Discussion:
Defining the set of all things coherently using a type hierarchy
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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>
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DKleinecke
2017-06-19 16:45:31 UTC
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Post by Pete Olcott
Defining the set of all things coherently
using a type hierarchy
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].
[Thing] is progressively divided up into mutually exclusive
categories until every possible category is exhaustively
specified. 
The progression between hierarchy levels is from generality to
specificity.  Each hierarchy level must be divided into exactly
one minimal increment of increased specificity.
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.
The purpose of the above analysis is to reverse-engineer the
optimal way to organize the knowledge ontology of the set of all
knowledge.
In other words - I think you saying there is a tree with
a root called "Thing" that composes all knowledge (in some
manner). Your discussion implies however more structure.
There is also a sequence (called ?) of levels each of
which is a set of tree elements of the same specificity.
Every node in the tree is the member of some level.

Am I reading you correctly?
Pete Olcott
2017-06-19 17:33:26 UTC
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Post by DKleinecke
Post by Pete Olcott
Defining the set of all things coherently
using a type hierarchy
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].
[Thing] is progressively divided up into mutually exclusive
categories until every possible category is exhaustively
specified.
The progression between hierarchy levels is from generality to
specificity. Each hierarchy level must be divided into exactly
one minimal increment of increased specificity.
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.
The purpose of the above analysis is to reverse-engineer the
optimal way to organize the knowledge ontology of the set of all
knowledge.
In other words - I think you saying there is a tree with
a root called "Thing" that composes all knowledge (in some
manner). Your discussion implies however more structure.
Yes.
Post by DKleinecke
There is also a sequence (called ?) of levels each of
which is a set of tree elements of the same specificity.
Example: Living-Thing is divided up into its next level of specificity.
Post by DKleinecke
Every node in the tree is the member of some level.
Am I reading you correctly?
The Tree of all knowledge (has a sub-tree of the knowledge of good and evil).
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
DKleinecke
2017-06-19 23:20:56 UTC
Permalink
Post by Pete Olcott
Post by DKleinecke
Post by Pete Olcott
Defining the set of all things coherently
using a type hierarchy
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].
[Thing] is progressively divided up into mutually exclusive
categories until every possible category is exhaustively
specified.
The progression between hierarchy levels is from generality to
specificity. Each hierarchy level must be divided into exactly
one minimal increment of increased specificity.
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.
The purpose of the above analysis is to reverse-engineer the
optimal way to organize the knowledge ontology of the set of all
knowledge.
In other words - I think you saying there is a tree with
a root called "Thing" that composes all knowledge (in some
manner). Your discussion implies however more structure.
Yes.
Post by DKleinecke
There is also a sequence (called ?) of levels each of
which is a set of tree elements of the same specificity.
Example: Living-Thing is divided up into its next level of specificity.
Post by DKleinecke
Every node in the tree is the member of some level.
Am I reading you correctly?
The Tree of all knowledge (has a sub-tree of the knowledge of good and evil).
I never know whether you just overlooked one of my questions
or are avoiding it. Just in hope here is my question again:

Is my reading of your "levels" correct?
Pete Olcott
2017-06-20 00:24:15 UTC
Permalink
Post by DKleinecke
Post by Pete Olcott
Post by DKleinecke
Post by Pete Olcott
Defining the set of all things coherently
using a type hierarchy
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].
[Thing] is progressively divided up into mutually exclusive
categories until every possible category is exhaustively
specified.
The progression between hierarchy levels is from generality to
specificity. Each hierarchy level must be divided into exactly
one minimal increment of increased specificity.
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.
The purpose of the above analysis is to reverse-engineer the
optimal way to organize the knowledge ontology of the set of all
knowledge.
In other words - I think you saying there is a tree with
a root called "Thing" that composes all knowledge (in some
manner). Your discussion implies however more structure.
Yes.
Post by DKleinecke
There is also a sequence (called ?) of levels each of
which is a set of tree elements of the same specificity.
Example: Living-Thing is divided up into its next level of specificity.
Post by DKleinecke
Every node in the tree is the member of some level.
Am I reading you correctly?
The Tree of all knowledge (has a sub-tree of the knowledge of good and evil).
I never know whether you just overlooked one of my questions
Is my reading of your "levels" correct?
Yes it looks like you have. I can't be sure.

You can imagine a Venn diagram right? Its one big circle. Now if we cut this one big circle up in tiny little pieces we can name each tiny little piece (the name of a set). We can also cut up these little pieces into smaller pieces. There is no possible way to form a set that contains itself using this system.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Pete Olcott
2017-06-22 04:02:48 UTC
Permalink
The list expressly forbids its own permutations.
Then it IS NOT a list of all things. Is the list of all things also a thing?
Then it would have to occur on itself, wouldn't it, which would mean it would
have to be infinite (in two dimensions -- deep as well as long).
If the list (1,2,3) is a thing then there are five other lists that are 5 DIFFERENT things that ALSO MUST be things.
What I really need is a taxonomy of all things: https://en.wikipedia.org/wiki/Taxonomy_(general)

In this case the set of natural numbers may be algorithmically compressed as this regular expression: [1-9][0-9]*

I am seeking to reverse-engineer the preexisting natural order of the set of all knowledge.

I am doing this to complete the formal specification of the formal semantics of linguistics as the mandatory sub-goal of a larger goal.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
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