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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 15:34, 14 April 2009
, 15:34, 14 April 2009→Commentary Note 11.11
Here is one generic picture of relational composition, cast in a style that hews pretty close to the line of potentials inherent in Peirce's syntax of this period.
Here is one generic picture of relational composition, cast in a style that hews pretty close to the line of potentials inherent in Peirce's syntax of this period.
{| align="center" cellspacing="6" width="90%"
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<pre>
<pre>
o-----------------------------------------------------------o
o-----------------------------------------------------------o
Figure 16. Anything that is a 'p' of a 'q' of Anything
Figure 16. Anything that is a 'p' of a 'q' of Anything
</pre>
</pre>
|}
From this we extract the "hypergraph picture" of relational composition:
From this we extract the "hypergraph picture" of relational composition:
{| align="center" cellspacing="6" width="90%"
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<pre>
<pre>
o-----------------------------------------------------------o
o-----------------------------------------------------------o
Figure 17. Relational Composition P o Q
Figure 17. Relational Composition P o Q
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</pre>
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All of the relevant information of these Figures can be compressed into the form of a "spreadsheet", or constraint satisfaction table:
All of the relevant information of these Figures can be compressed into the form of a "spreadsheet", or constraint satisfaction table:
{| align="center" cellspacing="6" width="90%"
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<pre>
<pre>
Table 18. Relational Composition P o Q
Table 18. Relational Composition P o Q
o---------o---------o---------o---------o
o---------o---------o---------o---------o
</pre>
</pre>
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So the following presents itself as a reasonable plan of study: Let's see how much easy mileage we can get in our exploration of functions by adopting the above templates as a paradigm.
So the following presents itself as a reasonable plan of study: Let's see how much easy mileage we can get in our exploration of functions by adopting the above templates as a paradigm.