Truth

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.

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.'" Encyclopedia of Philosophy, Vol.6: Performative Theory of Truth, auth:Gertrude Ezorsky, p88 (Macmillan, 1969)

Redundancy and related theories

According to the redundancy theory of truth, asserting that a statement is true is completely equivalent to asserting the statement itself. For example, making the assertion that " 'Snow is white' is true" is equivalent to asserting "Snow is white". Redundancy theorists infer from this premise that truth is a redundant concept; that is, it is merely a word that is traditionally used in conversation or writing, generally for emphasis, but not a word that actually equates to anything in reality. This theory is commonly attributed to Frank P. Ramsey, who 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".Encyclopedia of Philosophy, Supp., "Truth", auth:Michael Williams, p572-573 (Macmillan, 1996)Ramsey, F.P. (1927), "Facts and Propositions", Aristotelian Society Supplementary Volume 7, 153–170. Reprinted, pp. 34–51 in F.P. Ramsey, Philosophical Papers, David Hugh Mellor (ed.), Cambridge University Press, Cambridge, UK, 1990

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

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.

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

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.

Some notable philosophers' views on truth

Classical philosophers

Aquinas and the scholastics

Kant

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, Immanuel (1800), Introduction to Logic. Reprinted, Thomas Kingsmill Abbott (trans.), Dennis Sweet (intro.) (2005)

Nietzsche

Robert Wicks discusses Nietzsche's basic view of truth as follows:

Some scholars regard Nietzsche's 1873 unpublished essay, "On Truth and Lies in an Nonmoral Sense" ("Über Wahrheit und Lüge im außermoralischen Sinn") as a keystone in his thought. In this essay, Nietzsche rejects the idea of universal constants, and claims that what we call "truth" is only "a mobile army of metaphors, metonyms, and anthropomorphisms." His view at this time is that arbitrariness completely prevails within human experience: concepts originate via the very artistic transference of nerve stimuli into images; "truth" is nothing more than the invention of fixed conventions for merely practical purposes, especially those of repose, security and consistence.http://plato.stanford.edu/entries/nietzsche/#2

Heidegger

Foucault

Nishida

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,Susan Haack, “truth, truths, “truth,” and “truths” in the law, Journal of Philosophy, Science & Law, Volume 3, September 2003. though the actual use of the word "truth" in legal practice tends to be limited to certain very specific contexts.William M. Shields, J.D., ""Truth in Legal Practice", in Journal of PHilosophy, Science and Law, Volume 3, November 2003. 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.Ibid. 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,Black’s Law Dictionary, ed. Bryan A. Garner, 7th Edition, 1999, 1520. this use of the term in this specific manner deriving from common law dating back at least seven centuries.Docherty, Bonnie, "Defamation Law: Positive Jurisprudence" in Harvard Human Rights Journal, Vol 13, (Spring 2000) 264 ff. 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, op cit intro section of article. 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.Ibid. Shields's footnotes eliminated here. [link]

Truth in mathematics

Main articles: Model theory, Proof theory

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 within the system..See, e.g., Chaitin, Gregory L., The Limits of Mathematics (1997) esp. 89 ff. 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 M. Davis. "Hilbert's Tenth Problem is Unsolvable." American Mathematical Monthly 80, pp. 233-269, 1973, 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.Yandell, Benjamin H.. The Honors Class. Hilbert's Problems and Their Solvers (2002). Gödel and Paul Cohen showed that this hypothesis cannot be proved or disproved using the standard axioms of set theory.Chaitin, Gregory L., The Limits of Mathematics (1997) 1-28, 89 ff. 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

Truth in religion

Most religious traditions hold a body of truths that are part of the particular tradition. Such truths may be considered to be spiritually revealed, or may be developed through tradition, or may be a combination of both. Whatever these truths are for the particular religious tradition, they can be called part of the doctrine of that tradition.

Buddhism

The Four Noble Truths

The Four Noble Truths are the most fundamental Buddhist teachings and appear countless times throughout the most ancient Buddhist texts, the Pali Canon. They arose from Buddha's enlightenment, and are regarded in Buddhism as deep spiritual insight, not as philosophical theory, with Buddha noting in the Samyutta Nikaya: "These Four Noble Truths, monks, are actual, unnering, not otherwise. Therefore they are called noble truths." The Collected Discourses of the Buddha: A new translation of the Samyutta Nikaya, Bhikkhu Bodhi, 2000

The Four Noble Truths (Catvāry Āryasatyāni) are as follows:

• The truth of suffering. Suffering applies to the following: Birth, aging, illness, death; union with what is displeasing; separation from what is pleasing; and to not get what one wants.
• The truth that suffering originates within us from the craving for pleasure and for being or nonbeing.
• The truth that this craving can be eliminated (Nibbana). "The Nobility of the Truths", Bhikkhu Bodhi, 1992, [link]
• The truth that this elimination is the result of a methodical way or path that must be followed, which is known as the Noble Eightfold Path.
  

Christianity

Assertions of truth based upon history, revelation and testimony set forward in the Bible are central to Christian beliefs. Some denominations have asserted additional authorities as sources of doctrinal truth — for instance, in Roman Catholicism the Pope is asserted to be infallible on matters of church doctrine.See, e.g., Richard F. Costigan, The Consensus Of The Church And Papal Infallibility: A Study In The Background Of Vatican I (2005)

Biblical inerrancy

Some Christian traditions hold a doctrine called Biblical inerrancy, which asserts that the Bible is without error, that is, it can be said to be true as to all issues contained within, whether Old Testament or New. Various interpretations have been applied, depending on the tradition.See, e.g. Norman L. Geisler, Inerrancy (1980)Stephen T. Davis, The debate about the Bible: Inerrancy versus infallibility (1977) According to some interpretations of the doctrine, all of the Bible is without error, i.e., is to be taken as true, no matter what the issue. Other interpretations hold that the Bible is always true on important matters of faith, while yet other interpretations hold that the Bible is true but must be specifically interpreted in the context of the language, culture and time that relevant passages were written.See, e.g. Marcus J. Borg, Reading the Bible Again For the First Time: Taking the Bible Seriously But Not Literally (2002) 7-8

\"Double truth\" theories

In thirteenth century Europe, the Roman Catholic Church denounced what it described as theories of "double truth," i.e. theories to the effect that although a truth may be established by reason, its contrary ought to be believed as true as a matter of faith. The condemnation was aimed specifically at a "Latin Averroist" (see Averroës), Siger of Brabant, but it was more broadly an attempt to halt the spread of Aristotle's ideas, which the reconquest of Spain and, accordingly, access to the libraries of the Moors had re-introduced into the Latin literate world. See, e.g., Gilson, Etienne, "La doctrine de la double vérité," Études de philosophie médiévale (1921), pp. 51-69; translated as, History of Christian Philosophy in the Middle Ages (1955). At the time, much of the doctrine of the Roman Catholic Church was based upon neoplatonic ideas, and Aristoteleanism struck many as heresy. Siger and others seem to have conceded this, and to have used the sharp reason/faith distinction that came to be known as "double truth" as a way of legitimizing discussion of Aristotle despite that concession.See, e.g., [link]

Hinduism

Jainism

Notes