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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)

Revision as of 17:08, 12 April 2009

263 bytes removed ,  17:08, 12 April 2009
→‎Commentary Note 11.6
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===Commentary Note 11.6===
 
===Commentary Note 11.6===
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Let's continue to work our way through the rest of the first set of definitions, making up appropriate examples as we go.
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Let's continue working our way through the above definitions, constructing appropriate examples as we go.
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{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
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<math>E_1\!</math> exemplifies the quality of ''totality at <math>X.\!</math>''
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{| align="center" cellspacing="6" width="90%"
 
|
 
|
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Let ''P'' &sube; ''X'' &times; ''Y'' be an arbitrary 2-adic relation.  The following properties of ''P'' can be defined:
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:{| cellpadding="6"
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| ''P'' is "total" at ''X''
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| iff
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| ''P'' is (&ge;1)-regular at ''X''.
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|-
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| ''P'' is "total" at ''Y''
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| iff
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| ''P'' is (&ge;1)-regular at ''Y''.
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|-
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| ''P'' is "tubular" at ''X''
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| iff
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| ''P'' is (&le;1)-regular at ''X''.
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|-
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| ''P'' is "tubular" at ''Y''
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| iff
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| ''P'' is (&le;1)-regular at ''Y''.
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|}
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|}
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''E''<sub>1</sub> exemplifies the quality of "totality at ''X''".
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<pre>
 
<pre>
 
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</pre>
 
</pre>
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|}
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''E''<sub>2</sub> exemplifies the quality of "totality at ''Y''".
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<math>E_2\!</math> exemplifies the quality of ''totality at <math>Y.\!</math>''
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{| align="center" cellspacing="6" width="90%"
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|
 
<pre>
 
<pre>
 
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</pre>
 
</pre>
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|}
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''E''<sub>3</sub> exemplifies the quality of "tubularity at ''X''".
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<math>E_3\!</math> exemplifies the quality of ''tubularity at <math>X.\!</math>''
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{| align="center" cellspacing="6" width="90%"
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|
 
<pre>
 
<pre>
 
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</pre>
 
</pre>
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|}
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''E''<sub>4</sub> exemplifies the quality of "tubularity at ''Y''".
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<math>E_4\!</math> exemplifies the quality of ''tubularity at <math>Y.\!</math>''
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{| align="center" cellspacing="6" width="90%"
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|
 
<pre>
 
<pre>
 
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</pre>
 
</pre>
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|}
    
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
 
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
Jon Awbrey
12,080

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