Hi Marc --
it's interesting to wonder about "what it would be like" to directly
perceive mathematics -- but we also have to acknowledge when we ask
the question, what are the philosophical assumptions we're smuggling
along. For instance, the human brain is not capable of direct
perception of tables, either.
What raises a flag for me in your question is the following apparent
dichotomy:
1) "The human brain is not capable of direct perception of
mathematical entities"
2) "We could imagine some super-intelligence that possessed this
ability . . ."
It seems what you're encouraging us to do is this: think about of
what it's like when we see a table, and then say to ourselves
something like the following sentence: "It would be like that, but
with *math*". But what makes us think we can imagine this situation
coherently? Light from a table excites our photoreceptors in a well-
understood way - how could an equation do that?
I have always thought it strange how McGinn and others eagerly apply
"cognitive closure" to some of the very areas where we have made
recent amazing progress in understanding! In the case of math, what
exactly is it that motivates your intuition that there might be
something more that we're missing? And is it something that would
not apply trivially to any other thing (i.e. - I can look at a rock
on the ground, and say to myself, "There's something else about this
rock that I'm not sensing - but I could imagine a superintelligence
who could perceive what I'm missing." My ability to say this
sentence to myself doesn't demonstrate anything interesting about the
rock.)
Best regards
Pete
On Jan 27, 2006, at 1:08 AM, Marc Geddes wrote:
> 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"
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Received on Sun Jan 29 2006 - 01:07:37 PST