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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 22:01, 10 April 2009
, 22:01, 10 April 2009→Commentary Note 8.2
===Commentary Note 8.2===
===Commentary Note 8.2===
I will continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating its concepts.
I will continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating its concepts.
In the development of the story so far, we have a universe of discourse that can be characterized by means of the following system of equations:
In the development of the story so far, we have a universe of discourse that can be characterized by means of the following system of equations:
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<math>\begin{array}{*{15}{c}}
<math>\begin{array}{*{15}{c}}
1
\mathbf{1}
& = &
& = & \mathrm{B}
\mathrm{B}
& +\!\!, & \mathrm{C}
& +\!\!, &
& +\!\!, & \mathrm{D}
\mathrm{C}
& +\!\!, & \mathrm{E}
& +\!\!, &
& +\!\!, & \mathrm{I}
\mathrm{D}
& +\!\!, & \mathrm{J}
& +\!\!, &
& +\!\!, & \mathrm{O}
\mathrm{E}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\\[6pt]
\mathrm{b}
\mathrm{b}
& = &
& = & \mathrm{O}
\mathrm{O}
\\[6pt]
\\[6pt]
\mathrm{m}
\mathrm{m}
& = &
& = & \mathrm{C}
\mathrm{C}
& +\!\!, & \mathrm{I}
& +\!\!, &
& +\!\!, & \mathrm{J}
\mathrm{I}
& +\!\!, & \mathrm{O}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\\[6pt]
\mathrm{w}
\mathrm{w}
& = &
& = & \mathrm{B}
\mathrm{B}
& +\!\!, & \mathrm{D}
& +\!\!, &
& +\!\!, & \mathrm{E}
\mathrm{D}
& +\!\!, &
\mathrm{E}
\end{array}</math>
\end{array}</math>
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