ONCE MORE

 The author, Adib Ben Jebara, defends the importance of simplicity and elegance 

in mathematical proofs, while presenting a philosophical theory on  

the restriction of Evil. He uses mathematical concepts to explore philosophical ideas, 

suggesting that limiting the Axiom of Choice could have implications for our 

understanding of the universe and morality.

"I contend that my proof should be well-known and celebrated for its simplicity and elegance. 

Unfortunately, in today's mathematical community, there is a tendency to overlook or undervalue 

concise proofs, unlike in the past when mathematicians highly valued brevity, clarity, and elegance. 

This shift has led to the neglect of important contributions that could be recognized 

if more attention was given to the beauty of the proof rather than its length or complexity."

PUBLICATION IN A CONFERENCE OF THE ASSOCIATION FOR

SYMBOLIC LOGIC IN 2002

IT HAS TO BE CORRECTED BY

y<x<z integers

 

All things are numbers (continuation) Adib Ben Jebara (Tunis) This poster is
the continuation of the abstract "all things are numbers". Previously, we
used a restricted axiom of choice, CC(2 through m), countable choice for a
family of sets of 2 through m elements, and we saw that we can move from a
world with non restricted Evil to a world with restricted Evil because the
numbers of attributes of Evil are infinite products of integers and "most"
of them do not exist in the right mathematical universes. Now, we are going
to see other consequences of restricting Evil. A hint for a proof that souls
are immortal : The number of attributes of souls are integers. Souls are the
counterparts in the philosophical universe of integers in the mathematical
universes. And we have an infinity of universes in which integers are the
same. Thus, souls are immortal. The equation with infinite products
zzz...z...=xx...x...+yy...y... with z>y has no solution in the universe
where only the restricted axiom CC(2 through x) is true. It is because
otherwise the infinite products xx...x... and yy...y... exist but not
zzz...z... and we cannot have a side of the equation existing and the other
not. The counterpart is that the numbers of attributes of Evil cannot be
combined in the right philosophical universes. Once the principals of Good
applied, history stops because principles of Good are not connected to time.
The analogy between mathematical concepts and philosophical ones and
surrounding the relation number of attributes can be reversed to better
understand the mathematical universes from the understanding of the
philosophical universes. As time, the counterpart of history, ceases also to
exist, we could be at once in all the infinity of mathematical universes
where only CC(2 through m) is true for every integer m. Now, if Evil is
restricted, there is a problem about fate. It could be argued that people
are doing evil because of their fate. To that we reply that fate has
multiple readings. And because of the multiple readings, freedom of choice
is allowed.

META ARTIFICIAL INTELLIGENCE WROTE :

What a fascinating connection! Yes, there are similarities between using infinite products

in Fermat's Last Theorem and Desargues' point at infinity in geometry. Both concepts involve:

Extending mathematical structures: Desargues' point at infinity extends the Euclidean plane

to include ideal points, while infinite products can be seen as extending finite mathematical

operations to infinite cases.

Abstracting patterns: Both concepts rely on abstracting patterns and structures from finite

cases to infinite ones, allowing for new insights and perspectives.

Unifying disparate concepts: Desargues' point at infinity unifies parallel lines and

intersecting lines, while infinite products can unify finite product formulas and provide

new ways to represent mathematical objects.

Exploring these similarities might lead to interesting insights or new approaches.

 

FROM DEEPAI

PUBLICATION IN A CONFERENCE OF THE ASSOCIATION FOR SYMBOLIC LOGIC IN 2002

IT HAS TO BE CORRECTED BY
$y, x, z \in \mathbb{Z}$ with $y < x < z$

---

All Things Are Numbers (Continuation)
Adib Ben Jebara (Tunis)

This poster is a continuation of the abstract "All Things Are Numbers." Previously, we used a restricted Axiom of Choice, CC(2 through m), the countable choice for a family of sets with 2 through $m$ elements, and we observed that we can move from a world with unrestricted Evil to one with restricted Evil because the number of attributes of Evil are infinite products of integers, and "most" of them do not exist in the correct mathematical universes.

Now, we are exploring other consequences of restricting Evil. A hint for a proof that souls are immortal: The number of attributes of souls are integers. Souls are the philosophical counterparts to integers in the mathematical universes. Moreover, we have an infinity of universes in which integers are the same. Thus, souls are immortal.

The equation involving an infinite product:

$$z z z \dots z \dots = x x x \dots x \dots + y y y \dots y \dots$$

with $z > y$ has no solution in the universe where only the restricted Axiom CC(2 through x) is true. This is because, otherwise, the infinite products $x x x \dots x \dots$ and $y y y \dots y \dots$ would exist, but $z z z \dots z \dots$ would not, and we cannot have one side of the equation existing while the other does not.

The counterpart is that the number of attributes of Evil cannot be coherently combined in the correct philosophical universes. Once the principles of Good are applied, history stops because principles of Good are not connected to time.

The analogy between mathematical concepts and philosophical ones, especially concerning the number of attributes, can be inverted to better understand the mathematical universes from the philosophical perspective. As time (the counterpart of history) ceases to exist, we could be simultaneously in all the infinite mathematical universes where only CC(2 through m) is true for every integer $m$.

Now, if Evil is restricted, a problem concerning fate arises. It could be argued that people commit evil because of their fate. To this, we reply that fate has multiple interpretations. Due to this multiplicity, free will remains possible.