FOM: Evolution; Wittgenstein

[Olivier Souan]

About evolution, it should be useful to the role of the DNA in
evolution. You just need only 4 bases to code the entire genotype. Those
bases have not changed since the world is world. They will remain 4
forever. With those 4 bases, you can code the entire world of life. It
should be interesting to compare the DNA to a language or a logic. A
creative one indeed, but which follows precise laws.

It can be showed that the laws of evolution follow the laws of logic.
Let me give you an example : the laws of heredity.
Let p and q two genes. They can be valued as 0 - recessive gene or 1
-dominant gene. When 0 and 1 are confronted, 1 supersedes 0. It looks
much like a truth table for disjonction:
 p     v     q      gene 1,      gene 2   their combination
 0     0     0      recessive    recessive    recessive
 1     1     0      dominant     recessive    dominant
 0      1    1      recessive    dominant    dominant
 1      1    1      dominant     dominant    dominant

Since the formal laws of logic (or at least, boolean algebra) schematize
laws of heredity, they cannot be changed by heredity. In the same
spirit, a platonist biologist (d'Arcy Thompson?) could show that the
laws of evolution obey some laws of logic and mathematics; hence those
cannot be changed by evolution. Evolution always happen in an
preestablished frame of logical laws, much like movement in physics does
not happen haphazardly but is circumscribed by symmetry groups. To have
movement, evolution, you need an ontological and mathematical horizon in
which this movement is taking place. We are not in Wonderland, and
anything cannot give anything.
Whatever our brains may look like after 1,000,000 yrs of evolution, they
will be able to understand the necessity of the basic logical and
mathematical laws, because those brains would have been shaped after
those laws. If we are the products of nature, I can't see why we should
obey different laws.

***

I would also like to make an announcement for people living in France :

Wittgenstein et les fondements des mathématiques
Wittgenstein and the foundations of mathematics
Jeudi 30 avril 1998 / Thursday, April the 30th, 1998
9h30-18h30
Salle Dussane, Ecole Normale Supérieure, 45 rue d'Ulm - 75005 Paris

9h30 - Elisabeth Rigal (CNRS): Introduction

10h - François Schmitz (Univ. Nantes) : Normativité des propositions
mathématiques, inconcevabilité de leur négation, irréfutabilité par
l'expérience : De vieiles remarques pour une nouvelle manière de voir
les mathématiques?

11h15 - Pasquale Frascolla (ENS Pisa) : Wittgensein on Mathematical
Proof

14h - Mathieu Marion (Univ. Ottawa) : Pertinence et actualité de la
philosophie des mathématiques de Wittgenstein

15h15 - Juliet Floyd (Boston University) : Wittgenstein and Gödel on
Mathematics

16h30 - Discussion introducted by M. Bitbol, G. Longo, J. Petitot, E.
Rigal

Organisateurs : G. Longo (CNRS, DMI), E.Rigal (CNRS)
Send your questions to longo at dmi.ens.fr

Olivier
Souan                                                                                            
Student of Philosophy, and
Logic                                                       
Université Paris IV et Paris I
Sorbonne                                            
Tél: [011 33 from the US/ 010 33 from the UK] +                     
           [0*]1.46.33.92.34   (*0 to be added if calling from France)
Areas of interest : Phenomenology, Greek philosophy,
Logic and Set theory, Mathematics and its foundations