Difference between revisions of "Logic of information"

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The '''logic of information''', or the ''logical theory of information'', considers the information content of logical [[sign (semiotics)|sign]]s and expressions along the lines initially developed by [[Charles Sanders Peirce]].  In this line of work, the concept of information serves to integrate the aspects of signs and expressions that are separately covered, on the one hand, by the concepts of [[connotation and denotation|denotation]] and [[extension (semantics)|extension]], and on the other hand, by the concepts of [[connotation and denotation|connotation]] and [[comprehension (logic)|comprehension]].
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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
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Peirce began to develop these ideas in his lectures "On the Logic of Science" at [[Harvard University]] (1865) and the [[Lowell Institute]] (1866). Here is one of the starting points:
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The '''logic of information''', or the ''logical theory of information'', considers the information content of logical signs &mdash; everything from bits to books and beyond &mdash; along the lines initially developed by [[Charles Sanders Peirce]].&nbsp; In this line of development the concept of information serves to integrate the aspects of logical signs that are separately covered by the concepts of denotation and connotation, or, in roughly equivalent terms, by the concepts of extension and comprehension.
  
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<blockquote>
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Peirce began to develop these ideas in his lectures &ldquo;On the Logic of Science&rdquo; at Harvard University (1865) and the Lowell Institute (1866).&nbsp; Here is one of the starting points:
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<p>Let us now return to the information.  The information of a term is the measure of its superfluous [[comprehension (logic)|comprehension]].  That is to say that the proper office of the comprehension is to determine the [[extension (semantics)|extension]] of the term. For instance, you and I are men because we possess those attributes — having two legs, being rational, &tc. — which make up the comprehension of ''man''.  Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.</p>
 
  
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<p>Thus, let us commence with the term ''colour''; add to the comprehension of this term, that of ''red''. ''Red colour'' has considerably less extension than ''colour''; add to this the comprehension of ''dark''; ''dark red colour'' has still less [extension].  Add to this the comprehension of ''non-blue'' — ''non-blue dark red colour'' has the same extension as ''dark red colour'', so that the ''non-blue'' here performs a work of supererogation;  it tells us that no ''dark red colour'' is blue, but does none of the proper business of connotation, that of diminishing the extension at all.</p>
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{| align="center" cellpadding="8" width="90%"
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|
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<p>Let us now return to the information.&nbsp; The information of a term is the measure of its superfluous comprehension.&nbsp; That is to say that the proper office of the comprehension is to determine the extension of the term.&nbsp; For instance, you and I are men because we possess those attributes &mdash; having two legs, being rational, &tc. &mdash; which make up the comprehension of ''man''.&nbsp; Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.</p>
  
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<p>Thus information measures the superfluous comprehension. And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension. I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of ''information''. (C.S. Peirce, "The Logic of Science, or, Induction and Hypothesis" (1866), CE 1, 467).</p>
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<p>Thus, let us commence with the term ''colour'';&nbsp; add to the comprehension of this term, that of ''red''.&nbsp; ''Red colour'' has considerably less extension than ''colour'';&nbsp; add to this the comprehension of ''dark'';&nbsp; ''dark red colour'' has still less [extension].&nbsp; Add to this the comprehension of ''non-blue'' &mdash; ''non-blue dark red colour'' has the same extension as ''dark red colour'', so that the ''non-blue'' here performs a work of supererogation;&nbsp; it tells us that no ''dark red colour'' is blue, but does none of the proper business of connotation, that of diminishing the extension at all.</p>
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</blockquote>
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<p>Thus information measures the superfluous comprehension.&nbsp; And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension.&nbsp; I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of ''information''.&nbsp; (C.S. Peirce, &ldquo;The Logic of Science, or, Induction and Hypothesis&rdquo; (1866), CE&nbsp;1, 467).</p>
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|}
  
 
==References==
 
==References==
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* [[Charles Sanders Peirce (Bibliography)|Peirce, C.S., Bibliography]].
 
* [[Charles Sanders Peirce (Bibliography)|Peirce, C.S., Bibliography]].
  
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* De Tienne, André (2006), "Peirce's Logic of Information", Seminario del Grupo de Estudios Peirceanos, Universidad de Navarra, 28 Sep 2006.  [http://www.unav.es/gep/SeminariodeTienne.html Eprint].
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* De Tienne, André (2006), "Peirce's Logic of Information", Seminario del Grupo de Estudios Peirceanos, Universidad de Navarra, 28 Sep 2006.  [http://www.unav.es/gep/SeminariodeTienne.html Online].
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* Peirce, C.S. (1867), "Upon Logical Comprehension and Extension", [http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm Online].
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==Resources==
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* [http://vectors.usc.edu/thoughtmesh/publish/145.php Logic of Information &rarr; ThoughtMesh]
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==Syllabus==
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===Focal nodes===
  
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* Peirce, C.S. (1867), "Upon Logical Comprehension and Extension", [http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm Eprint].
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* [[Inquiry Live]]
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* [[Logic Live]]
  
