**From:** Marc Geddes (*m_j_geddes@yahoo.com.au*)

**Date:** Fri Jan 27 2006 - 02:54:29 MST

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Note:

People may wonder why I'm talking about what seems

like metaphysics again. But I'm discussing the nature

of mathematics here and since AI work is basically

pure mathematics, I'd say understanding the nature of

mathematics could be critical to AGI.

From: Marc, who is aiming to quickly 'close out' the

Singularity game in a spectacular blaze of glory.

O.K, let me now start to bring this game to a swift

and shocking end...

Ben Heaton said >>>

*>Just to check: is this related to the idea that, for
*

example, Fermat's Last Theorem was not true until a

proof for it was discovered?

No

*>If your idea is something more meaningful than that,
*

then can you give an example of a mathematical claim

that you think has even a slight metaphysical

possibility of being time-dependent? I'm not asking

for an example of one that definitely is, just one

where it wouldn't be obviously ridiculous to believe

that it might be. All the examples of mathematical

theorems I can think of lack any indexical references

to times, but if you know of something I'm

overlooking, I'd like to learn about it.

Deductive mathematical proofs cannot by definition be

time dependent. So if there are any time indexed

mathematical properties they must be inductive (in the

sense of probability theory).

If one subscribes to mathematical Platonism (the idea

that mathematical entities have objective existence)

then there may be a way to define the 'changes in

state' of these mathematical entities.

If you imagine a Platonically existing proof that no

mathematician has yet discovered, then imagine a proof

which every one knows about, one could say that the

mathematical entities which are the 'theorems'

(proofs) under go 'changes of state' when they change

from existing only in Platonic reality, to existing as

representations in the physical world. The

mathematical entity is not the same thing as a

particular instantiation of that entity in the

physical world. The mathematical entity can exist

purely Platonically, or it can 'project down' into the

physical world and be instantiated in physical matter.

When the entity 'projects into' the physical world,

it can be defined as having 'changed its state'. For

instance, a mathematical theorem which is not known by

any one is in a 'different state' to a mathematical

theorem which also exists in the minds of

mathematicians.

The time indexed mathematical theorems then, are

likely the one's expressing the relationship between

platonic properties, physical properties and mental

(volitional) properties (see the example I gave above

- a mathematical entity can be said to have 'changed

state' when it goes from existing only in the Platonic

realm , to becoming manifest in the physical and

mental realms).

Now these ideas may not help much in identifying

exactly what the time indexed mathematical properties

are, but they do, I hope, show you that platonic

mathematical entities are not necessarily the static,

timeless things many philosophers think they are.

Again, you may all ask, how is all this metaphysics

relevant to AGI work? Well, consciousness appears to

be intimately connected to the integration of

information. See:

http://www.sci-con.org/tiki-read_article.php?articleId=188

The integration of information is in turn intimately

connected to the discovery of mathematical truth. As

I suggested above, if platonic mathematical entities

can undergo 'changes of state' when they go from

existing only platonically to existing in someone's

mind and if the mathematical truths representing this

process are time indexed (or time dependent) then

consciousness itself (and information integration)

would be precisely equivalent to the 'movements' of

platonic mathematical entities or the sub-set of

mathematical truths that were time dependent...

"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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**Next message:**Olie L: "Re: META (Re: KILLTHREAD: Re: physical pain is bad)"**Previous message:**Pilot Pirx: "Re: Chris McKinstry (1967-2006)"**Maybe in reply to:**Marc Geddes: "My definitions of Intelligence, Consciousness, Mathematics and Universal Values"**Next in thread:**Richard Loosemore: "Re: My definitions of Intelligence, Consciousness, Mathematics and Universal Values"**Reply:**Richard Loosemore: "Re: My definitions of Intelligence, Consciousness, Mathematics and Universal Values"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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