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Directory:Jon Awbrey/Papers/Differential Logic (view source)
Revision as of 20:57, 9 June 2009
, 20:57, 9 June 2009→Note 13: markup
Peirce describes the action of an "elementary dual relative" in this way:
Peirce describes the action of an "elementary dual relative" in this way:
{| align="center" cellpadding="6" width="90%"
| [Let] A:B be taken to denote
| [Let] <math>A\!:\!B</math> be taken to denote the elementary relative which multiplied into <math>B\!</math> gives <math>A.\!</math>
|-
| C.S. Peirce, ''Collected Papers'', CP 3.123.
|
|}
| Peirce, 'Collected Papers', CP 3.123.
And though he is well aware that it is not at all necessary to arrange elementary relatives into arrays, matrices, or tables, when he does so he tends to prefer organizing dyadic relations in the following manner:
And though he is well aware that it is not at all necessary to arrange elementary relatives into arrays, matrices, or tables, when he does so he tends to prefer organizing dyadic relations in the following manner:
<pre>
{| align="center" cellpadding="6" width="90%"
|
<math>\begin{bmatrix}
A:A & A:B & A:C
\\
B:A & B:B & B:C
</pre>
\\
C:A & C:B & C:C
\end{bmatrix}</math>
|}
That conforms to the way that the last school of thought I matriculated into stipulated that we tabulate material:
That conforms to the way that the last school of thought I matriculated into stipulated that we tabulate material:
<pre>
{| align="center" cellpadding="6" width="90%"
|
<math>\begin{bmatrix}
e_{11} & e_{12} & e_{13}
\\
e_{21} & e_{22} & e_{23}
</pre>
\\
e_{31} & e_{32} & e_{33}
\end{bmatrix}</math>
|}
So, for example, let us suppose that we have the small universe <math>\{ A, B, C \},\!</math> and the 2-adic relation <math>\mathrm{m} = {}^{\backprime\backprime} \text{mover of} \, {}^{\prime\prime}</math> that is represented by this matrix:
So, for example, let us suppose that we have the small universe <math>\{ A, B, C \},\!</math> and the 2-adic relation <math>m = {}^{\backprime\backprime}\, \text{mover of}\, \underline{~~~~}\, {}^{\prime\prime}</math> that is represented by this matrix:
<pre>
{| align="center" cellpadding="6" width="90%"
m =
|
<math>
m ~=~
\begin{bmatrix}
m_{AA} (A:A) & m_{AB} (A:B) & m_{AC} (A:C)
\\
m_{BA} (B:A) & m_{BB} (B:B) & m_{BC} (B:C)
</pre>
\\
m_{CA} (C:A) & m_{CB} (C:B) & m_{CC} (C:C)
\end{bmatrix}
</math>
|}
Also, let <math>\mathrm{m}\!</math> be such that
Also, let <math>m\!</math> be such that
<pre>
<pre>