[FOM] The irrelevance of Friedman's polemics and results

H Z hzenilc at gmail.com
Thu Jan 26 20:51:41 EST 2006

On 1/27/06, Eray Ozkural <examachine at gmail.com> wrote:
> Has there been any attempt to
> objectively distinguish natural statements from unnatural
> statements, without appeal to authority?

For example, I have heard that, from the independence of the continuum
hypothesis from ZF, it is "more natural" to add some weaker axioms to
proof that the continuum has aleph_2 cardinality and in fact that
there is a technical definition about what does "more natural" mean in
such framework (and maybe in other mathematical branches). Even when
it seems (at least for me) to be "more natural" to consider the
continuum as aleph_1 simply because I cannot imagine a set with
cardinality between rational and irrational numbers (even when I heard
an explanation about how does that set could be seen as a set of
functions between those sets). I think my "more natural" view is
basically based on what did I learn as mathematician in the school.
Can someone maybe elaborate on this? Is there such technical
definition about being "more natural"?

On the other hand I have the impression that more and more mathematics
are made to fulfill referees requirements that at the same time are
also the authors of the papers that other referees of the same group
review. Does this endogamic way of doing math in recent times can make
us arrive to a point in which science is something more like a sect in
which only people adopting the standard profile can survive? Even
worst, most papers are just read by one person: its referee. Is this
the kind of science we like to do? Is there another way?

Hector Zenil
Master Research Student
Paris 1 University (Pantheon-Sorbonne)

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