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The meaning of the word truth extends from honesty, good faith, and sincerity in general, to agreement with fact or reality in particular.[1] The term has no single definition about which the majority of professional philosophers and scholars agree. Various theories of truth continue to be debated. There are differing claims on such questions as what constitutes truth; how to define and identify truth; the roles that revealed and acquired knowledge play; and whether truth is subjective, relative, objective, or absolute. This article introduces the various perspectives and claims, both today and throughout history. Image File history File links Size of this preview: 484 × 599 pixelsFull resolution (780 × 966 pixel, file size: 197 KB, MIME type: image/jpeg) Faithful reproductions of two-dimensional original works cannot attract copyright in the U.S. according to the rule in Bridgeman Art Library v. ...
Image File history File links Size of this preview: 484 × 599 pixelsFull resolution (780 × 966 pixel, file size: 197 KB, MIME type: image/jpeg) Faithful reproductions of two-dimensional original works cannot attract copyright in the U.S. according to the rule in Bridgeman Art Library v. ...
Narcisse (1728) François Lemoyne or François Le Moine, (born 1688 in Paris, died 4 June 1737 in Paris) was a French rococo painter. ...
See Truth for the discussion on the meaning of the word. ...
The semantic field of a word is the sum of the sememes expressed by it. ...
Honest redirects here, For other uses, see Honesty (disambiguation) Look up honesty in Wiktionary, the free dictionary. ...
Bona fide redirects here. ...
In the modern world, sincerity is the elusive virtue of speaking truly about ones feelings, thoughts, desires. ...
For the trade organisation, see Federation Against Copyright Theft. ...
For other uses, see Reality (disambiguation). ...
For other uses, see Definition (disambiguation). ...
In mathematics, theory is used informally to refer to a body of knowledge about mathematics. ...
This article is in need of attention. ...
Categories: Wikipedia cleanup | Stub ...
An objective or goal is a personal or organizational desired end point in development. ...
The Absolute is the totality of things; all that is, whether it has been discovered or not. ...
Etymology - Further information: Veritas and Aletheia
English truth is from Old English tríewþ, tréowþ, trýwþ, Middle English trewþe, cognate to Old High German triuwida, Old Norse tryggð. Like troth, it is a -th nominalisation of the adjective true (Old English tréowe). For other uses, see Veritas (disambiguation). ...
Aletheia in its current sense comes from Heideggers use of it as renewed attempt to understand Truth. ...
Old English (also called Anglo-Saxon[1], Old English: ) is an early form of the English language that was spoken in parts of what is now England and southern Scotland between the mid-fifth century and the mid-twelfth century. ...
Middle English is the name given by historical linguistics to the diverse forms of the English language spoken between the Norman invasion of 1066 and the mid-to-late 15th century, when the Chancery Standard, a form of London-based English, began to become widespread, a process aided by the...
The (Late Old High) German speaking area of the Holy Roman Empire around 950. ...
Old Norse or Danish tongue is the Germanic language once spoken by the inhabitants of the Nordic countries (for instance during the Viking Age). ...
To meet Wikipedias quality standards and to make a clear distinction between fact and fiction, this article may require cleanup. ...
English true is from Old English (West Saxon) (ge)tríewe, tréowe, cognate to Old Saxon (gi)trûui, Old High German (ga)triuwu (Modern German treu "faithful"), Old Norse tryggr, Gothic triggws.[2], all from a Proto-Germanic *trewwj- "having good faith". Old Norse trú, means "faith, word of honour; religious faith, belief"[3] (archaic English troth "loyalty, honesty, good faith", compare Ásatrú). This article concerns the English kingdom, not the Westland Wessex helicopter Wessex was one of the seven major Anglo-Saxon kingdoms (the Heptarchy) that preceded the kingdom of England. ...
Old Saxon, also known as Old Low German, is a Germanic language. ...
The (Late Old High) German speaking area of the Holy Roman Empire around 950. ...
German (called Deutsch in German; in German the term germanisch is equivalent to English Germanic), is a member of the western group of Germanic languages and is one of the worlds major languages. ...
Old Norse or Danish tongue is the Germanic language once spoken by the inhabitants of the Nordic countries (for instance during the Viking Age). ...
Gothic is an extinct Germanic language that was spoken by the Goths. ...
This article or section does not cite any references or sources. ...
