Sign relation - Revision history

Jon Awbrey: update

2015-11-15T21:35:04Z

update

← Older revision		Revision as of 21:35, 15 November 2015
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	In the context of 3-adic relations in general, Peirce provides the following illustration of the six ''converses'' of a 3-adic relation, that is, the six differently ordered ways of stating what is logically the same 3-adic relation:		In the context of 3-adic relations in general, Peirce provides the following illustration of the six ''converses'' of a 3-adic relation, that is, the six differently ordered ways of stating what is logically the same 3-adic relation:

	: So in a triadic fact, say, ~~the~~ example <br>		: So in a triadic fact, say, for example <br>
	{\| align="center" cellspacing="8" style="width:72%"		{\| align="center" cellspacing="8" style="width:72%"
	\| align="center" \| ''A'' gives ''B'' to ''C''		\| align="center" \| ''A'' gives ''B'' to ''C''
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	===Focal nodes===		===Focal nodes===

	~~{{col-begin}}~~
	~~{{col-break}}~~
	* [[Inquiry Live]]		* [[Inquiry Live]]
	~~{{col-break}}~~
	* [[Logic Live]]		* [[Logic Live]]
	~~{{col-end}}~~

	===Peer nodes===		===Peer nodes===

	~~{{col-begin}}~~
	~~{{col-break}}~~
	* [http://intersci.ss.uci.edu/wiki/index.php/Sign_relation Sign Relation @ InterSciWiki]		* [http://intersci.ss.uci.edu/wiki/index.php/Sign_relation Sign Relation @ InterSciWiki]
	* [http://mywikibiz.com/Sign_relation Sign Relation @ MyWikiBiz]		* [http://mywikibiz.com/Sign_relation Sign Relation @ MyWikiBiz]
	~~{{col-break}}~~		* [http://ref.subwiki.org/wiki/Sign_relation Sign Relation @ Subject Wikis]
			* [http://en.wikiversity.org/wiki/Sign_relation Sign Relation @ Wikiversity]
	* [http://beta.wikiversity.org/wiki/Sign_relation Sign Relation @ Wikiversity Beta]		* [http://beta.wikiversity.org/wiki/Sign_relation Sign Relation @ Wikiversity Beta]
	* [http://ref.subwiki.org/wiki/Sign_relation Sign Relation @ Subject Wikis]
	~~{{col-end}}~~

	===Logical operators===		===Logical operators===
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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.		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.

	~~{{col-begin}}~~		* [http://intersci.ss.uci.edu/wiki/index.php/Sign_relation Sign Relation], [http://intersci.ss.uci.edu/ InterSciWiki]
	~~{{col-break}}~~
	* [http://mywikibiz.com/Sign_relation Sign Relation], [http://mywikibiz.com/ MyWikiBiz]		* [http://mywikibiz.com/Sign_relation Sign Relation], [http://mywikibiz.com/ MyWikiBiz]
	* [http://mathweb.org/wiki/Sign_relation Sign Relation], [http://mathweb.org/ MathWeb Wiki]
	~~{{col-break}}~~
	* [http://planetmath.org/SignRelation Sign Relation], [http://planetmath.org/ PlanetMath]		* [http://planetmath.org/SignRelation Sign Relation], [http://planetmath.org/ PlanetMath]
			* [http://wikinfo.org/w/index.php/Sign_relation Sign Relation], [http://wikinfo.org/w/ Wikinfo]
			* [http://en.wikiversity.org/wiki/Sign_relation Sign Relation], [http://en.wikiversity.org/ Wikiversity]
	* [http://beta.wikiversity.org/wiki/Sign_relation Sign Relation], [http://beta.wikiversity.org/ Wikiversity Beta]		* [http://beta.wikiversity.org/wiki/Sign_relation Sign Relation], [http://beta.wikiversity.org/ Wikiversity Beta]
	~~{{col-break}}~~
	* [http://getwiki.net/-Sign_Relation Sign Relation], [http://getwiki.net/ GetWiki]
	* [http://en.wikipedia.org/w/index.php?title=Sign_relation&oldid=161631069 Sign Relation], [http://en.wikipedia.org/ Wikipedia]		* [http://en.wikipedia.org/w/index.php?title=Sign_relation&oldid=161631069 Sign Relation], [http://en.wikipedia.org/ Wikipedia]
	~~{{col-end}}~~

