Re: the need for relevance

Tonico wrote:

For Mr. HdB, the (mathematical, to be sure) fact that there exists a
bijection between the set of natural numbers and the set of even
natural numbers, and thus BY DEFINITION both the set of natural
numbers and the set of even natural numbers have the same cardinality,
is a contradiction.

Why? Because HE KNOWS there are half as many even natural numbers as
there are natural numbers! How does he know that? Who cares! He's said
that anyone knows that, and thus it is so. Period.

No and No. He's said that the actual infinite set of THE naturals does
not exist and that an infinite set of naturals can _only_ be conceived
as a _limiting_ case of a _finite_ set {0,1,2,3,4,5,6,7,8, ... ,n}.
Don't stop the reasoning about this finite set until you're done. Only
at the very end you say: let n become infinite: n -> oo . This is very
standard practice in common calculus. IMO it's the only way to approach
infinity, without running the risk of becoming metaphysical. Moreover,
this whole idea is far more comprehensible than all of your _nonsense_
about bijections between a set and a proper subset of itself. What you
actually do is not even _this_. You make _two_ sets, one with naturals
and one with evens, and you say there's a bijection between them. Duh!

Well, and what does this have to do with contradictions? The hell
knows, but HdB, from his non-mathematical point of view (one can't
blame him on this: he is not a mathematician, after all), has decided
the above bijection is one. Period.

Well, and even assuming all that: then what?! Nothing, but HdB thinks
that since mathematicians get money to do their maths, then they MUST
produce results that he and his friends can apply in what he has
decided is "the real world". Why does he thinks so? I don't know, but
this is one of the main points he has to attack, some times pretty
viciously, though usually pretty ridiculously and even in a very funny
way, mathematics and mathematicians.

So after all it is not, at all, about contradictions as we know them
from logics, with HdB, but about stuff that he can't really understand
and thus he calls it "a contradiction". Don't confuse!

There is one and only one real world. And we _both_ live in it. Whether
you like it or deny it or not. Anything that doesn't match with the real
world is contradictory to it. And if your logic does just that, then it
is much of _your_ problem, not mine. I don't claim that I understand the
real world. I only want to confess that it's, objectively, out there.
The following definition is my favorite one.

"Reality is that which, when you stop believing in it, doesn't go away".
(Philip K. ***)

Han de Bruijn

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