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

Revision as of 15:06, 8 April 2009

246 bytes added ,  15:06, 8 April 2009
→‎Commentary Note 9.6
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   −
Example 2.  Anything That Is Man
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Example 2.  Anything That Is A Man
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: 1,m = m
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{| align="center" cellpadding="6" width="90%"
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| <math>\mathbf{1,}\mathrm{m} ~=~ \mathrm{m}</math>
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: "anything that is man" = "man"
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|-
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| <math>\text{anything that is a man} ~=~ \text{man}</math>
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|-
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|
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<math>
 +
\begin{bmatrix}
 +
1 & 0 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 1 & 0 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 1 & 0 & 0 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 1 & 0 & 0 & 0
 +
\\
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0 & 0 & 0 & 0 & 1 & 0 & 0
 +
\\
 +
0 & 0 & 0 & 0 & 0 & 1 & 0
 +
\\
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0 & 0 & 0 & 0 & 0 & 0 & 1
 +
\end{bmatrix}
 +
\begin{bmatrix}
 +
0 \\ 1 \\ 0 \\ 0 \\ 1 \\ 1 \\ 1
 +
\end{bmatrix}
 +
=
 +
\begin{bmatrix}
 +
0 \\ 1 \\ 0 \\ 0 \\ 1 \\ 1 \\ 1
 +
\end{bmatrix}
 +
</math>
 +
|}
    
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
Line 2,452: Line 2,480:  
</pre>
 
</pre>
 
|}
 
|}
 +
 +
Example 3.  Man That Is Anything
 +
 +
: m,1 = m
 +
 +
: "man that is anything" = "man"
    
<pre>
 
<pre>
−
| 1 0 0 0 0 0 0 | | 0 |    | 0 |
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| 0 0 0 0 0 0 0 | | 1 |    | 0 |
 
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
 
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
−
| 0 0 1 0 0 0 0 | | 0 |    | 0 |
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| 0 0 0 0 0 0 0 | | 1 |    | 0 |
−
| 0 0 0 1 0 0 0 | | 0 |  =  | 0 |
+
| 0 0 0 0 0 0 0 | | 1 |  =  | 0 |
 
| 0 0 0 0 1 0 0 | | 1 |    | 1 |
 
| 0 0 0 0 1 0 0 | | 1 |    | 1 |
 
| 0 0 0 0 0 1 0 | | 1 |    | 1 |
 
| 0 0 0 0 0 1 0 | | 1 |    | 1 |
 
| 0 0 0 0 0 0 1 | | 1 |    | 1 |
 
| 0 0 0 0 0 0 1 | | 1 |    | 1 |
 
</pre>
 
</pre>
−
  −
Example 3.  Man That Is Anything
  −
  −
: m,1 = m
  −
  −
: "man that is anything" = "man"
      
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
Line 2,483: Line 2,511:  
</pre>
 
</pre>
 
|}
 
|}
 +
 +
Example 4.  Man That Is Noble
 +
 +
: m,n = "man that is noble"
    
<pre>
 
<pre>
−
| 0 0 0 0 0 0 0 | | 1 |    | 0 |
+
| 0 0 0 0 0 0 0 | | 0 |    | 0 |
 
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
 
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
 
| 0 0 0 0 0 0 0 | | 1 |    | 0 |
 
| 0 0 0 0 0 0 0 | | 1 |    | 0 |
−
| 0 0 0 0 0 0 0 | | 1 |  =  | 0 |
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| 0 0 0 0 0 0 0 | | 0 |  =  | 0 |
−
| 0 0 0 0 1 0 0 | | 1 |    | 1 |
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| 0 0 0 0 1 0 0 | | 0 |    | 0 |
−
| 0 0 0 0 0 1 0 | | 1 |    | 1 |
+
| 0 0 0 0 0 1 0 | | 0 |    | 0 |
 
| 0 0 0 0 0 0 1 | | 1 |    | 1 |
 
| 0 0 0 0 0 0 1 | | 1 |    | 1 |
 
</pre>
 
</pre>
−
  −
Example 4.  Man That Is Noble
  −
  −
: m,n = "man that is noble"
      
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
Line 2,512: Line 2,540:  
</pre>
 
</pre>
 
|}
 
|}
 +
 +
Example 5.  Noble That Is Man
 +
 +
: n,m = "noble that is man"
    
<pre>
 
<pre>
 
| 0 0 0 0 0 0 0 | | 0 |    | 0 |
 
| 0 0 0 0 0 0 0 | | 0 |    | 0 |
 
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
 
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
 +
| 0 0 1 0 0 0 0 | | 0 |    | 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 0 | | 1 |    | 0 |
 
| 0 0 0 0 0 0 0 | | 1 |    | 0 |
−
| 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 1 | | 1 |    | 1 |
 
| 0 0 0 0 0 0 1 | | 1 |    | 1 |
 
</pre>
 
</pre>
−
  −
Example 5.  Noble That Is Man
  −
  −
: n,m = "noble that is man"
      
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
Line 2,541: Line 2,569:  
</pre>
 
</pre>
 
|}
 
|}
−
  −
<pre>
  −
| 0 0 0 0 0 0 0 | | 0 |    | 0 |
  −
| 0 1 0 0 0 0 0 | | 1 |    | 1 |
  −
| 0 0 1 0 0 0 0 | | 0 |    | 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 0 | | 1 |    | 0 |
  −
| 0 0 0 0 0 0 1 | | 1 |    | 1 |
  −
</pre>
      
===Commentary Note 9.7===
 
===Commentary Note 9.7===
Jon Awbrey
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