SUO: Re: Critique Of Non-Functional Reason
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| A. Automated Reasoning (AR)
|
| The standard will be suitable for automated logical inference
| to support knowledge-based reasoning applications.
|
| B. Inter-Operability (IO)
|
| The standard will provide a basis for achieving Inter-Operability
| among various software and database applications.
Summary Of The Thread Up To This Point (cont.)
If for no better reason than to pursue a comparative and developmental study
of standards already in place, I took up the presentation of selections from
Quine's 'Mathematical Logic'. There is much that is admirable in this work.
Quine exhibits a level of finesse with a panoply of tricky logical wickets
that those of us in the "generations of the short attention span" (GOTSAS)
are not likely ever to match again. And he somehow manages to do it all
in natural language phrasings that you will be hard-pressed to find in
the jet-set symbolic e-fontery of your typical logic journal or math
monotonograph today.
I have no trouble with the fine distinctions that Quine takes such pains
to impress on us here -- if it were not that my simple mind cannot quite
preserve their traceries for more than a few days after I have once again
refreshed my memory in them -- what remains is barely that I am supposed
to say "if-then" for the "conditional", that is written "=>", and that
signifies a mode of "statement composition", in contrast to "implies"
for the "implication", which is a mode of "standing in relation" that
statements may enjoy, and that therefore must be stated in terms of
names for these statements, where these names for statements are
canonically obtained by quotation of them.
But none of that sticks in my sort of mind unless I can find
a briefer array of mnemonic devices to pin it all down, and
here what does the trick for me is to remember their types,
namely, the fact that there are distinct objects of thought
with types like these:
1. Modes of composing statements into composite statements,
via the logical connectives, have types like SC^k -> SC,
where "SC" indicates the type of a "sentential clause",
or a "statement" in Quine's nomenclature.
2. Statements of relation among statements are derived or produced
by operations with types like NP^k -> SC, where "NP" indicates
a "noun phrase" that happens in this case to name a statement.
That's about as summary as I can make it.
I need a nap to clear my head ...
Jon Awbrey
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