	[[Category:Artificial Intelligence]]		[[Category:Artificial Intelligence]]
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	[[Category:Philosophy]]		[[Category:Philosophy]]
	[[Category:Pragmatics]]		[[Category:Pragmatics]]
			[[Category:Pragmatism]]
			[[Category:Relation Theory]]
	[[Category:Semantics]]		[[Category:Semantics]]
	[[Category:Semiotics]]		[[Category:Semiotics]]
	[[Category:Syntax]]		[[Category:Syntax]]

Jon Awbrey: update

2013-11-04T20:22:06Z

update

@@ Line 678: / Line 678: @@
 | <math>\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \} \}.\!</math>
 |}
 ==Six ways of looking at a sign relation==

Jon Awbrey: update

2013-11-04T03:02:04Z

update

← Older revision		Revision as of 03:02, 4 November 2013
Line 537:		Line 537:
	One nice property possessed by the sign relations <math>L_\mathrm{A}\!</math> and <math>L_\mathrm{B}\!</math> is that their connotative components <math>\mathrm{Con}(L_\mathrm{A})\!</math> and <math>\mathrm{Con}(L_\mathrm{B})\!</math> form a pair of equivalence relations on their common syntactic domain <math>S = I.\!</math> It is convenient to refer to such a structure as a ''semiotic equivalence relation'' (SER) since it equates signs that mean the same thing to some interpreter. Each of the SERs, <math>\mathrm{Con}(L_\mathrm{A}), \mathrm{Con}(L_\mathrm{B}) \subseteq S \times I \cong S \times S\!</math> partitions the whole collection of signs into ''semiotic equivalence classes'' (SECs). This makes for a strong form of representation in that the structure of the interpreters' common object domain <math>\{ \mathrm{A}, \mathrm{B} \}\!</math> is reflected or reconstructed, part for part, in the structure of each of their ''semiotic partitions'' (SEPs) of the syntactic domain <math>\{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}.\!</math> But it needs to be observed that the semiotic partitions for interpreters <math>\mathrm{A}\!</math> and <math>\mathrm{B}\!</math> are not the same, indeed, they are orthogonal to each other. This makes it difficult to interpret either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of objective structure or invariant reality, independent of the individual interpreter's point of view.		One nice property possessed by the sign relations <math>L_\mathrm{A}\!</math> and <math>L_\mathrm{B}\!</math> is that their connotative components <math>\mathrm{Con}(L_\mathrm{A})\!</math> and <math>\mathrm{Con}(L_\mathrm{B})\!</math> form a pair of equivalence relations on their common syntactic domain <math>S = I.\!</math> It is convenient to refer to such a structure as a ''semiotic equivalence relation'' (SER) since it equates signs that mean the same thing to some interpreter. Each of the SERs, <math>\mathrm{Con}(L_\mathrm{A}), \mathrm{Con}(L_\mathrm{B}) \subseteq S \times I \cong S \times S\!</math> partitions the whole collection of signs into ''semiotic equivalence classes'' (SECs). This makes for a strong form of representation in that the structure of the interpreters' common object domain <math>\{ \mathrm{A}, \mathrm{B} \}\!</math> is reflected or reconstructed, part for part, in the structure of each of their ''semiotic partitions'' (SEPs) of the syntactic domain <math>\{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}.\!</math> But it needs to be observed that the semiotic partitions for interpreters <math>\mathrm{A}\!</math> and <math>\mathrm{B}\!</math> are not the same, indeed, they are orthogonal to each other. This makes it difficult to interpret either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of objective structure or invariant reality, independent of the individual interpreter's point of view.

