Truth theory - Revision history

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 [[Category:Peer Educational Resource]]
 [[Category:Artificial Intelligence]]
 [[Category:Critical Thinking]]
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 * [http://mathweb.org/wiki/Truth_theory Truth Theory @ MathWeb Wiki]
 * [http://netknowledge.org/wiki/Truth_theory Truth Theory @ NetKnowledge]
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 * [http://p2pfoundation.net/Truth_Theory Truth Theory @ P2P Foundation]
 * [http://semanticweb.org/wiki/Truth_theory Truth Theory @ SemanticWeb]
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 <font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
-A '''truth theory''' or a '''theory of truth''' is a conceptual framework that underlies a particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes use of a notion of truth.  A truth theory can be anything from an informal theory, based on implicit or tacit ideas, to a formal theory, constructed from explicit axioms and definitions and developed by means of definite ''rules of inference''.  The scope of a truth theory can be restricted to tightly-controlled and well-bounded universes of discourse or its horizon may extend to the limits of the human imagination.
+A '''truth theory''' or a '''theory of truth''' is a conceptual framework that underlies a particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes use of a notion of truth.  A truth theory can be anything from an informal theory, based on implicit or tacit ideas, to a formal theory, constructed from explicit axioms and definitions and developed by means of definite rules of inference.  The scope of a truth theory can be restricted to tightly-controlled and well-bounded universes of discourse or its horizon may extend to the limits of the human imagination.
 ==Truth in perspective==
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 Notions of truth are notoriously difficult to disentangle from many of our most basic concepts &mdash; meaning, reality, and values in general, to mention just a few.
-The subjects of meaning and truth are commonly treated together, the idea being that a thing must be meaningful before it 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'' and ''model theory''.  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.
+The subjects of meaning and truth are commonly treated together, the idea being that a thing must be meaningful before it 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'' and ''model theory''.  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 and 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.
 Beyond this minor note of accord, hardly universal, suggesting that meaning is necessary to truth, reflectors on the idea of truth just as quickly disperse into schools of thought that barely comprehend each other's thinking.  A few of the more notable points of departure are these:

