Peirce's 1870 “Logic Of Relatives ” • Comment 8.4

Post   : Peirce's 1870 “Logic Of Relatives” • Comment 8.4
http://inquiryintoinquiry.com/2014/02/19/peirces-1870-logic-of-relatives-%e2%80%a2-comment-8-4/
Posted : February 19, 2014 at 3:48 pm
Author : Jon Awbrey
Tags   : Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics

Peircers,

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 universe.

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 dyadic 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:

l1  =  lover of anything
     =  (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
     =  anything except J

lb  =  lover of a black
     =  (B:C +, C:B +, D:O +, E:I +, I:E +, O:D) × O
     =  D

lm  =  lover of a man
     =  (B:C +, C:B +, D:O +, E:I +, I:E +, O:D) × (C +, I +, J +, O)
     =  B +, D +, E

lw  =  lover of a woman
     =  (B:C +, C:B +, D:O +, E:I +, I:E +, O:D) × (B +, D +, E)
     =  C +, I +, O

s1  =  servant of anything
     =  (C:O +, E:D +, I:O +, J:D +, J:O) × (B +, C +, D +, E +, I +, J +, O)
     =  C +, E +, I +, J

sb  =  servant of a black
     =  (C:O +, E:D +, I:O +, J:D +, J:O) × O
     =  C +, I +, J

sm  =  servant of a man
     =  (C:O +, E:D +, I:O +, J:D +, J:O) × (C +, I +, J +, O)
     =  C +, I +, J

sw  =  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, ls is not 
equal to sl.

To be continued ...

-- 

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