	Information about the contrasting patterns of semiotic equivalence induced by the interpreters <math>\mathrm{A}\!</math> and <math>\mathrm{B}\!</math> is summarized in Tables 7a and 7b. The form of these Tables should ~~be sufficient~~ to explain what is meant by saying that the SEPs for <math>\mathrm{A}\!</math> and <math>\mathrm{B}\!</math> are orthogonal to each other.		Information about the contrasting patterns of semiotic equivalence induced by the interpreters <math>\mathrm{A}\!</math> and <math>\mathrm{B}\!</math> is summarized in Tables 7a and 7b. The form of these Tables should suffice to explain what is meant by saying that the SEPs for <math>\mathrm{A}\!</math> and <math>\mathrm{B}\!</math> are orthogonal to each other.

	<br>		<br>
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	{\| align="center" cellpadding="12" style="text-align:center; width:100%"		{\| align="center" cellpadding="12" style="text-align:center; width:100%"
	\| <math>\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \} \}\!</math>		\| <math>\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \} \}.\!</math>
	\|}		\|}

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	{\| align="center" cellpadding="12" style="text-align:center; width:100%"		{\| align="center" cellpadding="12" style="text-align:center; width:100%"
	\| <math>\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \} \}\!</math>		\| <math>\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \} \}.\!</math>
	\|}		\|}

Jon Awbrey: + links to NKOS

2013-11-03T17:32:09Z

+ links to NKOS

← Older revision		Revision as of 17:32, 3 November 2013
Line 768:		Line 768:

	* [http://www.helsinki.fi/science/commens/dictionary.html The Commens Dictionary of Peirce's Terms]		* [http://www.helsinki.fi/science/commens/dictionary.html The Commens Dictionary of Peirce's Terms]
	** [http://www.helsinki.fi/science/commens/terms/semeiotic.html ~~Entry for ''~~Semeiotic'']		** [http://www.helsinki.fi/science/commens/terms/semeiotic.html Semeiotic, Semiotic, Semeotic, Semeiotics]
			* [http://forum.wolframscience.com/archive/ A New Kind Of Science • Forum Archive]
			** [http://forum.wolframscience.com/archive/topic/647.html Excerpts from Peirce on Sign Relations]

	==Syllabus==		==Syllabus==

Jon Awbrey: update

2013-11-03T02:02:28Z

update

← Older revision		Revision as of 02:02, 3 November 2013
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	O		O
	& = &		& = &
	\{ \text{Ann}, \text{Bob} \} & = & \{ \~~text~~{A}, \~~text~~{B} \}		\{ \text{Ann}, \text{Bob} \} & = & \{ \mathrm{A}, \mathrm{B} \}
	\\[6pt]		\\[6pt]
	S		S
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	\{ {}^{\backprime\backprime} \text{Ann} {}^{\prime\prime}, {}^{\backprime\backprime} \text{Bob} {}^{\prime\prime}, {}^{\backprime\backprime} \text{I} {}^{\prime\prime}, {}^{\backprime\backprime} \text{you} {}^{\prime\prime} \}		\{ {}^{\backprime\backprime} \text{Ann} {}^{\prime\prime}, {}^{\backprime\backprime} \text{Bob} {}^{\prime\prime}, {}^{\backprime\backprime} \text{I} {}^{\prime\prime}, {}^{\backprime\backprime} \text{you} {}^{\prime\prime} \}
	& = &		& = &
	\{ {}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}, {}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}, {}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}, {}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime} \}		\{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}
	\\[6pt]		\\[6pt]
	I		I
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	\{ {}^{\backprime\backprime} \text{Ann} {}^{\prime\prime}, {}^{\backprime\backprime} \text{Bob} {}^{\prime\prime}, {}^{\backprime\backprime} \text{I} {}^{\prime\prime}, {}^{\backprime\backprime} \text{you} {}^{\prime\prime} \}		\{ {}^{\backprime\backprime} \text{Ann} {}^{\prime\prime}, {}^{\backprime\backprime} \text{Bob} {}^{\prime\prime}, {}^{\backprime\backprime} \text{I} {}^{\prime\prime}, {}^{\backprime\backprime} \text{you} {}^{\prime\prime} \}
	& = &		& = &
	\{ {}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}, {}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}, {}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}, {}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime} \}		\{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}
	\end{array}</math>		\end{array}</math>
	\|}		\|}
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	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\|-		\|-
	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\|}		\|}
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	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\|-		\|-
	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\| valign="bottom" \|		\| valign="bottom" \|
	<math>\begin{matrix}		<math>\begin{matrix}
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}
	\\[4pt]		\\[4pt]
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}		{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}
	\end{matrix}</math>		\end{matrix}</math>
	\|}		\|}

