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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 03:21, 19 October 2007
, 03:21, 19 October 2007→Commentary Note 8.4: markup
===Commentary Note 8.4===
===Commentary Note 8.4===
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.
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:
Here are the absolute terms:
1 = B +, C +, D +, E +, I +, J +, O
: 1 = B +, C +, D +, E +, I +, J +, O
b = O
: b = O
m = C +, I +, J +, O
: m = C +, I +, J +, O
w = B +, D +, E
: w = B +, D +, E
Here are the 2-adic relative terms:
Here are the 2-adic relative terms:
'l' = B:C +, C:B +, D:O +, E:I +, I:E +, O:D
: 'l' = B:C +, C:B +, D:O +, E:I +, I:E +, O:D
's' = C:O +, E:D +, I:O +, J:D +, J:O
: 's' = C:O +, E:D +, I:O +, J:D +, J:O
Here are a few of the simplest products among these terms:
Here are a few of the simplest products among these terms:
'l'1 = "lover of anybody"
: '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"
: '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"
: '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"
: '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"
: '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"
: '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"
: '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"
: '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 ---"
: '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 ---"
: '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
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'.
relative terms 'l' and 's' do not commute,
that is to say, 'ls' is not equal to 'sl'.
===Commentary Note 8.5===
===Commentary Note 8.5===