Jeff,
We agree. And thanks for citing the article about Riemann's hypothesis.
The only point I would ask: Please don't try to harmonize me -- i.e.,
put me in a mental straitjacket.
JBD
I've raised some questions about John Sowa's remarks about First
Order Predicate Logic being paradigmatic as a formal system of
logic. Like many who work in mathematical logic, John seems to
be impressed by (1) the expressive power and (2) the stability of
this system. Quite a number of mathematicians working today appear
to have come to the conclusion that this system of formal logic
should be taken as foundational for all of mathematics. I have
numerous reservations about adopting this posture towards the
predicate calculus.
I do not use the word 'foundation'. Instead, I use the word 'subset'.
First-order logic is a subset of English and most other languages.
Anybody who uses the following six words in English or their
equivalents in any other language is speaking or writing first-order
logic: and, or, not, if, some, every.
one thing that appears to be essential to the predicate calculus
being a first-order system is that it does not provide for the
representation of hypostatic abstraction within the logical
system itself. Other systems do...
Yes. That's the second semester of your logic course. When I
taught that course I mentioned earlier, the prerequisite was
"Knowledge of FOL and natural language syntax". The *first*
homework assignment was to translate ten English sentences to
FOL. That was just a check for the prerequisites.
I think the reference to possible future developments of a system
of signs is just as important as those that refer to developments
made in the past. Those future developments are, at any given time,
part of that sign's potentiality.
Yes. It's important to go beyond the first semester.
John
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