Re: the need for relevance

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

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.

Is this the working definition, then?

A contradiction in a theory T is a statement P which does not match
with the real world.

Is this what you mean when you say that ZFC has contradictions? If
so, perhaps you can go on to show me how it is that the claim "There
is no uniform probability distribution on N" is a contradiction. In
what way does that not match the real world? What does "match the
real world" mean?

Many thanks. Illuminating as ever.

I've been illuminating this over and over, on my website and in the
'sci.math' newsgroups. If the real world is consistent - and it IS,
because otherwise it would cease to exist - then mathematical stuff,
not giving outcomes that match with the real world, is inconsistent.

I have also explained there what "match with the real world" _means_:
there is a pathway from the Idealizations back to the physical world,
called Materialization, which is the inverse process of Idealization.
It is evident that materialization is not possible with pure fantasies,
giving kind of a watershed between the "good" and the "bad" axioms.

It is demonstrated in "Implementable Set Theory" that all axioms of ZFC
are consistent with the bit mapped implementation, where the axiom of
Infinity seems to be the only exception. If it is claimed that the bit
mapped implementation actually is the meaning of / what SETS ARE, then
Implementable Set Theory offers us a means to _judge_ the axiom system
(not the other way around). That judgement is negative for the axiom of
Infinity, not quite unexpectedly.

I've published more than enough about "uniform probability distribution
on N". In a nutshell: it's trivial for finite serts {0,1,2,3, ... ,n}
that a uniform probability distribution exists. Now replace the finite
set by an unfinished set {0,1,2,3, ... ,n,n+1, .. } and assume no upper
bound for (n) as soon as your calculation is finished. Results are that
e.g. the probability of a natural being divisible by 3 is 1/3 , because
the limit for of the finite set result approaches this value. There is
nothing of a mystery or "undefined" about all this.

Han de Bruijn

.

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