Re: Cantor Confusion

stephen@xxxxxxxxxx schreef:

functions, etc. as all of those things can be modelled with set theory.

The topic of functions has been handled separately on my web page:

http://hdebruijn.soo.dto.tudelft.nl/www/grondig/natural.htm#fd

In a nutshell: the mainstream definition is narrow-minded because the
whole notion of _TIME_ is lacking. Now don't tell me that this is just
a side-effect of your process called "abstraction". I would rather name
it collateral damage, of a narrow minded paradigm known as set theory.

Nobody can prove the Church-Turing thesis, but that does not prevent
people from being confident that our notion of computability is accurate.

It's a good thing that you mention Church. He and others have proposed
quite another paradigm than set theory. I would like to call it LABOUR.
What do you think about the following: anything in mathematics can be
founded on labour ! To say it otherwise: all mathematics is: functions.

Ah, and don't say now that functions are sets. Church et al. have been
working the other way around, with sensible results, such as functional
programming (and languages, like good old LISP).

Nobody can prove anything in science, but that does not prevent people from
placing a lot of confidence in it. For example, there is no proof that gravity acts on
all masses. I am surprised that you do not understand something as basic as that.

Absolute rigour is a phantom, even in mathematics.

Han de Bruijn

.

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