Jon Awbrey: update

2013-11-02T19:08:13Z

update

← Older revision		Revision as of 19:08, 2 November 2013
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	{\| align="center" style="width:92%"		{\| align="center" style="width:92%"
	\| width="50%" \|		\| width="50%" \|
	{\| align="center~~" border="1~~" cellpadding="10" cellspacing="0" style="text-align:center; width:92%"		{\| align="center" cellpadding="20" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:90%"
	\|+ style="height:30px" \| <math>\text{Table 7a.} ~~ \text{Semiotic Partition for Interpreter A}\!</math>		\|+ style="height:30px" \| <math>\text{Table 7a.} ~~ \text{Semiotic Partition for Interpreter A}\!</math>
	\|		\| <math>{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}\!</math>
	~~{\| align="center" border="0" cellpadding="10" cellspacing="0" style="text-align:center; width:100%"~~		\| <math>{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}\!</math>
	~~\| width="50%"~~ \| <math>{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}\!</math>
	~~\| width="50%"~~ \| <math>{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}\!</math>
	\|}
	\|-		\|-
	\|		\| style="border-top:1px solid black" \| <math>{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}\!</math>
	~~{\| align~~=~~"center~~" border~~="0" cellpadding="10" cellspacing="0" style="text~~-~~align:center; width~~:~~100%"~~		\| style="border-top:1px solid black" \| <math>{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}\!</math>
	~~\| width="50%~~" \| <math>{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}\!</math>
	\| ~~width~~="~~50%~~" \| <math>{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}\!</math>
	\|}
	\|}		\|}
	\| width="50%" \|		\| width="50%" \|
	{\| align="center~~" border="1~~" cellpadding="8" cellspacing="0" style="text-align:center; width:92%"		{\| align="center" cellpadding="20" cellspacing="1" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:90%"
	\|+ style="height:30px" \| <math>\text{Table 7b.} ~~ \text{Semiotic Partition for Interpreter B}\!</math>		\|+ style="height:30px" \| <math>\text{Table 7b.} ~~ \text{Semiotic Partition for Interpreter B}\!</math>
	\|		\| <math>{}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}\!</math>
	~~{\| align="center" border="0" cellpadding="10" cellspacing="0" style="text-align:center; width:50%"~~		\| style="border-left:1px solid black" \| <math>{}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime}\!</math>
	\|		\|-
	<math>~~\begin{matrix}~~		\| <math>{}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime}\!</math>
	{}^{\backprime\backprime} \~~text~~{A} {}^{\prime\prime}		\| style="border-left:1px solid black" \| <math>{}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}\!</math>
	\~~\[20pt]~~
	{}^{\backprime\backprime} \~~text~~{u} {}^{\prime\prime}
	\~~end{matrix}~~</math>
	\|}
	\|
	~~{\| align="center" border="0" cellpadding="10" cellspacing="0" style="text~~-~~align:center; width:50%"~~
	\|
	<math>~~\begin{matrix}~~
	{}^{\backprime\backprime} \~~text~~{i} {}^{\prime\prime}
	\~~\[20pt]~~
	{}^{\backprime\backprime} \~~text~~{B} {}^{\prime\prime}
	\~~end{matrix}~~</math>
	\|}
	\|}		\|}
	\|}		\|}

Jon Awbrey: update

2013-11-01T16:20:26Z

update

Show changes

Jon Awbrey: small fixes

2013-10-29T20:04:20Z

small fixes

← Older revision		Revision as of 20:04, 29 October 2013
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	<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].		<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].

