Difference between revisions of "Logic of information"

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
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The '''logic of information''', or the ''logical theory of information'', considers the information content of logical [[semiotics|signs]] &mdash; everything from bits to books and beyond &mdash; 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 (logic)|comprehension]].
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The '''logic of information''', or the ''logical theory of information'', considers the information content of logical [[semiotics|signs]] &mdash; everything from bits to books and beyond &mdash; 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 (logic)|extension]] and [[comprehension (logic)|comprehension]].
  
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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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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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<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>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 &mdash; having two legs, being rational, &tc. &mdash; 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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<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'' &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;  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>
  
 
<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>
 
<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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* [[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 Eprint].
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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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==See also==
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==Syllabus==
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===Focal nodes===
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{{col-begin}}
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{{col-break}}
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* [[Inquiry Live]]
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{{col-break}}
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* [[Logic Live]]
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{{col-end}}
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===Peer nodes===
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{{col-begin}}
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{{col-break}}
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* [http://mywikibiz.com/Logic_of_information Logic of Information @ MyWikiBiz]
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* [http://mathweb.org/wiki/Logic_of_information Logic of Information @ MathWeb Wiki]
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* [http://netknowledge.org/wiki/Logic_of_information Logic of Information @ NetKnowledge]
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{{col-break}}
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* [http://wiki.oercommons.org/mediawiki/index.php/Logic_of_information Logic of Information @ OER Commons]
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* [http://p2pfoundation.net/Logic_of_Information Logic of Information @ P2P Foundation]
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* [http://semanticweb.org/wiki/Logic_of_information Logic of Information @ SemanticWeb]
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{{col-end}}
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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]]
 +
{{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===
  
 
{{col-begin}}
 
{{col-begin}}
 
{{col-break}}
 
{{col-break}}
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* [[Information theory]]
 
 
* [[Inquiry]]
 
* [[Inquiry]]
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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]]
 
 
* [[Pragmatic theory of truth]]
 
* [[Pragmatic theory of truth]]
 
{{col-break}}
 
{{col-break}}
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* [[Pragmaticism]]
 
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* [[Pragmatism]]
 
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* [[Scientific method]]
 
 
* [[Semeiotic]]
 
* [[Semeiotic]]
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* [[Semiosis]]
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* [[Semiotic information]]
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{{col-break}}
 
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* [[Semiotics]]
 
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* [[Semiotic information theory]]
 
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* [[Sign relation]]
 
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* [[Sign relational complex]]
 
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* [[Triadic relation]]
 
 
{{col-end}}
 
{{col-end}}
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 +
===Related articles===
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
 +
 +
* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
  
 
==Resources==
 
==Resources==
  
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* [http://vectors.usc.edu/thoughtmesh/publish/145.php Logic of Information → ThoughtMesh]
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* [http://vectors.usc.edu/thoughtmesh/publish/145.php Logic of Information &rarr; ThoughtMesh]
  
 
==Document history==
 
==Document history==

Revision as of 17:28, 20 May 2010

☞ 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.

Syllabus

Focal nodes

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Peer nodes

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Logical operators

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Related topics

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Relational concepts

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

Information, Inquiry

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Related articles

Resources

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.

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