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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
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{{DISPLAYTITLE:Peirce's 1870 Logic Of Relatives}}
'''Author's Note.''' The text that follows is a collection of notes that will eventually be developed into a paper on [[Charles Sanders Peirce]]'s [[Logic of Relatives (1870)|1870 memoir on the logic of relative terms]]. [[User:Jon Awbrey|Jon Awbrey]] 06:06, 8 October 2007 (PDT)
'''Author's Note.''' The text that follows is a collection of notes that will eventually be developed into a paper on [[Charles Sanders Peirce]]'s [[Logic of Relatives (1870)|1870 memoir on the logic of relative terms]]. [[User:Jon Awbrey|Jon Awbrey]] 06:06, 8 October 2007 (PDT)
Giver of a Horse to a Lover of a Woman
Giver of a Horse to a Lover of a Woman
</pre>
</pre>
==Selection 8==
<pre>
<pre>
| The Signs for Multiplication (cont.)
| The Signs for Multiplication (cont.)
|
|
|'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870,
|'Memoirs of the American Academy', Volume 9, pages 317-378, 26 January 1870,
|'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).
|'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).
</pre>
==Commentary Note 8.1==
<pre>
To my way of thinking, CP 3.73 is one of the most remarkable passages
To my way of thinking, CP 3.73 is one of the most remarkable passages
in the history of logic. In this first pass over its deeper contents
in the history of logic. In this first pass over its deeper contents
w = B +, D +, E
w = B +, D +, E
</pre>
==Commentary Note 8.2==
<pre>
I will continue with my commentary on CP 3.73, developing
I will continue with my commentary on CP 3.73, developing
the Othello example as a way of illustrating its concepts.
the Othello example as a way of illustrating its concepts.
a winner over of Othello to Iago from Cassio, the elementary relative term
a winner over of Othello to Iago from Cassio, the elementary relative term
"I:O:I:C" belongs to the relative term "winner over of --- to --- from ---".
"I:O:I:C" belongs to the relative term "winner over of --- to --- from ---".
</pre>
==Commentary Note 8.3==
<pre>
Speaking very strictly, we need to be careful to
Speaking very strictly, we need to be careful to
distinguish a "relation" from a "relative term".
distinguish a "relation" from a "relative term".
multiplication, or relational composition, will need
multiplication, or relational composition, will need
to be adjusted accordingly.
to be adjusted accordingly.
</pre>
==Commentary Note 8.4==
<pre>
To familiarize ourselves with the forms of calculation
To familiarize ourselves with the forms of calculation
that are available in Peirce's notation, let us compute
that are available in Peirce's notation, let us compute
relative terms 'l' and 's' do not commute,
relative terms 'l' and 's' do not commute,
that is to say, 'ls' is not equal to 'sl'.
that is to say, 'ls' is not equal to 'sl'.
</pre>
==Commentary Note 8.5==
<pre>
Since multiplication by a 2-adic relative term
Since multiplication by a 2-adic relative term
is a logical analogue of matrix multiplication
is a logical analogue of matrix multiplication
| 0 0 1 0 0 0 1 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 |
| 0 0 1 0 0 0 1 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 |
| 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 |
</pre>
==Commentary Note 8.6==
<pre>
The foregoing has hopefully filled in enough background that we
The foregoing has hopefully filled in enough background that we
can begin to make sense of the more mysterious parts of CP 3.73.
can begin to make sense of the more mysterious parts of CP 3.73.
= D
= D
</pre>
==Selection 9==
<pre>
| The Signs for Multiplication (cont.)
| The Signs for Multiplication (cont.)
|
|