Bona fide redirects here. ...
Mjolnir, the hammer of Thor, is one of the major symbols of Ãsatrú. This article is about the reconstruction of Norse paganism in particular. ...
Thus, truth in its original sense is the quality of "faithfulness, fidelity, loyalty, sincerity, veracity",[4], and the narrowed sense "in agreement with fact or reality", in Anglo-Saxon expressed by sōþ, is a secondary development coupled to the process of "Enlightenment" in 17th century philosophy.[5] For the trade organisation, see Federation Against Copyright Theft. ...
For other uses, see Reality (disambiguation). ...
The Enlightenment (French: ; German: ; Italian: ; Portuguese: ) was an eighteenth century movement in European and American philosophy — some classifications also include 17th century philosophy (usually called the Age of Reason). ...
17th-century Western philosophy is conventionally seen as being dominated by the coming of symbolic mathematics and rationalism to philosophy, many of the most noted philosophers were also mathematicians. ...
All Germanic languages besides English have introduced a terminological distinction between truth "fidelity" and truth "factuality". To express "factuality", North Germanic opted for nouns derived from sanna "to assert, affirm", while continental West Germanic (German and Dutch) opted for continuations of wâra "faith, trust, pact" (cognate to Slavic věra "(religious) faith", but influenced by Latin verus). Romance languages use terms continuing Latin veritas, while Greek with aletheia and Slavic with pravda have unrelated terms. A North Germanic language is any of several Germanic languages spoken in Scandinavia, parts of Finland and on the islands west of Scandinavia. ...
West Germanic is the largest branch of the Germanic family of languages, including such languages as English, Dutch, and German. ...
For other uses, see Veritas (disambiguation). ...
The Romance languages, also called Romanic languages, are a subfamily of the Italic languages, specifically the descendants of the Vulgar Latin dialects spoken by the common people evolving in different areas after the break-up of the Roman Empire. ...
For other uses, see Veritas (disambiguation). ...
Aletheia in its current sense comes from Heideggers use of it as renewed attempt to understand Truth. ...
The major theories of truth Questions about what is a proper basis on which to decide how words, symbols, ideas and beliefs may properly be said to constitute truth, whether for a single person or an entire community or society, are among the many questions addressed by the theories introduced below.
Each of the five substantive theories below 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 published scholars 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.[6][7] There also have more recently arisen "deflationary" or "minimalist" theories of truth 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.[6][8][9] The deflationary theory of truth is a family of theories which all have in common the belief that assertions that predicate truth of a statement do not provide any substantive information or insight into the nature of truth. ...
Substantive theories
Correspondence theory -
Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs.[10] This type of theory attempts to posit a relationship between thoughts or statements on the one hand, and things or objects on the other. It is a traditional model which goes back at least to some of the classical Greek philosophers such as Socrates, Plato, and Aristotle.[11] This class of theories 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 reality. For example, there is a true distance to the moon when we humans attempt to go there, and this true distance is necessary to know so that the journey can be successfully made. The correspondence theory of truth states that something (for example, a proposition or statement or sentence) is rendered true by the existence of a fact with corresponding elements and a similar structure. ...
This page is about the Classical Greek philosopher. ...
For other uses, see Plato (disambiguation). ...
For other uses, see Aristotle (disambiguation). ...
The objective reality is reality which does not depend on our existence and the way of performing observations. ...
When someone sincerely agrees with an assertion, they might claim that it is the truth. ...
KNOW (91. ...
Correspondence theory traditionally operates on the assumption that truth is a matter of accurately copying "objective reality" and then representing it in thoughts, words and other symbols.[12] More modern theorists have stated that this ideal cannot be achieved independently of some analysis of additional factors. For example, language plays a role in that all languages have words that are not easily translatable into another. The German word Zeitgeist is one such example: one who speaks or understands the language may "know" what it means, but any translation of the word fails to accurately capture its full meaning (this is a problem with many abstract words, especially those derived in agglutinative languages). Thus, the language itself adds an additional parameter to the construction of an accurate truth predicate. Among the philosophers who grappled with this problem is Alfred Tarski, whose semantic theory is summarized further below in this article. This article is about the German word. ...
An agglutinative language is a language in which the words are formed by joining morphemes together. ...