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==See also==
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===Peer nodes===
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{|
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| valign=top |
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* [http://intersci.ss.uci.edu/wiki/index.php/Logic_of_information Logic of Information @ InterSciWiki]
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* [[Information theory]]
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* [http://mywikibiz.com/Logic_of_information Logic of Information @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Logic_of_information Logic of Information @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Logic_of_information Logic of Information @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logic_of_information Logic of Information @ Wikiversity Beta]
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===Logical operators===
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{{col-begin}}
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{{col-break}}
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* [[Exclusive disjunction]]
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* [[Logical conjunction]]
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* [[Logical disjunction]]
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* [[Logical equality]]
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{{col-break}}
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* [[Logical implication]]
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* [[Logical NAND]]
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* [[Logical NNOR]]
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* [[Logical negation|Negation]]
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{{col-end}}
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===Related topics===
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{{col-begin}}
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{{col-break}}
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* [[Ampheck]]
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* [[Boolean domain]]
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* [[Boolean function]]
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* [[Boolean-valued function]]
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* [[Differential logic]]
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{{col-break}}
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* [[Logical graph]]
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* [[Minimal negation operator]]
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* [[Multigrade operator]]
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* [[Parametric operator]]
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* [[Peirce's law]]
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{{col-break}}
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* [[Propositional calculus]]
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* [[Sole sufficient operator]]
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* [[Truth table]]
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* [[Universe of discourse]]
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* [[Zeroth order logic]]
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{{col-end}}
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===Relational concepts===
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{{col-begin}}
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{{col-break}}
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* [[Continuous predicate]]
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* [[Hypostatic abstraction]]
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* [[Logic of relatives]]
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* [[Logical matrix]]
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{{col-break}}
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* [[Relation (mathematics)|Relation]]
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* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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{{col-break}}
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* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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{{col-end}}
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===Information, Inquiry===
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{{col-begin}}
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{{col-break}}
 
* [[Inquiry]]
 
* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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* [[Descriptive science]]
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* [[Normative science]]
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{{col-break}}
 
* [[Pragmatic maxim]]
 
* [[Pragmatic maxim]]
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* [[Pragmatic theory of information]]
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* [[Truth theory]]
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* [[Pragmatic theory of truth]]
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{{col-end}}
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| valign=top |
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* [[Pragmaticism]]
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===Related articles===
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* [[Pragmatism]]
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* [[Scientific method]]
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{{col-begin}}
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* [[Semeiotic]]
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{{col-break}}
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* [[Semiosis]]
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* [http://intersci.ss.uci.edu/wiki/index.php/Semiotic_Information Semiotic Information]
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| valign=top |
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [[Semiotics]]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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* [[Semiotic information theory]]
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{{col-break}}
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* [[Sign relation]]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
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* [[Sign relational complex]]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
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* [[Triadic relation]]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
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|}
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{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
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{{col-end}}
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==Document history==
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 +
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
 +
 
 +
* [http://intersci.ss.uci.edu/wiki/index.php/Logic_of_information Logic of Information], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Logic_of_information Logic of Information], [http://mywikibiz.com/ MyWikiBiz]
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* [http://semanticweb.org/wiki/Logic_of_information Logic of Information], [http://semanticweb.org/ Semantic Web]
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* [http://vectors.usc.edu/thoughtmesh/publish/145.php Logic of Information], [http://vectors.usc.edu/thoughtmesh/ ThoughtMesh]
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* [http://wikinfo.org/w/index.php/Logic_of_information Logic of Information], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Logic_of_information Logic of Information], [http://en.wikiversity.org/ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logic_of_information Logic of Information], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://en.wikipedia.org/w/index.php?title=Logic_of_information&oldid=67770000 Logic of Information], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Artificial Intelligence]]
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[[Category:Charles Sanders Peirce]]
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[[Category:Cybernetics]]
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[[Category:Hermeneutics]]
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[[Category:Information Systems]]
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[[Category:Information Theory]]
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[[Category:Inquiry]]
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[[Category:Intelligence Amplification]]
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[[Category:Knowledge Representation]]
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[[Category:Linguistics]]
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[[Category:Logic]]
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[[Category:Mathematics]]
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[[Category:Philosophy]]
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[[Category:Pragmatics]]
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[[Category:Pragmatism]]
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[[Category:Science]]
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[[Category:Semantics]]
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[[Category:Semiotics]]
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[[Category:Systems Science]]

Latest revision as of 03:24, 16 November 2015

☞ This page belongs to resource collections on Logic and Inquiry.

The logic of information, or the logical theory of information, considers the information content of logical signs — everything from bits to books and beyond — along the lines initially developed by Charles Sanders Peirce.  In this line of development the concept of information serves to integrate the aspects of logical signs that are separately covered by the concepts of denotation and connotation, or, in roughly equivalent terms, by the concepts of extension and comprehension.

Peirce began to develop these ideas in his lectures “On the Logic of Science” at Harvard University (1865) and the Lowell Institute (1866).  Here is one of the starting points:

Let us now return to the information.  The information of a term is the measure of its superfluous comprehension.  That is to say that the proper office of the comprehension is to determine the extension of the term.  For instance, you and I are men because we possess those attributes — having two legs, being rational, &tc. — which make up the comprehension of man.  Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.

Thus, let us commence with the term colour;  add to the comprehension of this term, that of red.  Red colour has considerably less extension than colour;  add to this the comprehension of dark;  dark red colour has still less [extension].  Add to this the comprehension of non-blue — non-blue dark red colour has the same extension as dark red colour, so that the non-blue here performs a work of supererogation;  it tells us that no dark red colour is blue, but does none of the proper business of connotation, that of diminishing the extension at all.

Thus information measures the superfluous comprehension.  And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension.  I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of information.  (C.S. Peirce, “The Logic of Science, or, Induction and Hypothesis” (1866), CE 1, 467).

References

  • De Tienne, André (2006), "Peirce's Logic of Information", Seminario del Grupo de Estudios Peirceanos, Universidad de Navarra, 28 Sep 2006. Online.
  • Peirce, C.S. (1867), "Upon Logical Comprehension and Extension", Online.

Resources

Syllabus

Focal nodes

Peer nodes

Logical operators

Template:Col-breakTemplate:Col-breakTemplate:Col-end

Related topics

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Relational concepts

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Information, Inquiry

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Related articles

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

Retrieved from "https://mywikibiz.com/index.php?title=Logic_of_information&oldid=466895"