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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)

Revision as of 12:43, 6 April 2009

858 bytes added ,  12:43, 6 April 2009
→‎Commentary Note 8.5
Line 1,268: Line 1,268:  
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|
 
<math>\begin{array}{c|cccc}
 
<math>\begin{array}{c|cccc}
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          & \mathbf{1} & \mathrm{b} & \mathrm{m} & \mathrm{w}
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\text{  } & \mathbf{1} & \mathrm{b} & \mathrm{m} & \mathrm{w}
 
\\
 
\\
 
\text{---} & \text{---} & \text{---} & \text{---} & \text{---}
 
\text{---} & \text{---} & \text{---} & \text{---} & \text{---}
Line 1,655: Line 1,655:  
|}
 
|}
   −
: 'ls' = "lover of a servant of ---" =
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{| align="center" cellpadding="6" width="90%"
 +
|
 +
<math>\begin{matrix}
 +
\mathit{l}\mathit{s} & = & \operatorname{lover~of~a~servant~of}~(~) =
 +
\end{matrix}</math>
 +
|-
 +
|
 +
<math>
 +
\begin{bmatrix}
 +
0 & 1 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
1 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 0 & 0 & 1 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 1 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\end{bmatrix}
 +
\begin{bmatrix}
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\end{bmatrix}
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=
 +
\begin{bmatrix}
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0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\end{bmatrix}
 +
</math>
 +
|}
   −
<pre>
+
{| align="center" cellpadding="6" width="90%"
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| 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 |  | 0 0 0 0 0 0 1 |
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|
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| 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 |  | 0 0 0 0 0 0 0 |
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<math>\begin{matrix}
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| 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 |  | 0 0 0 0 0 0 0 |
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\mathit{s}\mathit{l} & = & \operatorname{servant~of~a~lover~of}~(~) =
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| 0 0 0 0 1 0 0 | | 0 0 1 0 0 0 0 | = | 0 0 0 0 0 0 1 |
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\end{matrix}</math>
−
| 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 1 |  | 0 0 1 0 0 0 0 |
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|-
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| 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 |  | 0 0 0 0 0 0 0 |
+
|
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| 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 |  | 0 0 0 0 0 0 0 |
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<math>
−
</pre>
+
\begin{bmatrix}
−
 
+
0 & 0 & 0 & 0 & 0 & 0 & 0
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: 'sl' = "servant of a lover of ---" =
+
\\
−
 
+
0 & 0 & 0 & 0 & 0 & 0 & 1
−
<pre>
+
\\
−
| 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 |  | 0 0 0 0 0 0 0 |
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0 & 0 & 0 & 0 & 0 & 0 & 0
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| 0 0 0 0 0 0 1 | | 1 0 0 0 0 0 0 |  | 0 0 1 0 0 0 0 |
+
\\
−
| 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 |  | 0 0 0 0 0 0 0 |
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0 & 0 & 1 & 0 & 0 & 0 & 0
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| 0 0 1 0 0 0 0 | | 0 0 0 0 1 0 0 | = | 0 0 0 0 0 0 1 |
+
\\
−
| 0 0 0 0 0 0 1 | | 0 0 0 1 0 0 0 |  | 0 0 1 0 0 0 0 |
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0 & 0 & 0 & 0 & 0 & 0 & 1
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| 0 0 1 0 0 0 1 | | 0 0 0 0 0 0 0 |  | 0 0 1 0 0 0 1 |
+
\\
−
| 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 |  | 0 0 0 0 0 0 0 |
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0 & 0 & 1 & 0 & 0 & 0 & 1
−
</pre>
+
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\end{bmatrix}
 +
\begin{bmatrix}
 +
0 & 1 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
1 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 0 & 0 & 1 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 1 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\end{bmatrix}
 +
=
 +
\begin{bmatrix}
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 1
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 0 & 0
 +
\end{bmatrix}
 +
</math>
 +
|}
    
===Commentary Note 8.6===
 
===Commentary Note 8.6===
Jon Awbrey
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