A boolean-valued function, in some usages a predicate or a proposition, is a function of the type , where is an arbitrary set, where is a generic 2-element set, typically , and where the latter is frequently interpreted for logical applications as . ...
// Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ...
The semantic theory of truth holds that any assertion that a sentence is true can be made only as a formal requirement regarding the language in which the proposition itself is expressed. ...
Proponents of several of the theories below have gone farther to assert that there are yet other issues necessary to the analysis, such as interpersonal power struggles, community interactions, personal biases and other factors involved in deciding what is seen as truth.
Coherence theory -
For coherence theories in general, truth requires a proper fit of elements within a whole system. Very often, though, coherence is taken to imply something more than simple logical consistency; often there is a demand that the propositions in a coherent system lend mutual inferential support to each other. So, for example, the completeness and comprehensiveness of the underlying set of concepts is a critical factor in judging the validity and usefulness of a coherent system.[13] 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 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. There are two distinct types of Coherentism. ...
Some variants of coherence theory are claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics.[14] However, formal reasoners are content to contemplate axiomatically independent and sometimes 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.[15] In mathematical logic, a sentence σ is called independent of a given first-order theory T if T neither proves nor refutes σ; that is, it is impossible to prove σ from T, and it is also impossible to prove from T that σ is false. ...
The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ...
Natural World (sometimes in the past titled Wildlife On One or Wildlife On Two) is a long-running BBC television series on natural history. ...
A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. ...
Coherence theories distinguish the thought of rationalist philosophers, particularly of Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley.[16] They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel. In epistemology and in its broadest sense, rationalism is any view appealing to reason as a source of knowledge or justification (Lacey 286). ...
Baruch Spinoza Benedictus de Spinoza (November 24, 1632 - February 21, 1677), named Baruch Spinoza by his synagogue elders and known as Bento de Spinoza or Bento dEspiñoza in the community in which he grew up. ...
Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ...
Georg Wilhelm Friedrich Hegel (August 27, 1770 - November 14, 1831) was a German philosopher born in Stuttgart, Württemberg, in present-day southwest Germany. ...
Francis Herbert Bradley (30 January 1846 - 18 September 1924) was a British philosopher. ...
Logical positivism grew from the discussions of Moritz Schlicks Vienna Circle and Hans Reichenbachs Berlin Circle in the 1920s and 1930s. ...
Otto Neurath (December 10, 1882-December 22, 1945) was an Austrian sociologist, political economist, and an unorthodox Marxist. ...
Carl Gustav Hempel (* January 8th, 1905 in Oranienburg, Germany † November 9th, 1997 in Princeton, New Jersey) was a philosopher of science and a student of logical positivism. ...
Constructivist theory -
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 premise that truth is socially constructed. Constructivism is a perspective in philosophy that views all of our knowledge as constructed, under the assumption that it does not necessarily reflect any external transcendent realities; it is contingent on convention, human perception, and social experience. ...
Constructivism is a perspective in philosophy that views all of our knowledge as constructed, under the assumption that it does not necessarily reflect any external transcendent realities; it is contingent on convention, human perception, and social experience. ...
For other uses, see Race (disambiguation). ...
This article is about human sexual perceptions. ...
Gender in common usage refers to the sexual distinction between male and female. ...
Giambattista Vico or Giovanni Battista Vico (June 23, 1668 – January 23, 1744) was an Italian philosopher, historian, and jurist. ...
Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief. ...
Georg Wilhelm Friedrich Hegel (August 27, 1770 - November 14, 1831) was a German philosopher born in Stuttgart, Württemberg, in present-day southwest Germany. ...
Marx is a common German surname. ...
Consensus theory -
Consensus theory holds that truth is whatever is agreed upon, or in some versions, might come to be agreed upon, by some specified group. Such a group might include all human beings, or a subset thereof consisting of more than one person. The consensus theory of truth, originated by Charles Sanders Peirce who called it pragmatism, and later pragmaticism, holds that a statement is true if it would be agreed to by all those who investigate it if investigation were carried sufficiently far in that particular direction. ...
The consensus theory of truth, originated by Charles Sanders Peirce who called it pragmatism, and later pragmaticism, holds that a statement is true if it would be agreed to by all those who investigate it if investigation were carried sufficiently far in that particular direction. ...
“Superset†redirects here. ...
