SUO: Re: Examples! Examples! Examples!
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EEE. Note 4
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Example 1. John Sowa's "Top Level Categories" (cont.)
So far in our formalization of TLC, we have the following ingredients:
1. An alphabet !A! = {a_1, ..., a_25} of 25 descriptives terms.
2. An alphabet !M! = {m_1, m_2, m_3, m_4} = {" ", "(", ",", ")"}
of punctuation marks.
3. The full alphabet !B! = !B!(!A!) = !A! |_| !M!.
4. The things that we think of as "sentences" or (propositional) "expressions"
are strings in a formal language L(!A!) that are formed from the elements
of !B!(!A!) according to the prescriptions of a certain formal grammar.
5. In particular, the axiom that I gave for (my present understanding of) TLC,
which is the sole member of its axiomset $A$, is a particular sentence !a!
in L(!A!) c !B!*. Namely, !a! is the string displayed in Table 1, here:
http://suo.ieee.org/email/msg09670.html
Aside. It's not really important right now,
but more details about the syntax, semantics,
and pragmatics of the Cactus Language can be
found here:
http://www.altheim.com/cs/cactus.html
This is the sort of computationally finitary specificity
that we should expect to get when we ask questions about
what's in the box of this or that module of this or that
lattice of theories. References to theories in general,
which are, in general, infinite sets of sentences, just
won't cut it when it comes down to the e-bearing wire.
Well, that was a little more formal detail than I had
in mind for this thread, which I will try to keep more
to the intuition building types of concrete observations.
Jon Awbrey
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