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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 17:30, 5 May 2009
, 17:30, 5 May 2009→Commentary Note 12.3
But doing the same thing for the compound relative term <math>(\mathit{s}^\mathit{l})^\mathrm{w}\!</math> is less immediate, the hang-up being that we have yet to define the case of logical involution that raises a 2-adic relative term to the power of a 2-adic relative term.
But doing the same thing for the compound relative term <math>(\mathit{s}^\mathit{l})^\mathrm{w}\!</math> is less immediate, the hang-up being that we have yet to define the case of logical involution that raises a 2-adic relative term to the power of a 2-adic relative term.
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{*{15}{c}}
X & = & \{ & a, & b, & c, & d, & e, & f, & g, & h, & i & \}
\\[6pt]
W & = & \{ & d, & f & \}
\\[6pt]
L & = & \{ & b\!:\!a, & b\!:\!c, & c\!:\!b, & c\!:\!d, & e\!:\!d, & e\!:\!e, & e\!:\!f, & g\!:\!f, & g\!:\!h, & h\!:\!g, & h\!:\!i & \}
\\[6pt]
S & = & \{ & b\!:\!a, & b\!:\!c, & d\!:\!c, & d\!:\!e, & f\!:\!e, & f\!:\!g, & h\!:\!g, & h\!:\!i & \}
\end{array}</math>
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
a b c d e f g h i
a b c d e f g h i
o o o o o o o o o X
o o o o o o o o o X
| |
/ \ 0 1 0 1 L
| | W,
| |
o o o o + - + + o X
o o o o o o o o o X
\ | / : : | |
\ \ / / \ | / \ \ / /
\ | / 0 0 1 1 S
\ / / \ | / \ \ / L
\|/ : : | |
\ / \ / \|/ \ / \ /
o o o o o o o o o X
\ / \ / \ / \ /
\ / \ / \ / \ / S
\ / \ / \ / \ /
o o o o o o o o o X
o o o o o o o o o X
a b c d e f g h i
a b c d e f g h i