Ampheck - Revision history

Jon Awbrey: update

2015-11-05T15:04:31Z

update

Jon Awbrey: update

2015-10-31T03:02:17Z

update

Jon Awbrey: sub \!~ for \! (due to changes in this LaTeX implementation)

2014-07-01T14:49:46Z

sub \!~ for \! (due to changes in this LaTeX implementation)

Jon Awbrey: ('''♈''')

2013-08-03T02:52:12Z

('''♈''')

Jon Awbrey: update

2013-08-02T21:22:43Z

update

Show changes

Jon Awbrey: + Category:Charles Sanders Peirce

2011-10-29T18:36:45Z

+ Category:Charles Sanders Peirce

Jon Awbrey: + Bold Aries Symbol = Dec '''♈''' = Hex '''♈"'

2010-11-30T23:00:02Z

+ Bold Aries Symbol = Dec '''♈''' = Hex '''♈"'

Jon Awbrey: /* Peer nodes */ + 2

2010-06-20T23:03:29Z

Peer nodes: + 2

Jon Awbrey: /* Information, Inquiry */

2010-05-23T11:24:57Z

Information, Inquiry

Jon Awbrey: /* Syllabus */ update

2010-05-22T03:56:04Z

Syllabus: update

@@ Line 145: / Line 145: @@
 * [http://mywikibiz.com/Ampheck Ampheck], [http://mywikibiz.com/ MyWikiBiz]
 * [http://planetmath.org/Ampheck Ampheck], [http://planetmath.org/ PlanetMath]
 * [http://en.wikiversity.org/wiki/Ampheck Ampheck], [http://en.wikiversity.org/ Wikiversity]
 * [http://beta.wikiversity.org/wiki/Ampheck Ampheck], [http://beta.wikiversity.org/ Wikiversity Beta]

@@ Line 4: / Line 4: @@
 <blockquote>
-<p>For example, <math>x \curlywedge y</math> signifies that <math>x\!~</math> is <math>\mathbf{f}</math> and <math>y\!~</math> is <math>\mathbf{f}</math>.  Then <math>(x \curlywedge y) \curlywedge z</math>, or <math>\underline {x \curlywedge y} \curlywedge z</math>, will signify that <math>z\!~</math> is <math>\mathbf{f}</math>, but that the statement that <math>x\!~</math> and <math>y\!~</math> are both <math>\mathbf{f}</math> is itself <math>\mathbf{f}</math>, that is, is ''false''.  Hence, the value of <math>x \curlywedge x</math> is the same as that of <math>\overline {x}</math>;  and the value of <math>\underline {x \curlywedge x} \curlywedge x</math> is <math>\mathbf{f}</math>, because it is necessarily false;  while the value of <math>\underline {x \curlywedge y} \curlywedge \underline {x \curlywedge y}</math> is only <math>\mathbf{f}</math> in case <math>x \curlywedge y</math> is <math>\mathbf{v}</math>;  and <math>( \underline {x \curlywedge x} \curlywedge x) \curlywedge (x \curlywedge \underline {x \curlywedge x})</math> is necessarily true, so that its value is <math>\mathbf{v}</math>.</p>
+<p>For example, <math>x \curlywedge y</math> signifies that <math>x\!</math> is <math>\mathbf{f}</math> and <math>y\!</math> is <math>\mathbf{f}</math>.  Then <math>(x \curlywedge y) \curlywedge z</math>, or <math>\underline {x \curlywedge y} \curlywedge z</math>, will signify that <math>z\!</math> is <math>\mathbf{f}</math>, but that the statement that <math>x\!</math> and <math>y\!</math> are both <math>\mathbf{f}</math> is itself <math>\mathbf{f}</math>, that is, is ''false''.  Hence, the value of <math>x \curlywedge x</math> is the same as that of <math>\overline {x}</math>;  and the value of <math>\underline {x \curlywedge x} \curlywedge x</math> is <math>\mathbf{f}</math>, because it is necessarily false;  while the value of <math>\underline {x \curlywedge y} \curlywedge \underline {x \curlywedge y}</math> is only <math>\mathbf{f}</math> in case <math>x \curlywedge y</math> is <math>\mathbf{v}</math>;  and <math>( \underline {x \curlywedge x} \curlywedge x) \curlywedge (x \curlywedge \underline {x \curlywedge x})</math> is necessarily true, so that its value is <math>\mathbf{v}</math>.</p>
 <p>With these two signs, the vinculum (with its equivalents, parentheses, brackets, braces, etc.) and the sign <math>\curlywedge</math>, which I will call the ''ampheck'' (from &#945;&#956;&#966;&#951;&#954;&#942;&#962;&nbsp;, cutting both ways), all assertions as to the values of quantities can be expressed. (C.S. Peirce, CP 4.264).</p>
 </blockquote>
-In the above passage, Peirce introduces the term ''ampheck'' for the 2-place logical connective or the binary logical operator that is currently called the ''joint denial'' in logic, the NNOR operator in computer science, or indicated by means of  phrases like "neither-nor" or "both not" in ordinary language.  For this operation he employs a symbol that the typographer most likely set by inverting the zodiac symbol for Aries ('''&#9800;'''), but set in the text above by means of the ''curly wedge'' symbol.
+In the above passage, Peirce introduces the term ''ampheck'' for the 2-place logical connective or the binary logical operator that is currently called the ''joint denial'' in logic, the NNOR operator in computer science, or indicated by means of  phrases like "neither-nor" or "both not" in ordinary language.  For this operation he employs a symbol that the typographer most likely set by inverting the zodiac symbol for Aries('''&#9800;'''), but set in the text above by means of the ''curly wedge'' symbol.
 In the same paper, Peirce introduces a symbol for the logically dual operator.  This was rendered by the editors of his ''Collected Papers'' as an inverted Aries symbol with a bar or a serif at the top, in this way denoting the connective or logical operator that is currently called the ''alternative denial'' in logic, the NAND operator in computer science, or invoked by means of phrases like "not-and" or "not both" in ordinary language.  It is not clear whether it was Peirce himself or later writers who initiated the practice, but on account of their dual relationship it became common to refer to these two operators in the plural, as the ''amphecks''.
@@ Line 35: / Line 35: @@
 ===Focal nodes===
 * [[Inquiry Live]]
 * [[Logic Live]]
 ===Peer nodes===
 * [http://intersci.ss.uci.edu/wiki/index.php/Ampheck Ampheck @ InterSciWiki]
 * [http://mywikibiz.com/Ampheck Ampheck @ MyWikiBiz]
-{{col-break}}
+* [http://ref.subwiki.org/wiki/Ampheck Ampheck @ Subject Wikis]
 * [http://beta.wikiversity.org/wiki/Ampheck Ampheck @ Wikiversity Beta]
 ===Logical operators===
@@ Line 140: / Line 133: @@
 * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 {{col-break}}
 * [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
 * [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 {{col-end}}
@@ Line 149: / Line 142: @@
 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/Ampheck Ampheck], [http://intersci.ss.uci.edu/ InterSciWiki]
 * [http://mywikibiz.com/Ampheck Ampheck], [http://mywikibiz.com/ MyWikiBiz]
 * [http://planetmath.org/Ampheck Ampheck], [http://planetmath.org/ PlanetMath]
 * [http://beta.wikiversity.org/wiki/Ampheck Ampheck], [http://beta.wikiversity.org/ Wikiversity Beta]
 * [http://en.wikipedia.org/w/index.php?title=Ampheck&oldid=62218032 Ampheck], [http://en.wikipedia.org/ Wikipedia]
 [[Category:Inquiry]]

