Tom, Ed, Leo, Paul, Henson, (01)
TJ
> why, in the formalization of predicate logic, was it decided
> that "Some X" would carry ontological commitment (02)
Nobody made that decision. It's a fact of perception. Every
observation can always be described with just two operators:
existential quantifier and conjunction. No other operators can
be observed. They can only be inferred. (03)
EJB
> I was taught formal logic as a mathematical discipline, not
> a philosophical discipline. I do not believe that mathematics
> has any interest in ontological commitment. (04)
That's true. And most of the people who developed formal logic
in the 20th c were mathematicians. They didn't worry about
the source or reliability of the starting axioms. (05)
Leo
> most ontologists of the realist persuasion will argue that there
> are no negated/negative ontological things. (06)
Whatever their persuasion, nobody can observe a negation. It's
always an inference or an assumption. (07)
PT
> on the inadequacy of mathematical logic for reasoning about
> the real world, see Veatch, "Intentional Logic: a logic based on
> philosophical realism". (08)
Many different logics can be and have been formalized for various
purposes. They may have different ontological commitments built in,
but the distinction of what is observed or inferred is critical. (09)
HG
> I keep wondering if this forum has anything useful to offer the
> science and engineering community. (010)
C. S. Peirce was deeply involved in experimental physics and
engineering. He was also employed as an associate editor of the
_Century Dictionary_, for which he wrote, revised, or edited over
16,000 definitions. My comments below are based on CSP's writings: (011)
1. Any sensory perception is evidence that something exists;
a simultaneous perception of something A and something B
is evidence for (Ex)(Ey)(A(x) & B(y)). (012)
2. Evidence for other operators must *always* be an inference: (013)
(a) Failure to observe P(x) does not mean there is no P. (014)
Example: "There is no hippopotamus in this room"
can only be inferred iff you have failed to observe
a hippo and know that it is big enough that you would
certainly have noticed one if it were present. (015)
(b) (p or q) cannot be directly observed. But you might infer
that a particular observation (e.g. "the room is lighted")
could be the result of two or more sources. (016)
(c) (p implies q) cannot be observed, as Hume discussed at length. (017)
(d) a universal quantifier can never be observed. No matter
how many examples of P(x) you see, you can never know that
you've seen them all (unless you have other information
that guarantees you have seen them all). (018)
TJ
> But now notice something: negation creates and removes ontological
> commitment. And this seems really strange. Why should negation do this? (019)
The commitment is derived from the same background knowledge that
enabled you to assert (or prevented you from asserting) the negation. (020)
> I'd also like to know if there are formal logics which do not
> impute this extravagant power of ontological commitment /
> de-commitment to the negation operator in predicate logics. (021)
Most formal logicians don't think about these issues -- for the
simple reason that most of them are mathematicians. They don't
think about observation and evidence. (022)
CSP realized the problematical issues with negation, but he also
knew that he needed to assume at least one additional operator.
And negation was the simplest of the lot. Those are the three
he assumed for his existential graphs. (But he later added
metalanguage, modality, and three values -- T, F, and Unknown.) (023)
John (024)
PS: The example "There is no hippopotamus in this room" came from
a remark by Bertrand Russell that he couldn't convince Wittgenstein
that there was no hippopotamus in the room. Russell didn't go
into any detail, but I suspect that Ludwig W. was trying to
explain the point that a negation cannot be observed. (025)
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