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

Revision as of 05:08, 4 April 2009

492 bytes added , 05:08, 4 April 2009

→‎Commentary Note 8.4

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Here are a few of the simplest products among these terms:

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~~: '~~l'1 = "lover of ~~anybody"~~

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

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|

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:: = (B:C +, C:B +, D:O +, E:I +, I:E +, O:D)(B +, C +, D +, E +, I +, J +, O)

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<math>\begin{array}{lll}

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\mathit{l}1

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:: = B +, C +, D +, E +, I +, O

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& = &

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\text{lover of anything}

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:: = ~~"anybody~~ except J"

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\\[6pt]

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& = &

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

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\\

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& &

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\times

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\\

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& &

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

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\\[6pt]

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& = &

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\mathrm{B} ~+\!\!,~ \mathrm{C} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E} ~+\!\!,~ \mathrm{I} ~+\!\!,~ \mathrm{O}

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\\[6pt]

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& = &

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\text{anything except}~\mathrm{J}

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\end{array}</math>

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|}

: 'l'b = "lover of a black"

Jon Awbrey

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