[Inquiry] Re: Logic Of Relatives -- Commentary

[Jon Awbrey]

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LOR.  Commentary Note 8.4

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To familiarize ourselves with the forms of calculation
that are available in Peirce's notation, let us compute
a few of the simplest products that we find at hand in
the Othello case.

Here are the absolute terms:

1  =  B +, C +, D +, E +, I +, J +, O

b  =  O

m  =  C +, I +, J +, O

w  =  B +, D +, E

Here are the 2-adic relative terms:

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

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

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

'l'1 = "lover of anybody"

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

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

     = "anybody except J"

'l'b = "lover of a black"

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

     = D

'l'm = "lover of a man"

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

     = B +, D +, E

'l'w = "lover of a woman"

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

     = C +, I +, O

's'1 = "servant of anybody"

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

     = C +, E +, I +, J

's'b = "servant of a black"

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

     = C +, I +, J

's'm = "servant of a man"

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

     = C +, I +, J

's'w = "servant of a woman"

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

     = E +, J

'ls' = "lover of a servant of ---"

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

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

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

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

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

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'.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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