Among the current advocates of consensus theory as a useful accounting of the concept of "truth" is the philosopher Jürgen Habermas.[17] Habermas maintains that truth is what would be agreed upon in an ideal speech situation.[18] Among the current strong critics of consensus theory is the philosopher Nicholas Rescher.[19] Jürgen Habermas (IPA: ; born June 18, 1929) is a German philosopher and sociologist in the tradition of critical theory and American pragmatism. ...
Nicholas Rescher (born July 15, 1928 in Hagen, Germany) is an American philosopher, affiliated for many years with the University of Pittsburgh, where he is currently University Professor of Philosophy and Chairman of the Center for the Philosophy of Science. ...
Pragmatic theory -
The three most influential forms of the pragmatic theory of truth were introduced around the turn of the 20th century by Charles S. Peirce, William James, and John Dewey. Although there are wide differences in viewpoint among these and other proponents of pragmatic theory, they hold in common that truth is verified and confirmed by the results of putting one's concepts into practice.[20] Pragmatic theory of truth refers to those accounts, definitions, and theories of the concept truth that distinguish the philosophies of pragmatism and pragmaticism. ...
Charles Sanders Peirce (IPA: /pÉs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ...
This article needs additional references or sources for verification. ...
John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ...
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."[21] 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. Charles Sanders Peirce (IPA: /pÉs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ...
Fallibilism refers to the philosophical doctrine that absolute certainty about knowledge is impossible; or at least that all claims to knowledge could, in principle, be mistaken. ...
A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ...
William James's version of 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."[22] 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"). This article needs additional references or sources for verification. ...
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.[23] John Dewey (October 20, 1859 – June 1, 1952) was an American philosopher, psychologist, and educational reformer, whose thoughts and ideas have been greatly influential in the United States and around the world. ...
Minimalist (deflationary) theories -
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 The deflationary theory of truth is a family of theories which all have in common the belief that assertions that predicate truth of a statement do not provide any substantive information or insight into the nature of truth. ...
- 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.[24][6]
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."[6] 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.) Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines do not exist. ...
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.[25]
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 signaling 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.'"[26] Strawson redirects here. ...
The notion speech act is a technical term in linguistics and the philosophy of language. ...
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".[27][28] The Redundancy theory of truth is a philosophical theory about the way in which the predicate is true functions in such sentences as Snow is white is true. In its simplest version, the redundancy theory holds that Snow is white is true says no more than does Snow is white...
The Redundancy theory of truth is a philosophical theory about the way in which the predicate is true functions in such sentences as Snow is white is true. In its simplest version, the redundancy theory holds that Snow is white is true says no more than does Snow is white...
Frank Plumpton Ramsey (February 22, 1903 – January 19, 1930) was a British mathematician who, in addition to mathematics, made significant contributions in philosophy and economics. ...
Periphrasis, like its Latin counterpart circumlocution, is a figure of speech where the meaning of a word or phrase is indirectly expressed through several or many words. ...
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, 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."[6] Alfred Tarski, original name Alfred Teitelbaum (b. ...
Time Saving Truth from Falsehood and Envy, François Lemoyne, 1737 For other uses, see Truth (disambiguation). ...
Nuel D. Belnap Jr. ...
A pro-sentence is a function word or expression that substitutes for a whole sentence whose content is recoverable from the context. ...
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".
Formal theories
Truth in mathematics -
There are two main approaches to truth in mathematics. They are the model theory of truth and the proof theory of truth. In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ...
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ...
In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ...
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ...
Historically, with the nineteenth 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. Boolean algebra is the finitary algebra of two values. ...
Propositional logic or sentential logic is the logic of propositions, sentences, or clauses. ...
For the algebra software named Axiom, see Axiom computer algebra system. ...
In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ...
Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...
In addition, from at least the time of Hilbert's program at the turn of the twentieth 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. Hilberts program, formulated by German mathematician David Hilbert in the 1920s, was to formalize all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. ...
In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...
In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ...
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.[29] Two examples of the latter can be found in Hilbert's problems. Work on Hilbert's 10th problem led in the late twentieth century to the construction of specific Diophantine equations for which it is undecidable whether they have a solution,[30] 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.[31] Gödel and Paul Cohen showed that this hypothesis cannot be proved or disproved using the standard axioms of set theory and a finite number of proof steps.[32] In the view of some, then, it is equally reasonable to take either the continuum hypothesis or its negation as a new axiom. Kurt Gödel (IPA: ) (April 28, 1906 Brünn, Austria-Hungary (now Brno, Czech Republic) – January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher. ...
