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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]].
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:
<blockquote>
<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>
<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>
<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>
</blockquote>
==References==
* [[Charles Sanders Peirce (Bibliography)|Peirce, C.S., Bibliography]].
* 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].
* Peirce, C.S. (1867), "Upon Logical Comprehension and Extension", [http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm Eprint].
==See also==
{|
| valign=top |
* [[Information theory]]
* [[Inquiry]]
* [[Pragmatic maxim]]
* [[Pragmatic theory of information]]
* [[Pragmatic theory of truth]]
| valign=top |
* [[Pragmaticism]]
* [[Pragmatism]]
* [[Scientific method]]
* [[Semeiotic]]
* [[Semiosis]]
| valign=top |
* [[Semiotics]]
* [[Semiotic information theory]]
* [[Sign relation]]
* [[Sign relational complex]]
* [[Triadic relation]]
|}
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:
<blockquote>
<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>
<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>
<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>
</blockquote>
==References==
* [[Charles Sanders Peirce (Bibliography)|Peirce, C.S., Bibliography]].
* 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].
* Peirce, C.S. (1867), "Upon Logical Comprehension and Extension", [http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm Eprint].
==See also==
{|
| valign=top |
* [[Information theory]]
* [[Inquiry]]
* [[Pragmatic maxim]]
* [[Pragmatic theory of information]]
* [[Pragmatic theory of truth]]
| valign=top |
* [[Pragmaticism]]
* [[Pragmatism]]
* [[Scientific method]]
* [[Semeiotic]]
* [[Semiosis]]
| valign=top |
* [[Semiotics]]
* [[Semiotic information theory]]
* [[Sign relation]]
* [[Sign relational complex]]
* [[Triadic relation]]
|}