	A '''sign relation''' is the basic construct in the theory of signs, also known as [[semeiotic]] or [[semiotics]], as developed by [[Charles Sanders Peirce]].		A '''sign relation''' is the basic construct in the theory of signs, also known as [[semeiotic]] or [[semiotics]], as developed by Charles Sanders Peirce.

	==Anthesis==		==Anthesis==
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	==Definition==		==Definition==

	One of Peirce's clearest and most complete definitions of a sign is one that he gives~~, not incidentally,~~ in the context of ~~defining "[[~~logic~~]]"~~, and so it is informative to view it in that setting.		One of Peirce's clearest and most complete definitions of a sign is one that he gives in the context of providing a definition for ''logic'', and so it is informative to view it in that setting.

	{\| align="center" cellpadding="6" width="90%"		{\| align="center" cellpadding="6" width="90%"
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	<p>Logic will here be defined as ''formal semiotic''. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign determined or created by it, into the same sort of correspondence with something, ''C'', its ''object'', as that in which itself stands to ''C''. It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has ''virtually'' been quite generally held, though not generally recognized. (C.S. Peirce, NEM 4, 20–21).</p>		<p>Logic will here be defined as ''formal semiotic''. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign determined or created by it, into the same sort of correspondence with something, ''C'', its ''object'', as that in which itself stands to ''C''. It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has ''virtually'' been quite generally held, though not generally recognized. (C.S. Peirce, NEM 4, 20–21).</p>
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	Some of the terms that Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.		Some of the terms that Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

	:* '''Correspondence.''' From the way that Peirce uses this term throughout his work, it is clear that he means what he elsewhere calls a "triple correspondence", and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of this term should not be taken to imply a dyadic ~~corresponence~~, like the kinds of “mirror image” correspondence between realities and representations that are bandied about in contemporary controversies about “correspondence theories of truth”.		:* '''Correspondence.''' From the way that Peirce uses this term throughout his work, it is clear that he means what he elsewhere calls a "triple correspondence", and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of this term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations that are bandied about in contemporary controversies about “correspondence theories of truth”.

	:* '''Determination.''' Peirce's concept of determination is broader in several directions than the sense of the word that refers to strictly deterministic causal-temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a ''formal'' or ''informational'' determination, as in saying "two points determine a line", rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called ''determination in measure'', that is, an order of determinism that admits a full spectrum of more and less determined relationships.		:* '''Determination.''' Peirce's concept of determination is broader in several directions than the sense of the word that refers to strictly deterministic causal-temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a ''formal'' or ''informational'' determination, as in saying "two points determine a line", rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called ''determination in measure'', that is, an order of determinism that admits a full spectrum of more and less determined relationships.
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	: ''Main article : [[Inquiry]]''		: ''Main article : [[Inquiry]]''

	There is a close relationship between the pragmatic theory of signs and the pragmatic theory of [[inquiry]]. In fact, the correspondence between the two studies exhibits so many congruences and parallels that it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, "thinking" in its best sense, "is a term denoting the various ways in which things acquire significance" ([[John Dewey]]). Thus, there is an active and intricate form of cooperation that needs to be appreciated and maintained between these converging modes of investigation. Its proper character is best understood by realizing that the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject which the theory of signs is specialized to treat from structural and comparative points of view.		There is a close relationship between the pragmatic theory of signs and the pragmatic theory of [[inquiry]]. In fact, the correspondence between the two studies exhibits so many congruences and parallels that it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (John Dewey). Thus, there is an active and intricate form of cooperation that needs to be appreciated and maintained between these converging modes of investigation. Its proper character is best understood by realizing that the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject which the theory of signs is specialized to treat from structural and comparative points of view.

