Chris, (01)
Your note arrived while I was responding to Pat's. Otherwise,
I would have responded to both in the same note. (02)
As I said to Pat, the criteria for both sets and types in
mathematics requires a proof, except for small finite sets. (03)
For anything that has to deal with the real world, the problem
of checking equality involves all the issues of epistemology,
philosophy of science, scientific method, and the practical
problems of slogging through the swamp to check facts. (04)
JFS>> Unfortunately, there was comparatively little work in analyzing
>> the application of logic to the real world. (05)
CP> I assume by 'logic' here you mean 'sets' - as these are what you
> are critiquing. (06)
I meant the entire process of conceptual analysis that must be done
prior to formalization. The traditional textbooks on logic from the
medieval Scholastics to the early 20th century devoted at least half
of the book to conceptual analysis and the mapping of language to logic.
But textbooks on symbolic logic would give a few examples of English
sentences translated to logic in Chapter 1 and ignore the issue
of conceptual analysis from then on. (07)
I recall an anecdote by Doug Lenat. His standard practice when
interviewing job applicants is to give them a short exam with
a few English sentences to be translated to FOL. (And most
applicants failed badly, even ones who had taken quite a few
courses on logic.) One applicant happened to be a professor
of logic. Lenat apologized when he handed him the exam and
said that he gave it to everybody. (08)
As it turned out, the professor failed the exam. But he
gave an excuse, "That's not what we teach our students."
That was certainly true. (09)
CP> I suspect people like Lewis, Heller, Jubien and Sider would
> find your comment odd (well, incorrect - well, logically false). (010)
Note my word "comparatively'. Those philosophers wrote good
books about selected topics in conceptual analysis and ontology.
But compared to the depth of work in 20th century mathematical
logic, they were hardly scratching the surface. They certainly
haven't given us an upper level ontology or a suitable basis
for solving the endless rounds of arguments on ontolog forum. (011)
CP> So (taking a classic case) using your proposed criteria,
> how does one prove whether or not these two are identical:
> - The author of Waverly
> - The person named Walter Scott
> Or
> - The person named Cicero
> - The person named Tully
>
> Does it depend upon the logic you use or the axioms in the system?
> Do you need question begging axioms such as (Cicero = Tully)
> to show they are identical. (012)
Proofs use whatever facts you have. There is nothing question
begging about doing your homework to find the facts. (013)
CP> Would you be happy with a situation where these were NOT identical?
> Because they were not "provably equivalent". (014)
I don't understand your question. If the facts show that they are
identical, then you've proved the point. Of course, that proof is
only relative to the degree of certainty of the historical evidence.
But modern databases have as much or more errors as any history book. (015)
John (016)
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