12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Friday November 29, 2024
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 16:09, 3 April 2009
, 16:09, 3 April 2009→Selection 8
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>1 ~=~ \mathrm{B} ~+\!\!,~ \mathrm{C} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E} ~+\!\!,~ \mathrm{I} ~+\!\!,~ \mathrm{J} ~+\!\!,~ \mathrm{O}</math>
|
<math>\begin{array}{*{15}{c}}
1
& = &
\mathrm{B}
& +\!\!, &
\mathrm{C}
& +\!\!, &
\mathrm{D}
& +\!\!, &
\mathrm{E}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\end{array}</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
|
|
<math>\begin{array}{ccl}
<math>\begin{array}{*{15}{c}}
\mathrm{b} & = & \mathrm{O}
\mathrm{b}
& = &
\mathrm{O}
\\[6pt]
\\[6pt]
\mathrm{m} & = & \mathrm{C} ~+\!\!,~ \mathrm{I} ~+\!\!,~ \mathrm{J} ~+\!\!,~ \mathrm{O}
\mathrm{m}
& = &
\mathrm{C}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\\[6pt]
\mathrm{w} & = & \mathrm{B} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E}
\mathrm{w}
& = &
\mathrm{B}
& +\!\!, &
\mathrm{D}
& +\!\!, &
\mathrm{E}
\end{array}</math>
\end{array}</math>
|}
|}
In the development of the story so far, we have a universe of discourse that can be characterized by means of the following system of equations:
In the development of the story so far, we have a universe of discourse that can be characterized by means of the following system of equations:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{*{15}{c}}
1
& = &
\mathrm{B}
& +\!\!, &
\mathrm{C}
& +\!\!, &
\mathrm{D}
& +\!\!, &
\mathrm{E}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\mathrm{b}
& = &
\mathrm{O}
\\[6pt]
\mathrm{m}
& = &
\mathrm{C}
& +\!\!, &
\mathrm{I}
& +\!\!, &
\mathrm{J}
& +\!\!, &
\mathrm{O}
\\[6pt]
\mathrm{w}
& = &
\mathrm{B}
& +\!\!, &
\mathrm{D}
& +\!\!, &
\mathrm{E}
\end{array}</math>
|}
This much provides a basis for collection of absolute terms that I plan to use in this example. Let us now consider how we might represent a sufficiently exemplary collection of relative terms.
If we consider the genesis of relative terms, for example, "lover of ——", "betrayer to —— of ——", or "winner over of —— to —— from ——", we may regard these fill-in-the-blank forms as being derived by way of a kind of ''rhematic abstraction'' from the corresponding instances of absolute terms.
: w = B +, D +, E
In other words:
:* The relative term "lover of ——" can be constructed by abstracting the absolute term "Emilia" from the absolute term "lover of Emilia". Since Iago is a lover of Emilia, the relate-correlate pair denoted by "Iago:Emilia" is a summand of the relative term "lover of ——".
:* The relative term "betrayer to —— of ——" can be constructed by abstracting the absolute terms "Othello" and "Desdemona" from the absolute term "betrayer to Othello of Desdemona". In as much as Iago is a betrayer to Othello of Desdemona, the relate-correlate-correlate triple denoted by "I:O:D" belongs to the relative term "betrayer to —— of ——".
:* The relative term "winner over of —— to —— from ——" can be constructed by abstracting the absolute terms "Othello", "Iago", and "Cassio" from the absolute term "winner over of Othello to Iago from Cassio". Since Iago is 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 ——".
===Commentary Note 8.3===
===Commentary Note 8.3===
