Re: Mathematics: Is it really what you think it is?

From: Stephen Paul King <stephenk1.domain.name.hidden>
Date: Mon, 30 Jan 2006 07:45:51 -0500

Hi Marc,

    I share with you a feeling that there is something missing in the static picture of mathematical truth as painted in Platonism; there is no fundamental sense of where Becoming originates. It has been a perpetual problem for Platonist to explain how to derive our sense of change from a fundamental Changelessness, although Bruno et al are making a good case.
    It seems to me, following ideas like those of Jakko Hintikka with his game theoretic idea in proof theory and Chaitin's Omega, that we might consider that Becoming is fundamental and that the tautologies of mathematical Truths can be considered as "fixed points" within the overall Becoming.

Kindest regards,

Stephen

  ----- Original Message -----
  From: Marc Geddes
  To: everything-list.domain.name.hidden
  Sent: Friday, January 27, 2006 4:08 AM
  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"
Received on Mon Jan 30 2006 - 07:50:23 PST