Pete Olcott
2017-06-19 03:28:39 UTC
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<p><font size="+1"><b>Defining the set of all things coherently
using a type hierarchy</b><b><br>
</b></font><br>
In my latest formulation the urelements are the leaves and the non
leaf nodes are a hierarchy of sets. The root node of this [type
hierarchy of all things] is [Thing]. <br>
<br>
[Thing] is progressively divided up into mutually exclusive
categories until every possible category is exhaustively
specified. </p>
<p>The progression between hierarchy levels is from generality to
specificity. Each hierarchy level must be divided into exactly
one minimal increment of increased specificity. <br>
<br>
If we were to form a list of all of the leaf nodes and non-leaf
nodes of this type hierarchy, we would have the concept of the set
of all things defined coherently. </p>
<p>The purpose of the above analysis is to reverse-engineer the
optimal way to organize the knowledge ontology of the set of all
knowledge.
<br>
</p>
<p><b></b><b>Copyright Pete Olcott 2017</b><br>
</p>
<br>
<div class="moz-signature">-- <br>
<p class="western" style="margin-bottom: 0in"><b><font
face="Arial, sans-serif"><font style="font-size: 12pt"
size="2">(Γ
</font><font style="font-size: 12pt" size="2">⊨ </font><sub><font
style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A) ≡ (</font><font style="font-size: 12pt" size="2">Γ </font><font
style="font-size: 12pt" size="2">⊢
</font><sub><font style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A)</font></font></b></p>
<p class="western" style="margin-bottom: 0in"><br>
</p>
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<p><font size="+1"><b>Defining the set of all things coherently
using a type hierarchy</b><b><br>
</b></font><br>
In my latest formulation the urelements are the leaves and the non
leaf nodes are a hierarchy of sets. The root node of this [type
hierarchy of all things] is [Thing]. <br>
<br>
[Thing] is progressively divided up into mutually exclusive
categories until every possible category is exhaustively
specified. </p>
<p>The progression between hierarchy levels is from generality to
specificity. Each hierarchy level must be divided into exactly
one minimal increment of increased specificity. <br>
<br>
If we were to form a list of all of the leaf nodes and non-leaf
nodes of this type hierarchy, we would have the concept of the set
of all things defined coherently. </p>
<p>The purpose of the above analysis is to reverse-engineer the
optimal way to organize the knowledge ontology of the set of all
knowledge.
<br>
</p>
<p><b></b><b>Copyright Pete Olcott 2017</b><br>
</p>
<br>
<div class="moz-signature">-- <br>
<p class="western" style="margin-bottom: 0in"><b><font
face="Arial, sans-serif"><font style="font-size: 12pt"
size="2">(Γ
</font><font style="font-size: 12pt" size="2">⊨ </font><sub><font
style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A) ≡ (</font><font style="font-size: 12pt" size="2">Γ </font><font
style="font-size: 12pt" size="2">⊢
</font><sub><font style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A)</font></font></b></p>
<p class="western" style="margin-bottom: 0in"><br>
</p>
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</body>
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