	==Examples of sign relations==		==Examples of sign relations==
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	==Semiotic equivalence relations==		==Semiotic equivalence relations==

	~~(Text in Progress)~~		<font size="3">☞</font> [http://planetmath.org/SemioticEquivalenceRelation PlanetMath • Semiotic Equivalence Relation]

	==Six ways of looking at a sign relation==		==Six ways of looking at a sign relation==

Jon Awbrey: update links

2013-10-27T16:16:01Z

update links

← Older revision		Revision as of 16:16, 27 October 2013
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	\| align="center" \| ''A'' gives ''B'' to ''C''		\| align="center" \| ''A'' gives ''B'' to ''C''
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	: we make no distinction in the ordinary logic of relations between the ''[[subject ~~(grammar)\|subject]] [[~~nominative]]'', the ''[[direct object]]'', and the ''[[indirect object]]''. We say that the proposition has three ''logical subjects''. We regard it as a mere affair of English grammar that there are six ways of expressing this: <br>		: we make no distinction in the ordinary logic of relations between the ''subject nominative'', the ''direct object'', and the ''indirect object''. We say that the proposition has three ''logical subjects''. We regard it as a mere affair of English grammar that there are six ways of expressing this: <br>
	{\| align="center" cellspacing="8" style="width:72%"		{\| align="center" cellspacing="8" style="width:72%"
	\| style="width:36%" \| ''A'' gives ''B'' to ''C''		\| style="width:36%" \| ''A'' gives ''B'' to ''C''
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	\| ''B'' leaves ''A'' for ''C''		\| ''B'' leaves ''A'' for ''C''
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	: These six sentences express one and the same indivisible phenomenon. (C.S. Peirce, "The Categories Defended", MS 308 (1903), EP 2, 170-171).		: These six sentences express one and the same indivisible phenomenon. (C.S. Peirce, “The Categories Defended”, MS 308 (1903), EP 2, 170–171).

	===IOS===		===IOS===
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	===OIS===		===OIS===

	<~~blockquote~~>		{\| align="center" cellpadding="6" width="90%"
	Words spoken are symbols or signs (σύμβολα) of affections or impressions (παθήματα) of the soul (ψυχή); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (σημεια), are the same for the whole of mankind, as are also the objects (πράγματα) of which those affections are representations or likenesses, images, copies (ομοιώματα). ([[Aristotle]], ''[[De Interpretatione]]'', 1.16<sup>a</sup>4).		\|
	</~~blockquote~~>		<p>Words spoken are symbols or signs (σύμβολα) of affections or impressions (παθήματα) of the soul (ψυχή); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (σημεια), are the same for the whole of mankind, as are also the objects (πράγματα) of which those affections are representations or likenesses, images, copies (ομοιώματα). (Aristotle, ''De Interpretatione'', 1.16<sup>a</sup>4).</p>
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	===OSI===		===OSI===
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	===SIO===		===SIO===

	<~~blockquote~~>		{\| align="center" cellpadding="6" width="90%"
	Logic will here be defined as ''formal semiotic''. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign determined or created by it, into the same sort of correspondence with something, ''C'', its ''object'', as that in which itself stands to ''C''. It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has ''virtually'' been quite generally held, though not generally recognized. (C.S. Peirce, "Application to the [[Carnegie Institution~~]]"~~, L75 (1902), NEM 4, 20-21).		\|
	</~~blockquote~~>		<p>Logic will here be defined as ''formal semiotic''. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign determined or created by it, into the same sort of correspondence with something, ''C'', its ''object'', as that in which itself stands to ''C''. It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has ''virtually'' been quite generally held, though not generally recognized. (C.S. Peirce, “Application to the Carnegie Institution”, L75 (1902), NEM 4, 20–21).</p>
			\|}

