Jerry and Joe,
I'll say more about related issues in the thread on ambiguities.
But I just wanted to comment on these points:
JAS: you throw everything possible into the predicate, leaving only
an indicated subject; I throw everything possible into the subject,
leaving only a continuous predicate.
JFS: I agree that those two methods are logically equivalent.
JLRC: Logically equivalent?
Logical equivalence has a precise mathematical meaning.
Yes. Jon and I discussed some issues about hypostatic abstraction,
as Peirce defined it for EGs. It's an equivalence operation that
transforms an EG for the statement "Opium puts people to sleep"
to and from an EG for the statement "Opium has dormitive virtue."
But the operation is only precise when it is applied to some
version of mathematical logic, such as EGs. For natural languages,
it can be a very good approximation, but not always.
That transformation is a reversible equivalence operation that maps
one EG to and from another.
Jerry
No version of logic after syllogisms made a binary distinction
between subject and predicate.
Again, I find this dogmatic statement to be a personal claim that is
without general scientific meaning. This statement is simply out of
touch with current state of inquiry into the nature of logic.
It's a precise observation about mathematical logics from Boolean
algebra to Peirce's several different versions of logic to the many
versions of mathematical logics in use today. One reason why they
don't make a binary distinction between subjects and predicates is
that the overwhelming majority of them don't have any syntactic
category named subject.
But there are some versions of controlled natural languages (CNLs),
which use a formally specified grammar that is adapted from the
much more complex grammar of some NL. Their grammars may have a
syntactic category named subject. But the semantics of those CNLs
is usually defined in terms of a mathematical logic that does not
have a category named subject.
Joe
What is the precise mathematical meaning of "logical equivalence?"
In every version of logic, if a proposition p implies a proposition q,
and q implies p, then p and q are defined to be logically equivalent.
In mathematical logics, this definition is precise. With informal
reasoning in ordinary language, nothing is perfect. But a good
criterion for reliability can be stated very simply:
"Are you willing to bet your life on the truth of that statement?"
Anybody who drives a car or rides in one, bets his or her life on
its reliability and on the behavior of other drivers on the road.
Most people win those bets most of the time. But sometimes they lose.
Jerry
JFS: You're grasping at straws to salvage a lost cause.
This is not even an argument. The sentence does reflect on its
author’s capacities.
It's not a comment on his capacity. It's a comment on his refusal to
admit the obvious. But as a teacher, I have a responsibility to adapt
to the students' background in order to make things clear to them. But
JAS doesn't like to be called a student. That may be why he refuses
to admit that the explanations are clear.
Jerry
JFS: And when you're relating two different notations, such as
English and EGs, you have to be absolutely precise about the grammar
and semantics of each one and their mappings to and from the other.
Roughly speaking, from a mathematical perspective and a scientific
perspective, both grammar and semantics lack precision.
I agree with Peirce that every statement is fallible. But Peirce
also said that all of us assume a large number of points that are
beyond any reasonable doubt. For example, we all believe that we
exist, and nearly everybody believes that other people exist. And
most of us are willing to drive cars and fly in airplanes.
In any case, I'll replace "absolutely precise" with the phrase
"as precise as humanly possible with all the aid you can muster".
That's the criterion Peirce used for his logic, and that's a goal
I strive to emulate. But Peirce admitted that he was fallible, and
so do I. But I also recognize that Peirce was far better than anyone
I know (including myself) in his skills for mapping language to logic.
John is very consistent in creating assertions that, in my opinion,
merely reflect personal opinion and yet claim authority.
Yes. Opinions about authority with respect to any endeavor must
be based on strong evidence that backs up any opinion.
Re language and logic: I have been publishing books and articles
on the subject since 1976, implementing software for mapping one
to the other, teaching courses on the subject at IBM and several
universities, and collaborating with colleagues on developing
practical applications that use the methods. For a list of
related publications, see http://jfsowa.com/pubs/
John
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