12,080
edits
Changes
Directory talk:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 21:12, 30 April 2009
, 21:12, 30 April 2009→Commentary Note 12.2
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
o o o o o o o o o o X
o o o o o o o o o o X
/ \
/ \ : | : |
/ \ L
/ \ 0 1 0 1 L
/ \
/ \ : | : |
o o o o o o o o o o X
o o o o + - + + o o X
\ | /
\ | / : : | |
\ | / S
\ | / 0 0 1 1 S
\|/
\|/ : : | |
o o o o o o o o o o X
o o o o o o o o o o X
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
It looks like we have a "servant of every lover of" link between <math>i\!</math> and <math>j\!</math> if and only if <math>i \cdot S \supseteq L \cdot j.</math> It looks like the vacuous inclusions will make this rather non-intuitive.
It looks like we have a "servant of every lover of" link between <math>i\!</math> and <math>j\!</math> if and only if <math>i \cdot S \supseteq L \cdot j.</math> It looks like the vacuous inclusions will make this rather non-intuitive.
Recall the analogy between involution and implication:
{| align="center" cellspacing="6" width="90%"
|
<math>
\begin{bmatrix}
0^0 & = & 1
\\
0^1 & = & 0
\\
1^0 & = & 1
\\
1^1 & = & 1
\end{bmatrix}
\begin{bmatrix}
0 \Leftarrow 0 & = & 1
\\
0 \Leftarrow 1 & = & 0
\\
1 \Leftarrow 0 & = & 1
\\
1 \Leftarrow 1 & = & 1
\end{bmatrix}
</math>
|}
===Commentary on Selection 12===
===Commentary on Selection 12===