John, (01)
I go with all that except for one important thing. Sure, the
law of contradiction and arithmetics like 1+1=2 can be taken
as given, and I also believe that nothing more secure can be
given. (02)
But, in ontology, there are also as secure foundations as the
ones above in mathematics. And e.g. the law of contradiction
holds in both, and logic and ontology are very much entangled.
Then again, the statement that there is only one world is
clearly an ontological, and not so much a logical principle. (03)
> 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. (04)
By one WORLD I simply mean the totality of all things that
exist in any sort of a way. If something exists, it is a
part of the WORLD. This principle can be considerer also as
a convention, but if you deny it, paradoxes follow. (05)
This principle goes beyond e.g. realismidealism and
realismnominalism debates. Even idealism works under it.
We can however easily prove that classical realism is more
*econimical* a theory than classical idealism. Note that
this proof requires the axiom. (06)
Idealist says that everything is inside his mind.
So, his mind = world. Now, he anyway can feel his
head. He also feels his legs. Both of these must
anyhow be inside his mind. So, he must make a
separation between his mind that *is* the world, and
the mind that is inside his head. And his head is
inside his mindworld. (07)
Because all this is clearly uneconomical, if not
paradoxical, realism that assumes a reality outside
of our own minds is practically a better option.
I think that this is again one good reason to accept
the axiom. It makes ontology simpler and more
comprehensible. I mean, really, is there any reason
for you not to just accept it, especially when its
denial leads to paradoxes? I argue that it is better
to accept it than to assume a dogmatic attitude that
no foundational axioms for ontology should be accepted. (08)
Avril (09)
Lainaus "John F. Sowa" <sowa@xxxxxxxxxxx>: (010)
> Avril,
>
> There are three points about science:
>
> 1. Nothing is known for absolute certainty.
>
> 2. But there is a great deal that is known to a very
> high degree of approximation.
>
> 3. And for many important domains, it is possible to
> quantify the experimental error.
>
> This provides a solid foundation for action, and it provides
> criteria for ruling out completely erroneous ideas.
>
> JFS>> I'll accept the point that reality is one.
>
> 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.
>
> 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.
>
> 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?
>
> That's more of a slogan than something that would be worth making
> into a course. If you want to print it on Tshirt and give it to
> incoming freshmen, be my guest. But I don't see much point in it.
>
> AS> But mathematics, at least the foundational questions, are not
> > any more secure than philosophical ontology.
>
> 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.
>
> 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.
>
> 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.
>
> John
>
>
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