@@ Line 4: / Line 4: @@
 <blockquote>
-<p>For example, <math>x \curlywedge y</math> signifies that <math>x\!</math> is <math>\mathbf{f}</math> and <math>y\!</math> is <math>\mathbf{f}</math>.  Then <math>(x \curlywedge y) \curlywedge z</math>, or <math>\underline {x \curlywedge y} \curlywedge z</math>, will signify that <math>z\!</math> is <math>\mathbf{f}</math>, but that the statement that <math>x\!</math> and <math>y\!</math> are both <math>\mathbf{f}</math> is itself <math>\mathbf{f}</math>, that is, is ''false''.  Hence, the value of <math>x \curlywedge x</math> is the same as that of <math>\overline {x}</math>;  and the value of <math>\underline {x \curlywedge x} \curlywedge x</math> is <math>\mathbf{f}</math>, because it is necessarily false;  while the value of <math>\underline {x \curlywedge y} \curlywedge \underline {x \curlywedge y}</math> is only <math>\mathbf{f}</math> in case <math>x \curlywedge y</math> is <math>\mathbf{v}</math>;  and <math>( \underline {x \curlywedge x} \curlywedge x) \curlywedge (x \curlywedge \underline {x \curlywedge x})</math> is necessarily true, so that its value is <math>\mathbf{v}</math>.</p>
+<p>For example, <math>x \curlywedge y</math> signifies that <math>x\!~</math> is <math>\mathbf{f}</math> and <math>y\!~</math> is <math>\mathbf{f}</math>.  Then <math>(x \curlywedge y) \curlywedge z</math>, or <math>\underline {x \curlywedge y} \curlywedge z</math>, will signify that <math>z\!~</math> is <math>\mathbf{f}</math>, but that the statement that <math>x\!~</math> and <math>y\!~</math> are both <math>\mathbf{f}</math> is itself <math>\mathbf{f}</math>, that is, is ''false''.  Hence, the value of <math>x \curlywedge x</math> is the same as that of <math>\overline {x}</math>;  and the value of <math>\underline {x \curlywedge x} \curlywedge x</math> is <math>\mathbf{f}</math>, because it is necessarily false;  while the value of <math>\underline {x \curlywedge y} \curlywedge \underline {x \curlywedge y}</math> is only <math>\mathbf{f}</math> in case <math>x \curlywedge y</math> is <math>\mathbf{v}</math>;  and <math>( \underline {x \curlywedge x} \curlywedge x) \curlywedge (x \curlywedge \underline {x \curlywedge x})</math> is necessarily true, so that its value is <math>\mathbf{v}</math>.</p>
 <p>With these two signs, the vinculum (with its equivalents, parentheses, brackets, braces, etc.) and the sign <math>\curlywedge</math>, which I will call the ''ampheck'' (from &#945;&#956;&#966;&#951;&#954;&#942;&#962;&nbsp;, cutting both ways), all assertions as to the values of quantities can be expressed. (C.S. Peirce, CP 4.264).</p>

