Re: Existence of reals and observation of them

On 15 dec, 20:36, lwal...@xxxxxxxxx wrote:
On Dec 14, 6:40 am, Randy Poe <poespam-t...@xxxxxxxxx> wrote:

On Dec 13, 7:57 pm, "*** T. Winter" <***.Win...@xxxxxx> wrote:
No, I do not think that is what HdB meant. Any mathematician should
acknowledge that there can be alternative methods. However, what HdB
proposes is to throw away set-theory, and going on from there, without
proposing any reasonable alternative on which we can base analysis and
many other fields.
More than that. Han has proposed we discard mathematical
rigor entirely, that to be bound by axioms and logic
is "dogmatic".

What's ironic about this is that in another thread,
one dealing with K-12 mathematics education ("Panel
Sees Algebra As Key to Improvements in Math Options"),
HdB has written:

Robert Israel wrote:
But the most basic benefit of Euclid-style geometry, not just for future
mathematics courses, is that it is an introduction to logic and proof,
something that can be useful in many areas of life.
Right! And that piece of basic education is very much lacking nowadays.
Euclid-style geometry at least gives you an idea what good argumentation
and "proving something" should be like. It could help in e.g. preventing
politicians from doing anything they want, by misleading people with any
"evidence" they like to come up with.

So apparently, HdB supports full mathematical rigor in
geometry, but not in set theory or real analysis.

The rigor, as I've learned it with Euclidian Geometry, is far from
"full mathematical rigor". The latter (for geometry) seems to have
been accomplished by David Hilbert, who needed _a lot_ more axioms
that Euclid's famous five, in order to be "rigorous" in the modern
way. My sympathy goes to the more straightforward system by Euclid,
because I haven't seen any decent exposure of Hilbert's "irmproved"
Euclidian geometry in the first place.

Han de Bruijn
.

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