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

Revision as of 01:28, 5 April 2009

706 bytes added , 01:28, 5 April 2009

→‎Commentary Note 8.4

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\mathit{l}\mathit{s}

& = &

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\text{lover of a servant of} \, \underline{~~~~}

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\text{lover of a servant of}\, \underline{~~~~}

\\[6pt]

& = &

Line 1,184: Line 1,184:

|}

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~~: 'sl'~~ = "servant of a lover of ~~---"~~

+

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

−

+

|

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

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<math>\begin{array}{lll}

−

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\mathit{s}\mathit{l}

−

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

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& = &

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\text{servant of a lover of}\, \underline{~~~~}

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\\[6pt]

+

& = &

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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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\\

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

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\\[6pt]

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& = &

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

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\end{array}</math>

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|}

−

Among other things, one observes that the relative terms 'l' and 's' do not commute, that is to say, ~~'ls'~~ is not equal to ~~'sl'~~.

+

Among other things, one observes that the relative terms <math>\mathit{l}\!</math> and <math>\mathit{s}\!</math> do not commute, that is to say, <math>\mathit{l}\mathit{s}\!</math> is not equal to <math>\mathit{s}\mathit{l}.\!</math>

===Commentary Note 8.5===

Jon Awbrey

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