Alan Mathison Turing, OBE, FRS (23 June 1912 – 7 June 1954) was an English mathematician, logician, and cryptographer. ...
Hilberts problems are a list of twenty-three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900. ...
Matiyasevichs theorem, proven in 1970 by Yuri Matiyasevich, implies that Hilberts tenth problem is unsolvable. ...
In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ...
In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. ...
In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. ...
Paul Joseph Cohen (April 2, 1934 – March 23, 2007[1]) was an American mathematician. ...
This article is about a logical statement. ...
Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...
Semantic theory of truth The semantic theory of truth has as its general case for a given language: The semantic theory of truth holds that any assertion that a sentence is true can be made only as a formal requirement regarding the language in which the proposition itself is expressed. ...
- '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. // Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ...
Logic (from ancient Greek λόγος (logos), meaning reason) is the study of arguments. ...
In philosophy and logic, the liar paradox encompasses paradoxical statements such as: I am lying now. ...
Donald Davidson (March 6, 1917 – August 30, 2003) was an American philosopher and the Willis S. and Marion Slusser Professor Emeritus of Philosophy at the University of California, Berkeley. ...
Truth-conditional semantics is the name for an approach to semantics of natural language that sees the meaning of a sentence being the same as, or reducible to, the truth conditions of that sentence. ...
Radical interpretation in philosophy means working out the meaning of words, sentences and whole languages from scratch, by observing how they are used. ...
Coherentism - Wikipedia, the free encyclopedia /**/ @import /skins-1. ...
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. Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ...
Part of the foundation of mathematics, Russells paradox (also known as Russells antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction. ...
Alfred North Whitehead, OM (February 15, 1861 Ramsgate, Kent, England – December 30, 1947 Cambridge, Massachusetts, USA) was an English-born mathematician who became a philosopher. ...
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ...
At the broadest level, type theory is the branch of mathematics and logic that first creates a hierarchy of types, then assigns each mathematical (and possibly other) entity to a type. ...
In computer science, a type system defines how a programming language classifies values and expressions into types, how it can manipulate those types and how they interact. ...
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: Saul Aaron Kripke (born in November 13, 1940 in Bay Shore, New York) is an American philosopher and logician now emeritus from Princeton and teaches as distinguished professor of philosophy at CUNY Graduate Center. ...
- 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.[33] In logic, the principle of bivalence states that for any proposition P, either P is true or P is false. ...
Notable philosophers' views Image File history File links Download high resolution version (1029x2501, 771 KB) File links The following pages link to this file: Truth Talk:Truth Jules Joseph Lefebvre ...
Image File history File links Download high resolution version (1029x2501, 771 KB) File links The following pages link to this file: Truth Talk:Truth Jules Joseph Lefebvre ...
Jules Joseph Lefebvre (1836 – 1911) was a French figure painter. ...
Ancient philosophers The ancient Greek origins of the words "true" and "truth" have some consistent definitions throughout great spans of history that were often associated with topics of logic, geometry, mathematics, deduction, induction, and natural philosophy. Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ...
For other uses, see Geometry (disambiguation). ...
For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ...
Look up deduction in Wiktionary, the free dictionary. ...
Look up induction in Wiktionary, the free dictionary. ...
Natural philosophy or the philosophy of nature, known in Latin as philosophia naturalis, is a term applied to the objective study of nature and the physical universe that was regnant before the development of modern science. ...
Socrates', Plato's and Aristotle's ideas about truth are commonly seen as consistent with correspondence theory. In his Metaphysics, Aristotle stated: “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true”.[34] The Stanford Encyclopedia of Philosophy proceeds to say of Aristotle: This page is about the Classical Greek philosopher. ...
For other uses, see Plato (disambiguation). ...
For other uses, see Aristotle (disambiguation). ...
