"All things are numbers"/Pythagoreans

This is an attempt to apply the mathematical infinite to philosophical concepts involving the infinite and which we view as a part of philosophical reality such as the universe of Plato 's Dialectic. The idea to write such a text came from reading some philophical texts of Albert Lautman and of Jean Cavailles. "All things are numbers" is not to be taken literally. Let us assume the attributes of God are counted by the alephs. And the attributes of Good are counted by Dedekind cardinals. If we assume the numbers of the attributes of Evil are the infinite products of integers, we can see , from the model, the problem of the existence of Evil.

With the axiom of choice ,all infinite products of integers exist, but without the axiom of choice,some of them do not exist. It is the case with the restricted axiom of choice. The axiom is : CC(n) true from 2 to m, with CC(n),countable choice for families of sets of number of elements n. (It was proved by Mr A. Blass that such an axiom exists). The infinite product of integers exist if it is the same integer n repeated

infinitely , n from 2 and up to m included. We see that Evil is infinite but restricted.

The infinite numbers of Evil are founded not on otherness but on sameness. As the numbers of attributes are themselves important attributes, the Evil itself is somehow founded on sameness. About Good, we see from the numbers of Good that Good is not subordinated to God. About God,we see the link between God and Evil, as their numbers of attributes can sometimes be the same. If God is the set of the laws of nature and the laws of ethics, laws of ethics are elements of both God and Good. We should investigate the consequences of the mathematical universe being not a model but that it can be one

of an infinity of models.

How about the physical universe ? Could there be an infinity of physical universes ? Let us define Good as the set of laws of ethics and of patterns of good behavior. and Evil as the set of offenses to laws of ethics. The axiom of choice would be the counterpart of a rule of blind faith. It is possible to move from a world without Good to a world with Good in the way we move from a mathematical universe where the axiom of choice is true to the universes where only the restricted axiom of choice is true. In the new world, questions of philosophy will be changed, with less linear ordering of concepts. But we could be moving from the risk of fanaticism of those who believe in God to the risk of dogmatism of those who believe in Good.

The world, which is finite, has to be explained by the universe of philosophy, such as the universe of Plato's Dialectic, with some concepts involving the infinite. The understanding of the philosophical universe requests both faith and doubt about the existence of the infinite. We understand better the philosophical reality by understanding the reality of set theory. The knowledge of the mathematical infinite helps us to understand the finite, in mathematics and in the finite world as well. The model shows

that Good and Evil are not symmetrical sides of a reality.

Also, Good is somehow self-sufficient and that is not the case for Evil. As for the Devil, it is only a way to make Evil a character. That God is a set of laws does not mean necessarily that there is no after life. The question remains: what kind of after life could there be ? Such a research was not undertaken, before this, because of the partitioning of disciplines. I thank Mr Andreas Blass, of the university of Michigan, who provided some mathematical background.

Adib Ben Jebara.

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