[FOM] The Lucas-Penrose Thesis vs The Turing Thesis

[Eray Ozkural]

On 10/4/06, Steven Ericsson-Zenith <steven at semeiosis.org> wrote:
> The right and remarkable result of modern symbolic systems is that we
> can indeed embody machines with aspects of our intelligence - but
> this does not allow us to infer that such machines experience.  This
> brings us back to the merit of taking experience seriously as a
> phenomenon in the world.

Neither do we know that the machines do not experience anything.

However, even if machines turned out to be complete "zombies"
in the jargon of Chalmers, I suspect that this will not have any bearing
on the subject at hand, namely the capacity of machines to do
mathematics. Although in philosophy, by "consciousness" we understand
something like "subjective experience", it should be noted that functionally
(as neuroscientists/psychologists) we usually focus on cognitive functions
such as self-awareness, reflection, self-reflection, reification, that is, those
functions that are about "knowledge of one's self and actions". Thus, for
instance, a conscious "agent" can represent its beliefs, and then use these
in its reasoning. Such functions seem essential to do mathematics, although
it is not so clear what constitutes "doing mathematics". From a FOM
point of view, it is helpful to recognize what axioms we seem to commit to,
while doing mathematics, which seems like a self-aware activity. One can
also conceive of many other conscious activities. For instance, while learning
to do mathematics, the student tries a number of solution methods, and
re-uses methods that worked before.

We can also imagine a "mind" that completely lacks higher-level reasoning
and learning outlined above, but has an arguably rich sensory experience.
That mind would not seem capable of doing mathematics, so it does not
seem that "experience" in itself helps a mathematician much.

Regards,

-- 
Eray Ozkural, PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
ai-philosophy: http://groups.yahoo.com/group/ai-philosophy