Directory:Jon Awbrey/Papers/Semiotic Information - Revision history

Jon Awbrey: update

2016-10-29T14:10:02Z

update

Jon Awbrey at 21:55, 5 July 2013

2013-07-05T21:55:03Z

Jon Awbrey at 21:44, 5 July 2013

2013-07-05T21:44:28Z

Jon Awbrey: add categories

2013-07-05T21:42:18Z

add categories

Jon Awbrey: cleanup quotation marks

2012-12-23T01:54:07Z

cleanup quotation marks

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2012-12-23T01:32:19Z

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2012-12-23T01:30:04Z

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Jon Awbrey: /* What's it good for? */

2012-12-22T04:15:21Z

What's it good for?

Jon Awbrey: Category:Charles Sanders Peirce

2011-10-30T20:24:45Z

Category:Charles Sanders Peirce

Jon Awbrey: /* Related articles and projects */ fix link screwed up at last system changeover

2010-06-28T13:52:13Z

Related articles and projects: fix link screwed up at last system changeover

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 {{DISPLAYTITLE:Semiotic Information}}
 '''Semiotic information''' is the information content of signs as conceived within the [[semeiotic]] or [[sign-relational]] framework developed by [[Charles Sanders Peirce]].
@@ Line 261: / Line 263: @@
 * [[Boolean function]]
 * [[Boolean-valued function]]
 * [[Logical graph]]
 * [[Logical matrix]]
@@ Line 270: / Line 273: @@
 * [[Propositional calculus]]
 * [[Semeiotic]]
 * [[Sign relation]]
 * [[Triadic relation]]
@@ Line 276: / Line 280: @@
 {{col-end}}
-===Related articles and projects===
+===Related articles===
-* [[Futures Of Logical Graphs]]
+{{col-begin}}
-* [[Semiotic Theory Of Information]]
+{{col-break}}
-* [[Directory:Jon_Awbrey/Papers/Information_%3D_Comprehension_%C3%83%E2%80%94_Extension|Information = Comprehension &times; Extension]]
+* [http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_Logic_Of_Information Peirce's Logic Of Information]
-* [[Inquiry Driven Systems]]
+* [http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension Information = Comprehension × Extension]
-* [[Introduction to Inquiry Driven Systems]]
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
-* [[Peirce’s Logic Of Information]]
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
-* [[Pragmatic Theory Of Information]]
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
-* [[Propositional Equation Reasoning Systems]]
+{{col-break}}
 [[Category:Charles Sanders Peirce]]

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 The average uncertainty reduction per sign of the language is computed by taking a ''weighted average'' of the reductions that occur in the channel, where the weight of each reduction is the number of options or outcomes that fall under the associated sign.
-:* The uncertainty reduction of <math>(\log 5 - \log 3)</math> gets a weight of 3.
+:* The uncertainty reduction of <math>(\log 5 - \log 3)\!</math> gets a weight of 3.
-:* The uncertainty reduction of <math>(\log 5 - \log 2)</math> gets a weight of 2.
+:* The uncertainty reduction of <math>(\log 5 - \log 2)\!</math> gets a weight of 2.
 Finally, the weighted average of these two reductions is:
-: <math>{1 \over {2 + 3}}(3(\log 5 - \log 3) + 2(\log 5 - \log 2))</math>
+: <math>{1 \over {2 + 3}}(3(\log 5 - \log 3) + 2(\log 5 - \log 2))\!</math>
-Extracting the general pattern of this calculation yields the following worksheet for computing the capacity of a 2-symbol channel with frequencies that partition as ''n''&nbsp;=&nbsp;''k''<sub>1</sub>&nbsp;+&nbsp;''k''<sub>2</sub>.
+Extracting the general pattern of this calculation yields the following worksheet for computing the capacity of a 2-symbol channel with frequencies that partition as <math>n = k_1 + k_2.\!</math>
 {| cellspacing="6"
 | Capacity
-| of a channel {"A", "B"} that bears the odds of 60 "A" to 40 "B"
+| of a channel {&ldquo;A&rdquo;, &ldquo;B&rdquo;} that bears the odds of 60 &ldquo;A&rdquo; to 40 &ldquo;B&rdquo;
 |-
 | &nbsp;
-| <math>=\quad {1 \over n}(k_1(\log n - \log k_1) + k_2(\log n - \log k_2))</math>
+| <math>=\quad {1 \over n}(k_1(\log n - \log k_1) + k_2(\log n - \log k_2))\!</math>
 |-
 | &nbsp;
-| <math>=\quad {k_1 \over n}(\log n - \log k_1) + {k_2 \over n}(\log n - \log k_2)</math>
+| <math>=\quad {k_1 \over n}(\log n - \log k_1) + {k_2 \over n}(\log n - \log k_2)\!</math>
 |-
 | &nbsp;
-| <math>=\quad -{k_1 \over n}(\log k_1 - \log n) -{k_2 \over n}(\log k_2 - \log n)</math>
+| <math>=\quad -{k_1 \over n}(\log k_1 - \log n) -{k_2 \over n}(\log k_2 - \log n)\!</math>
 |-
 | &nbsp;
-| <math>=\quad -{k_1 \over n}(\log {k_1 \over n}) - {k_2 \over n}(\log {k_2 \over n})</math>
+| <math>=\quad -{k_1 \over n}(\log {k_1 \over n}) - {k_2 \over n}(\log {k_2 \over n})\!</math>
 |-
 | &nbsp;
-| <math>=\quad -(p_1 \log p_1 + p_2 \log p_2)</math>
+| <math>=\quad -(p_1 \log p_1 + p_2 \log p_2)\!</math>
 |-
 | &nbsp;
-| <math>=\quad - (0.6 \log 0.6 + 0.4 \log 0.4)</math>
+| <math>=\quad - (0.6 \log 0.6 + 0.4 \log 0.4)\!</math>
 |-
 | &nbsp;
-| <math>=\quad 0.971</math>
+| <math>=\quad 0.971\!</math>
 |}
@@ Line 249: / Line 249: @@
 * [[Charles Sanders Peirce (Bibliography)]]
-* Peirce, C.S. (1867), "Upon Logical Comprehension and Extension", [http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm Online].
+* Peirce, C.S. (1867), &ldquo;Upon Logical Comprehension and Extension&rdquo;, [http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm Online].
 ==See also==

