# Work ䷆

## Peirce’s 1870 “Logic of Relatives” • Comment 10.5

### HTML + LaTeX

#### Display 1

$\begin{array}{*{15}{c}} \mathrm{w} & = & \mathrm{B} & +\!\!, & \mathrm{D} & +\!\!, & \mathrm{E} \\[6pt] \mathit{l} & = & \mathrm{B} \!:\! \mathrm{C} & +\!\!, & \mathrm{C} \!:\! \mathrm{B} & +\!\!, & \mathrm{D} \!:\! \mathrm{O} & +\!\!, & \mathrm{E} \!:\! \mathrm{I} & +\!\!, & \mathrm{I} \!:\! \mathrm{E} & +\!\!, & \mathrm{J} \!:\! \mathrm{D} & +\!\!, & \mathrm{O} \!:\! \mathrm{D} \\[6pt] \mathit{s} & = & \mathrm{C} \!:\! \mathrm{O} & +\!\!, & \mathrm{E} \!:\! \mathrm{D} & +\!\!, & \mathrm{I} \!:\! \mathrm{O} & +\!\!, & \mathrm{J} \!:\! \mathrm{D} & +\!\!, & \mathrm{J} \!:\! \mathrm{O} \end{array}$

#### Display 2

$\begin{array}{lll} \mathit{l}, & = & \text{lover that is}\, \underline{~~~~}\, \text{of}\, \underline{~~~~} \\[6pt] & = & (\mathrm{B\!:\!B\!:\!C} ~+\!\!,~ \mathrm{C\!:\!C\!:\!B} ~+\!\!,~ \mathrm{D\!:\!D\!:\!O} ~+\!\!,~ \mathrm{E\!:\!E\!:\!I} ~+\!\!,~ \mathrm{I\!:\!I\!:\!E} ~+\!\!,~ \mathrm{J\!:\!J\!:\!D} ~+\!\!,~ \mathrm{O\!:\!O\!:\!D}) \\[12pt] \mathit{l},\!\mathit{s}\mathrm{w} & = & (\mathrm{B\!:\!B\!:\!C} ~+\!\!,~ \mathrm{C\!:\!C\!:\!B} ~+\!\!,~ \mathrm{D\!:\!D\!:\!O} ~+\!\!,~ \mathrm{E\!:\!E\!:\!I} ~+\!\!,~ \mathrm{I\!:\!I\!:\!E} ~+\!\!,~ \mathrm{J\!:\!J\!:\!D} ~+\!\!,~ \mathrm{O\!:\!O\!:\!D}) \\ & & \times \\ & & (\mathrm{C\!:\!O} ~+\!\!,~ \mathrm{E\!:\!D} ~+\!\!,~ \mathrm{I\!:\!O} ~+\!\!,~ \mathrm{J\!:\!D} ~+\!\!,~ \mathrm{J\!:\!O}) \\ & & \times \\ & & (\mathrm{B} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E}) \end{array}$

#### Display 3

$\begin{array}{lll} \mathit{l},\!\mathit{s}\mathrm{w} & = & \mathit{l},\!\mathit{s}(\mathrm{B} ~~+\!\!,~~ \mathrm{D} ~~+\!\!,~~ \mathrm{E}) \\[6pt] & = & \mathit{l},\!\mathit{s}\mathrm{B} ~~+\!\!,~~ \mathit{l},\!\mathit{s}\mathrm{D} ~~+\!\!,~~ \mathit{l},\!\mathit{s}\mathrm{E} \end{array}$

#### Display 4

$\begin{array}{lll} \mathit{l},\!\mathit{s}\mathrm{w} & = & \text{lover and servant of a woman} \\[6pt] & = & \text{lover that is a servant of a woman} \\[6pt] & = & \text{lover of a woman that is a servant of that woman} \\[6pt] & = & \mathrm{J} \end{array}$