About the philosophy of the negation of the axiom of choice

Adib · November 9, 2007

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

Apt F3 Residence Badr Manar 1 Tunis 2092 Tunisia

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