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

Revision as of 03:34, 8 April 2009

848 bytes added ,  03:34, 8 April 2009
→‎Commentary Note 9.5
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Naturally enough, the diagonal extensions are represented by diagonal matrices:
 
Naturally enough, the diagonal extensions are represented by diagonal matrices:
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<br>
      
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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|
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|-
 
|
 
|
 
<math>\begin{array}{c|ccccccc}
 
<math>\begin{array}{c|ccccccc}
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\end{array}</math>
 
\end{array}</math>
 
|}
 
|}
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<br>
      
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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|
 +
|-
 
|
 
|
 
<math>\begin{array}{c|ccccccc}
 
<math>\begin{array}{c|ccccccc}
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|}
 
|}
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<pre>
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{| align="center" cellspacing="6" width="90%"
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!n!| B C D E I J O
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|
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---o---------------
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|-
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  B | 0 0 0 0 0 0 0
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|
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C | 0 1 0 0 0 0 0
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<math>\begin{array}{c|ccccccc}
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D | 0 0 1 0 0 0 0
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\mathrm{n,} &
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E | 0 0 0 0 0 0 0
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\mathrm{B}  &
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I | 0 0 0 0 0 0 0
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\mathrm{C}  &
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J | 0 0 0 0 0 0 0
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\mathrm{D}  &
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O | 0 0 0 0 0 0 1
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\mathrm{E}  &
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</pre>
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\mathrm{I}  &
 +
\mathrm{J}  &
 +
\mathrm{O}
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\\
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---} &
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\text{---}
 +
\\
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\mathrm{B} & 0 &  &  &  &  &  &
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\\
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\mathrm{C} &  & 1 &  &  &  &  &
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\\
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\mathrm{D} &  &  & 1 &  &  &  &
 +
\\
 +
\mathrm{E} &  &  &  & 0 &  &  &
 +
\\
 +
\mathrm{I} &  &  &  &  & 0 &  &
 +
\\
 +
\mathrm{J} &  &  &  &  &  & 0 &
 +
\\
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\mathrm{O} &  &  &  &  &  &  & 1
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\end{array}</math>
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|}
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<pre>
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{| align="center" cellspacing="6" width="90%"
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!w!| B C D E I J O
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|
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---o---------------
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|-
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  B | 1 0 0 0 0 0 0
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|
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C | 0 0 0 0 0 0 0
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<math>\begin{array}{c|ccccccc}
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D | 0 0 1 0 0 0 0
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\mathrm{w,} &
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E | 0 0 0 1 0 0 0
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\mathrm{B}  &
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I | 0 0 0 0 0 0 0
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\mathrm{C}  &
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J | 0 0 0 0 0 0 0
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\mathrm{D}  &
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O | 0 0 0 0 0 0 0
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\mathrm{E}  &
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</pre>
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\mathrm{I}  &
 +
\mathrm{J}  &
 +
\mathrm{O}
 +
\\
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---}  &
 +
\text{---} &
 +
\text{---}
 +
\\
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\mathrm{B} & 1 &  &  &  &  &  &
 +
\\
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\mathrm{C} &  & 0 &  &  &  &  &
 +
\\
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\mathrm{D} &  &  & 1 &  &  &  &
 +
\\
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\mathrm{E} &  &  &  & 1 &  &  &
 +
\\
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\mathrm{I} &  &  &  &  & 0 &  &
 +
\\
 +
\mathrm{J} &  &  &  &  &  & 0 &
 +
\\
 +
\mathrm{O} &  &  &  &  &  &  & 0
 +
\end{array}</math>
 +
|}
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Cast into the bigraph picture of 2-adic relations, the diagonal extension of an absolute term takes on a very distinctive sort of "straight-laced" character:
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Cast into the bigraph picture of 2-adic relations, the diagonal extension of an absolute term takes on a very distinctive sort of ''straight-laced'' character:
    
<pre>
 
<pre>
Jon Awbrey
12,140

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