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"
Received on Fri Jan 27 2006 - 04:42:24 PST