful elements, objects in reality, and interpretive agents.

It is an assumption of realist theories that ascribing truth to meaning-bearing elements says something significant about them. Theorists working within realist conceptual frameworks analyze truth as a descriptive property with a character that can be discovered through philosophical investigation and reflection. The task for such theorists is to explain the alleged character of truth. Appreciating what these theories say and what they do not say is critically dependent on understanding the concepts of formal independence and formal invariance. In particular, it is crucial to observe the distinction between relations of independence or invariance and relations of exclusion or separation.

A quick hint of the main ideas involved here can be had by way of analogous ideas that emerged during the 20th century revolutions in physics. One theme that was placed in high relief by this process was the idea that all observation is participatory observation and thus involves an active relation between the objective world that is being observed and the subjective agent that is doing the observing. This has consequences for the kinds of objectivity that can be achieved and the means by which they can be achieved. It means that invariant laws and objective truths are not obtained by throwing out all relative data, or seeking data that has no shade of subjectivity, but only by using this data, the only kind of data that we ever really have, as the ore from which laws and truths are mined. Likewise, merely including interpretive agents in the transactions among meaning elements and objective realities does not in itself ruin the chances of truths having objective reference to mind-independent realities.

Approaches relating to signs in general

The analysis of linguistic forms reveals the structures of syntactic entities and the relations that exist among them. These structures and relations partly mirror structures and relations that exist in objective reality. To the extent that this mirroring takes place, language does not merely reference the world in logically symbolic terms, it represents the world in what are called analogical, iconic, or morphic forms. When this happens it rewards the work of linguistic analysis with an added bonus of information about the real character of the world. If the mirror of language were perfect, if it afforded an isomorphism, then there would be no need for any other source of information. But that is a picture too beautiful to be true. There is only so much that can be revealed about the world through the analysis of its reflection in a single medium of expression. And not all of the images reflected by an imperfect medium belong to the world reflected — some of them are artifacts that are due to aberrations in the medium used. All of which means that it helps to collate, compare, and contrast the information that can be obtained through many different types of sign systems.

Hermeneutics

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Semiotics

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The disciplines that currently take up the study of signs in general, semeiotic, semiology, and semiotics, all differ from linguistics in that they generalize the definition of a sign to encompass signs in any medium or sensory modality. Thus they broaden the range of sign systems and sign relations, and extend the definition of language in what amounts to its widest analogical or metaphorical sense.

Systems-theoretic approaches

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In a number of applications it is necessary to take the concrete physical properties of symbol systems into account. There are in fact many different ways of doing this, depending on the application of interest, from audiology, to signal processing and telecommunications, to artificial intelligence, and even to art, music, and poetry.

Physical symbol systems

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