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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 04:00, 24 April 2009
, 04:00, 24 April 2009→Commentary Note 11.11
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| P o Q |
| P o Q |
| ____________^____________ |
| ____________O____________ |
| / \ |
| / \ |
| / P Q \ |
| / P Q \ |
| / @ @ \ |
| / O O \ |
| / / \ / \ \ |
| / / \ / \ \ |
| / / \ / \ \ |
| / / \ / \ \ |
| o o o o o o |
| o o o o o o |
| X X Y Y Z Z |
| X X Y Y Z Z |
| 1,__# #'p'__$ $'q'__% %1 |
| 1,__! !'p'__@ @'q'__# #1 |
| o o o o o o |
| o o o o o o |
| \ / \ / \ / |
| \ / \ / \ / |
| \ / \ / \ / |
| \ / \ / \ / |
| \ / \ / \ / |
| \ / \ / \ / |
| @ @ @ |
| O O O |
| !1! !1! !1! |
| !1! !1! !1! |
| |
| |
| |
| |
| P P o Q Q |
| P P o Q Q |
| @ @ @ |
| O O O |
| / \ / \ / \ |
| / \ / \ / \ |
| / \ / \ / \ |
| / \ / \ / \ |
| \ / \ / \ / |
| \ / \ / \ / |
| \ / \___ ___/ \ / |
| \ / \___ ___/ \ / |
| @ @ @ |
| O O O |
| !1! !1! !1! |
| !1! !1! !1! |
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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%"
<br>
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
Table 18. Relational Composition P o Q
|+ '''Table 18. Relational Composition P o Q'''
|-
| # !1! | !1! | !1! |
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" |
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| P # X | Y | |
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| Q # | Y | Z |
|-
| style="border-right:1px solid black" | <math>P\!</math>
| P o Q # X | | Z |
| <math>X\!</math>
| <math>Y\!</math>
</pre>
|
|-
| style="border-right:1px solid black" | <math>Q\!</math>
|
| <math>Y\!</math>
| <math>Z\!</math>
|-
| style="border-right:1px solid black" | <math>P \circ Q</math>
| <math>X\!</math>
|
| <math>Z\!</math>
|}
|}
<br>
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.