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 <font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
-A '''truth theory''' or a '''theory of truth''' is a conceptual framework that underlies a particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes use of a notion of truth.  A truth theory can be anything from an informal theory, based on implicit or tacit ideas, to a ''formal theory'', constructed from explicit axioms and definitions and developed by means of definite ''[[rules of inference]]''.  The scope of a truth theory can be restricted to tightly-controlled and well-bounded universes of discourse or its horizon may extend to the limits of the human imagination.
+A '''truth theory''' or a '''theory of truth''' is a conceptual framework that underlies a particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes use of a notion of truth.  A truth theory can be anything from an informal theory, based on implicit or tacit ideas, to a formal theory, constructed from explicit axioms and definitions and developed by means of definite ''rules of inference''.  The scope of a truth theory can be restricted to tightly-controlled and well-bounded universes of discourse or its horizon may extend to the limits of the human imagination.
 ==Truth in perspective==
@@ Line 7: / Line 7: @@
 Notions of truth are notoriously difficult to disentangle from many of our most basic concepts &mdash; meaning, reality, and values in general, to mention just a few.
-The subjects of meaning and truth are commonly treated together, the idea being that a thing must be meaningful before it 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]]'' and ''[[model theory]]''.  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.
+The subjects of meaning and truth are commonly treated together, the idea being that a thing must be meaningful before it 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'' and ''model theory''.  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.
 Beyond this minor note of accord, hardly universal, suggesting that meaning is necessary to truth, reflectors on the idea of truth just as quickly disperse into schools of thought that barely comprehend each other's thinking.  A few of the more notable points of departure are these:
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 # Merely resolving that meaning precedes truth, logically speaking, only brings up a host of new questions, since the meaning of the word ''meaning'' is notoriously hard to pin down.  There are just to start at least two different dimensions of meaning that are commonly recognized, namely, ''[[connotation|connotative meaning]]'' and ''[[denotation|denotative meaning]]''.
-In one classical formulation, truth is defined as the good of [[logic]], where logic is treated as a [[normative science]], that is, an [[inquiry]] into a ''good'' or a ''value'' that seeks knowledge of it and the means to achieve it.  In this scheme of ideas, truth is the positive quality of a sign that indicates the right course of action for reaching a value that we value for its own sake.  As such, truth takes its place among [[justice]] and [[beauty]], whose normative sciences are [[ethics]] and [[aesthetics]], respectively.  Viewed in this light, it is pointless to discuss truth in isolation from a frame of reference that encompasses the topics of inquiry, knowledge, logic, meaning, practice, and value, all very broadly conceived.
+In one classical formulation, truth is defined as the good of [[logic]], where logic is treated as a [[normative science]], that is, an [[inquiry]] into a ''good'' or a ''value'' that seeks knowledge of it and the means to achieve it.  In this scheme of ideas, truth is the positive quality of a sign that indicates the right course of action for reaching a value that we value for its own sake.  As such, truth takes its place among justice and beauty, whose normative sciences are [[ethics]] and [[aesthetics]], respectively.  Viewed in this light, it is pointless to discuss truth in isolation from a frame of reference that encompasses the topics of inquiry, knowledge, logic, meaning, practice, and value, all very broadly conceived.
 In contexts bounded by formal linguistic analysis, a '''truth theory''' is defined as "a theory providing the truth definition for a language" (Blackburn, 382).  A ''truth definition'' is in turn defined as "a definition of the predicate "__is&nbsp;true" for a language that satisfies ''convention T'', the material adequacy condition laid down by [[Tarski]]" (Blackburn, 382).
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 ==Historical overview==
-In an ancient fragment of text called the ''Dissoi Logoi'', a 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.
+In an ancient fragment of text called the ''Dissoi Logoi'', a 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 and Kneale, 16).  This same tension between strings of characters and their meanings remains with us to this day.
 In his early work &#928;&#949;&#961;&#953; &#917;&#961;&#956;&#951;&#957;&#949;&#953;&#945;s (''Peri Hermeneias'' or ''[[On Interpretation]]'') [[Aristotle]] strikes a chord that not only sets the key for a number of philosophical movements down through the ages but supplies the initial motif for many themes in the logic of meaning and truth that are still undergoing active development in our time.
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 # The passage mentions three principal domains of elements, namely, the ''objects'' (pragmata), the ''signs'' (semeia, symbola), and the psychological elements (pathemata).  The last domain extends over the full range of a human being's affective and cognitive experiences, for brevity summed up as ''ideas'' and ''impressions'', where these words are taken in their broadest conceivable senses.
 # This means that the phenomena under investigation have to do with the types of [[three-place relation]]s that conceivably exist among three domains of this sort.  As a general rule, three-place relations can be very complex, and a commonly-tried strategy for approaching their complexity is to consider the [[two-place relation]]s that are left when the presence of a selected domain is simply ignored.
-# There are two types of [[two-place relation]] on the face of the overall three-place relation that Aristotle takes the trouble to mention, namely these: <p> Sign <math>\longrightarrow</math> Idea.  Words spoken are signs or symbols of pathemata. <p> Idea <math>\longrightarrow</math> Object.  Pathemata are icons (homoiomata) of pragmata.
+# There are two types of two-place relation on the face of the overall three-place relation that Aristotle takes the trouble to mention, namely these:<p>Sign <math>\longrightarrow</math> Idea.  Words spoken are signs or symbols of pathemata.</p><p>Idea <math>\longrightarrow</math> Object.  Pathemata are icons (homoiomata) of pragmata.</p>
-# More incidentally, but still bearing heavily on many later discussions, Aristotle holds that the relation between writing and speech is analogous to the relation between speech and the realm of experiences, feelings, and thoughts. <p> Writing <math>\longrightarrow</math> Speech.  Written words are symbols of spoken words. <p> Speech <math>\longrightarrow</math> Ideation.  Spoken words are symbols of impressions.
+# More incidentally, but still bearing heavily on many later discussions, Aristotle holds that the relation between writing and speech is analogous to the relation between speech and the realm of experiences, feelings, and thoughts.<p>Writing <math>\longrightarrow</math> Speech.  Written words are symbols of spoken words.</p><p> Speech <math>\longrightarrow</math> Ideation.  Spoken words are symbols of impressions.</p>
 ==Elements of theory==

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 <font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
-A '''truth theory''' or a '''theory of truth''' is a [[conceptual framework]] that underlies a particular conception of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion that either mentions or makes use of a notion of truth.  A truth theory can be anything from a ''casual theory'', based on implicit, informal, and vaguely articulated ideas, to a ''[[formal theory]]'', constructed from explicit [[axiom]]s and [[definition]]s and developed by means of definite ''[[rules of inference]]''.  The scope of a truth theory can be restricted to tightly-controlled and well-bounded universes of discourse or its horizon may extend to the limits of the human imagination.
+A '''truth theory''' or a '''theory of truth''' is a conceptual framework that underlies a particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes use of a notion of truth.  A truth theory can be anything from an informal theory, based on implicit or tacit ideas, to a ''formal theory'', constructed from explicit axioms and definitions and developed by means of definite ''[[rules of inference]]''.  The scope of a truth theory can be restricted to tightly-controlled and well-bounded universes of discourse or its horizon may extend to the limits of the human imagination.
 ==Truth in perspective==