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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)

Revision as of 02:15, 10 April 2009

274 bytes added , 02:15, 10 April 2009

→‎Commentary Note 10.5

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And next we derive the following results:

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~~:{| cellpadding="4"~~

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~~| 'l',~~

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~~| =~~

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~~| colspan="2" | "lover that is --- of ---"~~

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|-

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~~|  ~~

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~~| =~~

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~~| colspan="2" | B:B:C +, C:C:B +, D:D:O +, E:E:I +, I:I:E +, J:J:D +, O:O:D~~

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|}

{| align="center" cellspacing="6" width="90%"

|

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<math>\begin{array}{~~lll~~}

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<math>\begin{array}{l}

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\mathit{l},\!\mathit{s}\mathrm{w}

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\mathit{l}, ~=

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~~& = &~~

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\\[6pt]

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\text{lover that is}\, \underline{~~~~}\, \text{of}\, \underline{~~~~} ~=

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\\[6pt]

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(\mathrm{B}\!:\!\mathrm{B}\!:\!\mathrm{C} ~+\!\!,~ \mathrm{C}\!:\!\mathrm{C}\!:\!\mathrm{B} ~+\!\!,~ \mathrm{D}\!:\!\mathrm{D}\!:\!\mathrm{O} ~+\!\!,~ \mathrm{E}\!:\!\mathrm{E}\!:\!\mathrm{I} ~+\!\!,~ \mathrm{I}\!:\!\mathrm{I}\!:\!\mathrm{E} ~+\!\!,~ \mathrm{J}\!:\!\mathrm{J}\!:\!\mathrm{D} ~+\!\!,~ \mathrm{O}\!:\!\mathrm{O}\!:\!\mathrm{D})

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\\[12pt]

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\mathit{l},\!\mathit{s}\mathrm{w} ~=

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\\[6pt]

(\mathrm{B}\!:\!\mathrm{B}\!:\!\mathrm{C} ~+\!\!,~ \mathrm{C}\!:\!\mathrm{C}\!:\!\mathrm{B} ~+\!\!,~ \mathrm{D}\!:\!\mathrm{D}\!:\!\mathrm{O} ~+\!\!,~ \mathrm{E}\!:\!\mathrm{E}\!:\!\mathrm{I} ~+\!\!,~ \mathrm{I}\!:\!\mathrm{I}\!:\!\mathrm{E} ~+\!\!,~ \mathrm{J}\!:\!\mathrm{J}\!:\!\mathrm{D} ~+\!\!,~ \mathrm{O}\!:\!\mathrm{O}\!:\!\mathrm{D})

\\

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~~& &~~

\times

\\

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~~& &~~

(\mathrm{C}\!:\!\mathrm{O} ~+\!\!,~ \mathrm{E}\!:\!\mathrm{D} ~+\!\!,~ \mathrm{I}\!:\!\mathrm{O} ~+\!\!,~ \mathrm{J}\!:\!\mathrm{D} ~+\!\!,~ \mathrm{J}\!:\!\mathrm{O})

\\

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~~& &~~

\times

\\

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~~& &~~

(\mathrm{B} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E})

\end{array}</math>

Jon Awbrey

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