Avril, (01)
There are three points about science: (02)
1. Nothing is known for absolute certainty. (03)
2. But there is a great deal that is known to a very
high degree of approximation. (04)
3. And for many important domains, it is possible to
quantify the experimental error. (05)
This provides a solid foundation for action, and it provides
criteria for ruling out completely erroneous ideas. (06)
JFS>> I'll accept the point that reality is one. (07)
AS> If we start to talk about truth, I think that the above
> statement is the first thing that has to be accepted as an
> axiom, along with the law of contradiction. If these are not
> accepted, then anything goes, and sentences loose their meaning. (08)
That statement was by Azamat, and I was accepting it for the
sake of argument. But even then, I'm not really sure what it
means to say "reality is one". I would rather restate the point
by saying that I agree that there is a reality outside of our
own minds and that our sensory organs can tell us a great deal
about it. (09)
AS> And isn't that part of the objective one truth that *should*
> be inflicted on everybody? Suppose that this was taught for every
> student in every university. Can you see anything wrong in it? (010)
That's more of a slogan than something that would be worth making
into a course. If you want to print it on T-shirt and give it to
incoming freshmen, be my guest. But I don't see much point in it. (011)
AS> But mathematics, at least the foundational questions, are not
> any more secure than philosophical ontology. (012)
I go along with Peirce, Kronecker, Wittgenstein, and others:
Mathematics is a method of reasoning, and it has no need for
foundations. There may be particular mathematical theories
whose foundations require further analysis -- e.g., calculus
in the 19th century and the theory of infinitesimals in the 20th.
But those are specific theories, not mathematics as a subject. (013)
Mathematical logic is an application of mathematics to the analysis
of reasoning. Most professional mathematicians ignore what the
logicians are doing as basically irrelevant to their work. (014)
Note that when Goedel proved his incompleteness theorem, he assumed
arithmetic as given -- because even logicians had more faith in
arithmetic than they had in any version of logic or set theory. (015)
John (016)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (017)
|