@@ Line 9: / Line 9: @@
 </blockquote>
-In the above passage, Peirce introduces the term ''ampheck'' for the 2-place logical connective or the binary logical operator that is currently called the ''joint denial'' in logic, the NNOR operator in computer science, or indicated by means of  phrases like "neither-nor" or "both not" in ordinary language.  For this operation he employs a symbol that the typographer most likely set by inverting the zodiac symbol for Aries, but set in the text above by means of the ''curly wedge'' symbol.
+In the above passage, Peirce introduces the term ''ampheck'' for the 2-place logical connective or the binary logical operator that is currently called the ''joint denial'' in logic, the NNOR operator in computer science, or indicated by means of  phrases like "neither-nor" or "both not" in ordinary language.  For this operation he employs a symbol that the typographer most likely set by inverting the zodiac symbol for Aries ('''&#9800;'''), but set in the text above by means of the ''curly wedge'' symbol.
 In the same paper, Peirce introduces a symbol for the logically dual operator.  This was rendered by the editors of his ''Collected Papers'' as an inverted Aries symbol with a bar or a serif at the top, in this way denoting the connective or logical operator that is currently called the ''alternative denial'' in logic, the NAND operator in computer science, or invoked by means of phrases like "not-and" or "not both" in ordinary language.  It is not clear whether it was Peirce himself or later writers who initiated the practice, but on account of their dual relationship it became common to refer to these two operators in the plural, as the ''amphecks''.

@@ Line 178: / Line 178: @@
 [[Category:Peer Educational Resource]]
 [[Category:Automata Theory]]
 [[Category:Combinatorics]]
 [[Category:Computer Science]]

@@ Line 9: / Line 9: @@
 </blockquote>
-In the above passage, Peirce introduces the term ''ampheck'' for the 2-place logical connective or the binary logical operator that is currently called the ''[[joint denial]]'' in logic, the NNOR operator in computer science, or indicated by means of  phrases like "neither-nor" or "both not" in ordinary language.  For this operation he employs a symbol that the typographer most likely set by inverting the [[zodiac]] symbol for [[Aries]], but set in the text above by means of the ''curly wedge'' symbol.
+In the above passage, Peirce introduces the term ''ampheck'' for the 2-place logical connective or the binary logical operator that is currently called the ''[[joint denial]]'' in logic, the NNOR operator in computer science, or indicated by means of  phrases like "neither-nor" or "both not" in ordinary language.  For this operation he employs a symbol that the typographer most likely set by inverting the [[zodiac]] symbol for [[Aries]] ('''&#9800;'''), but set in the text above by means of the ''curly wedge'' symbol.
 In the same paper, Peirce introduces a symbol for the logically dual operator.  This was rendered by the editors of his ''Collected Papers'' as an inverted Aries symbol with a bar or a serif at the top, in this way denoting the connective or logical operator that is currently called the ''[[alternative denial]]'' in logic, the NAND operator in computer science, or invoked by means of phrases like "not-and" or "not both" in ordinary language.  It is not clear whether it was Peirce himself or later writers who initiated the practice, but on account of their dual relationship it became common to refer to these two operators in the plural, as the ''amphecks''.

@@ Line 49: / Line 49: @@
 * [http://mathweb.org/wiki/Ampheck Ampheck @ MathWeb Wiki]
 * [http://netknowledge.org/wiki/Ampheck Ampheck @ NetKnowledge]
 {{col-break}}
 * [http://p2pfoundation.net/Ampheck Ampheck @ P2P Foundation]
 * [http://semanticweb.org/wiki/Ampheck Ampheck @ SemanticWeb]
 {{col-end}}

@@ Line 127: / Line 127: @@
 {{col-break}}
 * [[Pragmatic maxim]]
-* [[Pragmatic theory of truth]]
+* [[Truth theory]]
 {{col-end}}

@@ Line 118: / Line 118: @@
 {{col-break}}
 * [[Inquiry]]
 * [[Logic of information]]
 {{col-break}}
@@ Line 125: / Line 128: @@
 * [[Pragmatic maxim]]
 * [[Pragmatic theory of truth]]
 {{col-end}}
 ===Related articles===
 * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]