[FOM] Progress in Philosophy

[Eray Ozkural]

On 3/13/07, laureano luna <laureanoluna at yahoo.es> wrote:
> And now think of the ontological consequences of
> rejecting naive realism. I would say that at least
> some ontological options are ruled out together with
> naive realism.

Some of Godel's defenses of realism seem to save it
from arguing against his mathematical realism via the
(observed failure of ) naive realism case alone. In
particular we may wish to consider the possibility that
physicalism and mathematical realism can be both true. Although
Platonist sort of realism is not a case I would like to defend,
I think that if the world is a universal computer, and if the
brain works in virtue of being a universal computer, then
there is a causal connection among objects that may be
considered "mathematical" in their own right, as computers
are mathematical in the sense of following a rigid mathematical
model (i.e., consider the connection to a formal axiomatic system). [*]

Thus, one may hypothesize that in addition to the complex network
of causality (i.e., small physical interactions), there is a deeper
causation between the abstract facts that delineate the
computational structure of two respective physical
systems. The difference between Platonist and Aristotelean
interpretetations can then be made clearer, and I think Godel has made
it somewhat clear in his philosophical writing, although I think that
his dismissal of the Aristotelian position is not based on argument. He seems
to have acted merely on his personal preferences, and I do not believe
that his "disjunctive argument" is supported at all.

If I am not mistaken, he considered the mathematical objects to
reside in a second order of reality. Again, somewhat compatible
with above descriptions although a typical physicalist position
does not seem to favor such dualism.

Therefore, in addition to rejecting naive realism, we should
do better to work out the cognitive basis of doing any mathematics
*at all* and try to understand the reality of mathematics. Currently,
I think we shall need no other understanding other than a) inductive
inference b) a simple cognitive architecture that explains perception
and planning.

Any requests for clarification welcome. My terse writing may
come off as hard to read.

Best,

[*] Likewise for any mathematical similarity between the physical
foundation of space time, and the medium in which the brain
operates. Obviously, this similarity itself may act as "implicit" a priori
knowledge, as a sort of seed from which mathematical facts emerge.
For instance, all kinds of minds are subject to the halting problem.
No mind can solve it in its whole glamour.

-- 
Eray Ozkural, PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://myspace.com/malfunct
ai-philosophy: http://groups.yahoo.com/group/ai-philosophy