Aristotle sounds much more like a genuine correspondence theorist in the Categories (12b11, 14b14), where he talks of “underlying things” that make statements true and implies that these “things” (pragmata) are logically structured situations or facts (viz., his sitting, his not sitting). Most influential is his claim in De Interpretatione (16a3) that thoughts are “likenessess” (homoiosis) of things. Although he nowhere defines truth in terms of a thought's likeness to a thing or fact, it is clear that such a definition would fit well into his overall philosophy of mind.[34] Very similar statements can also be found in Plato (Cratylus 385b2, Sophist 263b).[34]
In ancient Indian philosophy and Buddhist philosophy, Gautama Buddha developed the theory of the Four Noble Truths, which are one of the most fundamental teachings of Buddhism and commonly appear in the earliest Buddhist texts, the Pali Canon.[35] The term Indian philosophy may refer to any of several traditions of philosophical thought, including: Hindu philosophy Buddhist philosophy Jain philosophy Sikh philosophy Carvaka atheist philosophy Lokayata materialist philosophy Tantric religious philosophy Bhakti religious philosophy Sufi religious philosophy Ahmadi religious philosophy Political and military philosophy such as that of Chanakya...
Buddhist Teachings deals extensively with problems in metaphysics, phenomenology, ethics, and epistemology. ...
Siddhartha and Gautama redirect here. ...
The Four Noble Truths (Pali: CattÄri ariyasaccÄni, Sanskrit: CatvÄri ÄryasatyÄni, Chinese: Sìshèngdì, Thai: à¸à¸£à¸´à¸¢à¸ªà¸±à¸ˆà¸ªà¸µà¹ˆ, Ariyasaj Sii) are one of the most fundamental Buddhist teachings. ...
A statue of the Sakyamuni Buddha in Tawang Gompa, India. ...
Standard edition of the Thai Pali Canon The Pali Canon is the standard scripture collection of the Theravada Buddhist tradition. ...
Medieval philosophers In early Islamic philosophy, Avicenna (Ibn Sina) defined truth as: Early Muslim philosophy is considered influential in the rise of modern philosophy. ...
(Persian: ابن سينا) (c. ...
What corresponds in the mind to what is outside it.[36] Avicenna elaborated on his definition of truth in his Metaphysics: Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ...
The truth of a thing is the property of the being of each thing which has been established in it.[37] In medieval Christian philosophy, Thomas Aquinas wrote an elegant re-statement of Aristotle's view in his Summa I.16.1: It is proposed that this article be deleted, because of the following concern: Filled with OR and completely unsourced. ...
Saint Thomas Aquinas, O.P.(also Thomas of Aquin, or Aquino; c. ...
Veritas est adæquatio intellectus et rei.
(Truth is the conformity of the intellect to the things.) In his Quodlibeta, Thomas Aquinas wrote a commentary on Avicenna's definition of truth in his Metaphysics and explained it as follows: Saint Thomas Aquinas, O.P.(also Thomas of Aquin, or Aquino; c. ...
The truth of each thing, as Avicenna says in his Metaphysica, is nothing else than the property of its being which has been established in it. So that is called true gold which has properly the being of gold and attains to the established determinations of the nature of gold. Now, each thing has properly being in some nature because it stands under the complete form proper to that nature, whereby being and species in that nature is.[37]
Modern philosophers
Kant Immanuel Kant discussed the correspondence theory of truth in the following manner. Kant's criticism of correspondence theory is one of numerous examples of why so many thinkers who examine the question of truth are not satisfied to rest with this first theory that usually comes to mind. Kant redirects here. ...
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.[38] Image File history File links Kant_2. ...
Image File history File links Kant_2. ...
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.[39] For other uses, see Definition (disambiguation). ...
Kierkegaard When Søren Kierkegaard, as his character Johannes Climacus, wrote that "Truth is Subjectivity", he does not advocate for subjectivism in its extreme form (the theory that something is true simply because one believes it to be so), but rather that the objective approach to matters of personal truth cannot shed any light upon that which is most essential to a person's life. Objective truths are concerned with the facts of a person's being, while subjective truths are concerned with a person's way of being. Kierkegaard agrees that objective truths for the study of subjects like mathematics, science, and history are relevant and necessary, but argues that objective truths do not shed any light on a person's inner relationship to existence. At best, these truths can only provide a severely narrowed perspective that has little to do with one's actual experience of life.[40] Søren Aabye Kierkegaard (IPA: , but usually Anglicized as ; ) 5 May 1813 – 11 November 1855) was a prolific 19th century Danish philosopher and theologian. ...
This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...