← Older revision		Revision as of 21:44, 5 July 2013
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	[[Category:Scientific Method]]		[[Category:Scientific Method]]
	[[Category:Semiotics]]		[[Category:Semiotics]]
		+	[[Category:Sign Relations]]

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 * [[Pragmatic Theory Of Information]]
 * [[Propositional Equation Reasoning Systems]]
 [[Category:Charles Sanders Peirce]]

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 |                      ooooo                      |
 |                                                 |
-|                        Ө                 n = 5  |
+|                        O                 n = 5  |
 |                                                 |
 o-------------------------------------------------o
@@ Line 62: / Line 62: @@
 |}
-This pictures a juncture, represented by "Ө", where there are ''n'' options for the outcome of a conduct, and we have no clue as to which it must be.  In a sense, the degree of this node, in this case ''n''&nbsp;=&nbsp;5, measures the uncertainty that we have at this point.
+This pictures a juncture, represented by "O", where there are ''n'' options for the outcome of a conduct, and we have no clue as to which it must be.  In a sense, the degree of this node, in this case ''n''&nbsp;=&nbsp;5, measures the uncertainty that we have at this point.
 This is the minimal sort of setting in which a sign can make any sense at all.  A sign has significance for an agent, interpreter,  or observer because its actualization, its being given or its being present, serves to reduce the uncertainty of a decision that the agent has to make, whether it concerns the actions that the agent ought to take in order to achieve some objective of interest, or whether it concerns the predicates that the agent ought to treat as being true of some object in the world.

@@ Line 8: / Line 8: @@
 The good of information is its use in reducing our uncertainty about some issue that comes before us.  Generally speaking, uncertainty comes in several flavors, and so the information that serves to reduce uncertainty can be applied in several different ways.  The situations of uncertainty that human agents commonly find themselves facing have been investigated under many headings, literally for ages, and the classifications that subtle thinkers arrived at long before the dawn of modern information theory still have their uses in setting the stage of an introduction.
-Picking an example of a subtle thinker almost at random, the philosopher-scientist [[Immanuel Kant]] divided the principal questions of human existence into three parts:
+Picking an example of a subtle thinker almost at random, the philosopher-scientist Immanuel Kant divided the principal questions of human existence into three parts:
 :* What's true?
@@ Line 14: / Line 14: @@
 :* What's to hope?
-The third question is a bit too subtle for the present frame of discussion, but the first and second are easily recognizable as staking out the two main axes of information theory, namely, the dual dimensions of ''[[information]]'' and ''[[control theory|control]]''.  Roughly the same space of concerns is elsewhere spanned by the dual axes of ''[[competence]]'' and ''[[performance]]'', ''[[specification]]'' and ''[[optimization]]'', or just plain ''[[knowledge]]'' and ''[[skill]]''.
+The third question is a bit too subtle for the present frame of discussion, but the first and second are easily recognizable as staking out the two main axes of information theory, namely, the dual dimensions of ''information'' and ''control''.  Roughly the same space of concerns is elsewhere spanned by the dual axes of ''competence'' and ''performance'', ''specification'' and ''optimization'', or just plain ''knowledge'' and ''skill''.
 A question of ''what's true'' is a ''descriptive question'', and there exist what are called ''[[descriptive science]]s'' devoted to answering descriptive questions about any domain of phenomena that one might care to name.

← Older revision		Revision as of 20:24, 30 October 2011
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−	~~<!--semantic tags-->~~	+	[[Category:Charles Sanders Peirce]]
−	[[~~Author~~:~~:Jon Awbrey\| ]]~~
−	~~[[Paper Name::Semiotic Information\| ]]~~
−	~~[[Paper Of::Directory:Jon Awbrey\| ~~]]