----- Original Message -----
Sent: Friday, January 27, 2006 4:08
Subject: Mathematics: Is it really what
you think it is?
Open question here: What is mathematics? ;)
A series of intuitions I've been having have started to suggest to me
that mathematics may not at all be what we think it is!
The idea of 'cognitive closure' (Colin McGinn) looms large
here. The human brain is not capable of direct perception of
mathematical entities. We cannot 'see' mathematics directly in the same
way we 'see' a table for instance. This of course may not say much
about the nature of mathematics, but more about the limitations of the human
brain. Suppose then, that some variant of platonism is
true and mathematical entities exist 'out there' and there is *in
principle* a modality ( a method of sensory perception like hearing,
sight, taste) for direct perception of mathematics. We could imagine
some super-intelligence that possessed this ability to directly perceive
mathematics. What would this super-intelligence 'see' ?
Perhaps there's something of enormous importance about the nature of
mathematics that every one has over-looked so far, something that would be
obvious to the super-intelligence with the mathematical modality? Are we
all over-looking some incredible truths here? Again, McGinn's idea of
cognitive closure is that the human brain may be 'cognitively closed' with
respect to some truths because the physical equipment is not up to the job -
like the way a dog cannot learn Chinese for instance.
For one thing: Are platonic mathematical entities really static and
timeless like platonist philosophers say? What if platonic mathematical
entities can 'change state' somehow ? What if they're dynamic? And
what if the *movement* of platonic mathematics entities *are* Qualia
(conscious experiences). Are there any mathematical truths which may be
time indexed (time dependent)? Or are all mathematical
truths really fixed?
The Platonists says that mathematics under-pins reality, but what is the
*relationship* between mathematical, mental (teleological) and physical
properties? How do mental (teleological/volitional) and physical
properties *emerge* from mathematics? That's what every one is
missing and what has not been explained.
So... think on my questions. Is there something HUGE we all
missing as regards the nature of mathematics? Is mathematics really what
you think it is? ;)
"Till shade is gone, till
water is gone, into the shadow with teeth bared, screaming defiance with the
last breath, to spit in Sightblinder's eye on the last day"