	===SOI===		===SOI===

	<~~blockquote~~>		{\| align="center" cellpadding="6" width="90%"
	A ''Sign'' is anything which is related to a Second thing, its ''Object'', in respect to a Quality, in such a way as to bring a Third thing, its ''Interpretant'', into relation to the same Object, and that in such a way as to bring a Fourth into relation to that Object in the same form, ''ad infinitum''. (CP 2.92; quoted in Fisch 1986: 274)		\|
	</~~blockquote~~>		<p>A ''Sign'' is anything which is related to a Second thing, its ''Object'', in respect to a Quality, in such a way as to bring a Third thing, its ''Interpretant'', into relation to the same Object, and that in such a way as to bring a Fourth into relation to that Object in the same form, ''ad infinitum''. (CP 2.92, quoted in Fisch 1986, p. 274)</p>
			\|}

	==References==		==References==

	==Bibliography==		==Bibliography==

	===Primary sources===		===Primary sources===

	* [[Charles Sanders Peirce (Bibliography)]]		* [[Charles Sanders Peirce (Bibliography)]]

	===Secondary sources===		===Secondary sources===

	* Awbrey, ~~Jon~~, and Awbrey, ~~Susan~~ (1995), "Interpretation as Action : The Risk of Inquiry", ''Inquiry : Critical Thinking Across the Disciplines'' 15, ~~40–52~~. [http://~~www~~.chss.montclair.edu/inquiry/fall95/awbrey.html Online].		* Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, ''Inquiry : Critical Thinking Across the Disciplines'' 15(1), pp. 40–52. [http://web.archive.org/web/19970626071826/http://chss.montclair.edu/inquiry/fall95/awbrey.html Archive]. [http://independent.academia.edu/JonAwbrey/Papers/1302117/Interpretation_as_Action_The_Risk_of_Inquiry Online].

	* Deledalle, Gérard (2000), ''C.S. Peirce's Philosophy of Signs'', Indiana University Press, Bloomington, IN.		* Deledalle, Gérard (2000), ''C.S. Peirce's Philosophy of Signs'', Indiana University Press, Bloomington, IN.

	* Eisele, Carolyn (1979), in ''Studies in the Scientific and Mathematical Philosophy of C.S. Peirce'', [[Richard Milton Martin]] (ed.), Mouton, The Hague.		* Eisele, Carolyn (1979), in ''Studies in the Scientific and Mathematical Philosophy of C.S. Peirce'', Richard Milton Martin (ed.), Mouton, The Hague.

	* Esposito, Joseph (1980), ''Evolutionary Metaphysics: The Development of Peirce's Theory of Categories'', Ohio University Press (?).		* Esposito, Joseph (1980), ''Evolutionary Metaphysics : The Development of Peirce's Theory of Categories'', Ohio University Press (?).

	* Fisch, Max (1986), ''Peirce, Semeiotic, and Pragmatism'', Indiana University Press, Bloomington, IN.		* Fisch, Max (1986), ''Peirce, Semeiotic, and Pragmatism'', Indiana University Press, Bloomington, IN.
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	* Murphey, M. (1961), ''The Development of Peirce's Thought''. Reprinted, Hackett, Indianapolis, IN, 1993.		* Murphey, M. (1961), ''The Development of Peirce's Thought''. Reprinted, Hackett, Indianapolis, IN, 1993.

	* [[Walker ~~Percy]]~~ (2000), pp. 271-291 in ''Signposts in a Strange Land'', P. Samway (ed.), Saint Martin's Press.		* Percy, Walker (2000), pp. 271–291 in ''Signposts in a Strange Land'', P. Samway (ed.), Saint Martin's Press.

	==Resources==		==Resources==

Jon Awbrey: update

2013-10-27T15:40:09Z

update

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