About set theory with urelements and elementary particles
Platonists seek a reality in mathematics, associated with the
truth of axioms.
Logicists and formalists are concerned about consistency and
independence of axioms but not really about their truth.
I suggest, as a Platonist, that the axioms definitely true
are those applied to previously unsolved mathematical problems
or to physics or social sciences or ethics.
For the case of the axiom of choice, I state that the negation
of the axiom of choice is true because I apply it to quantum
mechanics and cosmology which are part of physics.
It is because of the lack of interdisciplinary research that
the status of the axiom of choice remains ambiguous.
People do not think unity of knowledge a good thing.
Let U be the set of Urelements (non sets) applied to locations,
i in U1xU2xU3x....Uix....does not have to be a count of time. We
consider simply sequences of locations.
Let S be a finite well ordered subset of U, we can define
a distance by counting the number of urelements between two
urelements +1.
This applies for space and time as well.
Mr Andreas Blass pointed out the lack of useful coordinates and
that there is no vector space because it would be non denumerable.
About the Sochor-Jech embedding theorem, Mr Andeas Blass pointed
out that the embedding is complicated, involving sets of sets of
ordinals.
As time as U is not well ordered, except in S above, there are
less causality relationships at the level of elementary particles
than at our level because causality is based on time ordered.
Adib Ben Jebara
adib.jebara@topnet.tn