While objective truths are final and static, subjective truths are continuing and dynamic. The truth of one's existence is a living, inward, and subjective experience that is always in the process of becoming. The values, morals, and spiritual approaches a person adopts, while not denying the existence of objective truths of those beliefs, can only become truly known when they have been inwardly appropriated through subjective experience. Thus, Kierkegaard criticizes all systematic philosophies which attempt to know life or the truth of existence via theories and objective knowledge about reality. As Kierkegaard claims, human truth is something that is continually occurring, and a human being cannot find truth separate from the subjective experience of one's own existing, defined by the values and fundamental essence that consist of one's way of life.[41]
Nietzsche Friedrich Nietzsche believed the search for truth or 'the will to truth' was a consequence of the will to power of philosophers. He thought that truth should be used as long as it promoted life and the will to power, and he thought untruth was better than truth if it had this life enhancement as a consequence. As he wrote in Beyond Good and Evil, "The falseness of a judgment is to us not necessarily an objection to a judgment... The question is to what extent it is life-advancing, life-preserving, species-preserving, perhaps even species-breeding..." (aphorism 4). He proposed the will to power as a truth only because according to him it was the most life affirming and sincere perspective one could have. Friedrich Wilhelm Nietzsche (October 15, 1844 – August 25, 1900) (IPA: ) was a nineteenth-century German philosopher. ...
Robert Wicks discusses Nietzsche's basic view of truth as follows:
Some scholars regard Nietzsche's 1873 unpublished essay, "On Truth and Lies in a 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.[42]
Heidegger -
Aletheia in its current sense comes from Heideggers use of it as renewed attempt to understand Truth. ...
Gandhi Mohandas "Mahatma" Gandhi dedicated his life to the wider purpose of discovering truth, or Satya. He tried to achieve this by learning from his own mistakes and conducting experiments on himself. He called his autobiography The Story of My Experiments with Truth. Gandhi stated that the most important battle to fight was overcoming his own demons, fears, and insecurities. Gandhi summarized his beliefs first when he said "God is Truth". He would later change this statement to "Truth is God". Thus, Truth in Gandhi's philosophy is God. Mohandas Karamchand Gandhi (October 2, 1869 – January 30, 1948) (Devanagari: मोहनदास करमचन्द गांधी, Gujarati મોહનદાસ કરમચંદ ગાંધી), called...
Satya is a true badman. ...
Cover of the first English edition of 1793 of Benjamin Franklins autobiography. ...
“Fiend†redirects here. ...
For other uses, see Fear (disambiguation). ...
This article discusses the term God in the context of monotheism and henotheism. ...
Whitehead Alfred North Whitehead a British mathematician who became an American philosopher, said: "There are no whole truths; all truths are half-truths. It is trying to treat them as whole truths that play the devil".
The logical progression or connection of this line of thought is to conclude that truth can lie, since half-truths are deceptive and may lead to a false conclusion. Half-truths are deceptive statements, that include some element of truth. ...
A conclusion is a final proposition, which is arrived at after the consideration of evidence, arguments or premises. ...
Nishida According to Kitaro Nishida, "[k]nowledge of things in the world begins with the differentiation of unitary consciousness into knower and known and ends with self and things becoming one again. Such unification takes form not only in knowing but in the valuing (of truth) that directs knowing, the willing that directs action, and the feeling or emotive reach that directs sensing."[43] Nishida Kitaro Nishida Kitaro (西田 幾多郎 Nishida KitarÅ; 1870, Ishikawa Prefecture – 1945) was a prominent Japanese philosopher, founder of what has been called the Kyoto School of philosophy. ...
Fromm Erich Fromm finds that trying to discuss truth as "absolute truth" is sterile and that emphasis ought to be placed on "optimal truth". He considers truth as stemming from the survival imperative of grasping one's environment physically and intellectually, whereby young children instinctively seek truth so as to orient themselves in "a strange and powerful world". The accuracy of their perceived approximation of the truth will therefore have direct consequences on their ability to deal with their environment. Fromm can be understood to define truth as a functional approximation of reality. His vision of optimal truth is described partly in "Man from Himself: An Inquiry into the Psychology of Ethics" (1947), from which excerpts are included below. Erich Fromm Erich Pinchas Fromm (March 23, 1900 – March 18, 1980) was an internationally renowned Jewish-German-American social psychologist, psychoanalyst, and humanistic philosopher. ...
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