ONT Re: Zeroth Order Ontology
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ZOO 18
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In: ZOO. http://suo.ieee.org/ontology/thrd1.html#05155
Re: ZOO 17. http://suo.ieee.org/ontology/msg05213.html
One of the problems, or maybe it was more like a philosophical worry,
that used to trouble me a lot from the days of my very first studies
in algebra, was a problem about the "ontological status of variables".
But the recognition of an arithmetic that underlies whatever algebra
one happens to be studying, together with the conception of epiforms,
was finally effective in resolving these difficulties for me. Taken
in tandem, these supply us with a thoroughly unmysterious and purely
combinatorial way of grasping what's essential and what's accidental
in the relation between the arithmetic and the corresponding algebra.
We typically take our first steps from the arithmetic to the algebra
by way of the devices of variables and substitutions, but it quickly
becomes obvious that these are inessential artifices, that serve but
to detract from the intrinsic structure of the actual subject matter.
o-----------------------------------------------------------o
| |
| e_3 |
| |
| o o o o o o o o o Epiforms L_3 |
| / \ |
| / \ |
| / \ |
| / \ |
| o e_1 o e_2 o o o o o Formulas L_2 |
| \ / |
| \ / |
| \ / |
| \ / |
| o o Objects L_0 |
| |
o-----------------------------------------------------------o
| |
| o |
| | |
| @ @ Values B |
| |
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Consider once again the case of the epiform e_3 that encompasses the
formulas e_1 and e_2. What is paramount is not the particular style
of expression that one uses for the epiform e_3, whether it involves
signs that take on a variety of values, or the mechanical details of
the substitution process, but only the fact that a formal analogy is
being noted between the expression e_1 and the expression e_2. Then,
by dint of the very circumstance that the analogy exists, there must
be an abstract property that is borne in common by these expressions.
Once we recognize this property, it does not matter how we notate it.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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