Philosophy and the axiom of choice
"All things are numbers" pythagoricians,
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 exist).
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 beleive 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 partitionment of disciplines.
I thank Mr Andreas Blass, of the university of
Michigan, who provided some mathematical background.
Adib BEN JEBARA ajebara@excite.com
A hint for a proof that souls are immortal
All things are numbers
Integers are for souls
Souls are the counterpart in the physical world
of integers in the mathematical universe
And we have an infinity of universes in
which inntegers are the same
Thus, souls are immortal
Please, send some comments...
click for the philosophical text which was published :
http://www.logic.at/lc2001/files/ben_jebara.adib.txt
Thanks.
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