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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 03:34, 8 April 2009
, 03:34, 8 April 2009→Commentary Note 9.5
Naturally enough, the diagonal extensions are represented by diagonal matrices:
Naturally enough, the diagonal extensions are represented by diagonal matrices:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
|
|-
|
|
<math>\begin{array}{c|ccccccc}
<math>\begin{array}{c|ccccccc}
\end{array}</math>
\end{array}</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
|
|-
|
|
<math>\begin{array}{c|ccccccc}
<math>\begin{array}{c|ccccccc}
|}
|}
<pre>
{| align="center" cellspacing="6" width="90%"
|
---o---------------
|-
B | 0 0 0 0 0 0 0
|
<math>\begin{array}{c|ccccccc}
\mathrm{n,} &
\mathrm{B} &
\mathrm{C} &
\mathrm{D} &
\mathrm{E} &
</pre>
\mathrm{I} &
\mathrm{J} &
\mathrm{O}
\\
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---}
\\
\mathrm{B} & 0 & & & & & &
\\
\mathrm{C} & & 1 & & & & &
\\
\mathrm{D} & & & 1 & & & &
\\
\mathrm{E} & & & & 0 & & &
\\
\mathrm{I} & & & & & 0 & &
\\
\mathrm{J} & & & & & & 0 &
\\
\mathrm{O} & & & & & & & 1
\end{array}</math>
|}
<pre>
{| align="center" cellspacing="6" width="90%"
|
---o---------------
|-
B | 1 0 0 0 0 0 0
|
<math>\begin{array}{c|ccccccc}
\mathrm{w,} &
\mathrm{B} &
\mathrm{C} &
\mathrm{D} &
\mathrm{E} &
</pre>
\mathrm{I} &
\mathrm{J} &
\mathrm{O}
\\
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---} &
\text{---}
\\
\mathrm{B} & 1 & & & & & &
\\
\mathrm{C} & & 0 & & & & &
\\
\mathrm{D} & & & 1 & & & &
\\
\mathrm{E} & & & & 1 & & &
\\
\mathrm{I} & & & & & 0 & &
\\
\mathrm{J} & & & & & & 0 &
\\
\mathrm{O} & & & & & & & 0
\end{array}</math>
|}
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:
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>