About the philosophy of the negation of the axiom of choice
I refer to set theory with urelements ZFU as in "The axiom of choice",
Thomas Jech, North Holland 1973.
Let us assume the negation of the axiom of choice and that
space of particles is U of ZFU.
Let U1xU2X....XUiX...... be the void set with Ui a set of
locations.
We can see the Existence and the Non Existence linked, contradicting
the Existence of Parmenides and the Becoming of Heraclites.
We can see the Infinite and the Void tied up in an unexpected way.
We can see that Non Existence is closer to the Infinite than to the
finite.
We can see that we can apprehend space with mathematics in a way that we
cannot apprehend with direct experimentation.
We can see that space is not so much fundamental data, contradicting Kant.
It is to the philosophy of Plato and of Albert Lautman that we refer.
As the Big Crunch and the Big Bang are explained by the use of the negation of
the axiom of choice upon space, we can see the existence of a cyclical
phenomenon.
In the future, ZFU should be considered the foundations of mathematics.
Historically it was an attempt to show that the negation of the axiom of
choice is consistent with the other axioms.
So, we see how the progress of science induces a change in the status of a
theory.
That physical space is infinite (with a quantity of matter finite) puts us in
the border Between mathematics and physics.
We can see the usefulness of interdisciplinary research.
Giordano Bruno was sentenced to death by fire on 1600 in Italy for saying
that the Universe is infinite.
Nowadays, people still find it hard to think of an infinite physical space.
Adib Ben Jebara
http://www.freewebs.com/adibbenjebara
