'Mind Space' metaphor - relation between Symbolic, Bayesian and Analogical inference

[marc.geddes]

I came up with this metaphor which hopefully indicates the
relationship between the three main types of inference (Symbolic,
Bayesian and Analogical).

---

Picture a mind as a space, and 'the laws of mind' are analogous to the
principles of cognitive science.

Now in this 'mind space' picture the 'mind objects' - I suggest these
are logical predicates - symbolic representions of real objects. How
do these 'mind objects' interact? I suggest picturing 'mind forces'
as analogous to the 'strengths of relationships' between the mind
objects (predicates or variables) so 'mind forces' are probability
distributions. But what about the background geometry of mind space?
I suggest picturing 'curvatures' in the geometry of mind space as
analogous to concepts (categories or analogies).

Then Symbolic logic is the laws governing the mind objects (rules for
manipulating predicates). Bayes (Probability Theory) is the laws
govering the mind forces (rules about probability distributions), and
Analogical inference (categorizaton) is the laws governing the
geometry of mind space itself (concept learning and manipulation).

---

If my metaphor is valid, the radical implication is that analogical
inference is the true foundation of logic, and Bayes is merely a
special case of it. Why? Consider that *apparent* Newtonian forces
operating across physical space are actually just special cases of
curvatures in the geometry of space-time itself. What I'm suggesting
is *exactly* analogous to that physical picture. I'm suggesting that
*apparent* probabilistic operations in mind space are actually just
special cases of 'curvatures' in the 'geometry' of mind space
(categorization and analogy formation).

---

The question of course is whether my metaphor is valid. I'm very
confident, but I could be wrong. Comments or thoughts welcome.

[Bruno Marchal]

You may be right. But it is still an open problem to just define
probability (except the probability one) in the mechanist settting.
Rich metaphor, but a promise for a lot of work, to make this precise
enough in the mechanist frame. It would mean that not only we have a
measure (and a linear base of observable/operators) but also a richer
differential structure. Who knows? You may try to be more precise,
even without taking the mechanist constraint into consideration.

With non-mechanism, you may consider Penrose's (very speculative) idea
that mind reduces the wave by being related to gravitation (space-time
curve). Not sure it makes really sense, but then, with non-comp, we
may try ... everything.

It seems obvious to me that Bayes is a particular case of inference.
There are *many* others.

Bruno

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http://iridia.ulb.ac.be/~marchal/

[John Mikes]

Dear Marc,

you emerged from the conventional figment of a 'physical world' view and elevated into the concept of "mind" (what I don't know where, what and how to define...) - anyway, to think in mental terms instead of the conventional physical figments.

 

Then you use the complacent terms of the abandoned physical sciences to include into your better ideas. The 'definitely' human restrictions into the 'non-restricted' totality.

Space, objects, human logics, (in first line: a Bayesian probability as we, humans, imagine how the 'next' will arrive in an unlimited openness) even 'geometry of mind', the forces, - all the human restrictions into the unlimited in which we humans are only a tiny part?

 

I think your ideas are acceptable as a step forward from the conventional (reductionistic) human thinking, but I would see a more distinct 'possibility' of free ways, which - alas - are not yet available, not even the words are there to apply when going into them.

(The worst thing is a reference to 'cognitive science' which established this unknowable domain as fully explained (as of today) in our so far learned (misunderstood?)physical/physiologica/behavioral figments and their conventional explanations.) 

 

Please, excuse my critical (negative?) attitude without proposing a better mousetrap. I developed my 'scientific agnosticism' pertinent to the totality (wholeness) of which we (in our epistemic enrichment) so far got hold of a tiny fraction and feel 'so smart'.  I jumped onto your idea: it is a try in the right direction and I am for every step forward. Please think about it, your startup is commendable.

 

Happy 2010

 

John M

 

[marc.geddes]

On Dec 31 2009, 5:10 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> You may be right. But it is still an open problem to just define  
> probability (except the probability one) in the mechanist settting.
> Rich metaphor, but a promise for a lot of work, to make this precise  
> enough in the mechanist frame. It would mean that not only we have a  
> measure (and a linear base of observable/operators) but also a richer  
> differential structure. Who knows? You may try to be more precise,  
> even without taking the mechanist constraint into consideration.

Yes. I'm looking for an applied logic of uncertainty associated with
sets or categories. Can you name such a logic?

>
> With non-mechanism, you may consider Penrose's (very speculative) idea  
> that mind reduces the wave by being related to gravitation (space-time  
> curve). Not sure it makes really sense, but then, with non-comp, we  
> may try ... everything.
>
> It seems obvious to me that Bayes is a particular case of inference.  
> There are *many* others.
>
> Bruno

I think Penrose is nonsense if taken literally, he's looking at the
wrong level of organization, mind has got nothing to do with
fundamental physics directly I think. But speaking *metaphorically*
it can lead to good ideas. So speaking metaphorically only,
information integration in the mind (categorization) could be said to
be analogous to space-time curvature. And then the probabilities are
analogous to the apparent forces. But I'll stick to comp I think.

[Mike Dougherty]

On Fri, Jan 1, 2010 at 2:13 AM, marc.geddes <marc....@gmail.com> wrote:

I think Penrose is nonsense if taken literally, he's looking at the
wrong level of organization, mind has got nothing to do with
fundamental physics directly I think.  But speaking *metaphorically*
it can lead to good ideas.  So speaking metaphorically only,
information integration in the mind (categorization) could be said to
be analogous to space-time curvature.  And then the probabilities are
analogous to the apparent forces.  But I'll stick to comp I think.

I imagine it much like fishing.  There is a deep sea of ideas on top of which my mind floats.  I cast out a line with a particular hook/bait and troll through the idea space and reel-in those that "fit" the hook.  Sometimes I don't have enough details, so I get back an incomplete result.  Other times I may not have the patience (enough fishing line) to reach deeply enough to find the perfect match.  Some ideas are ideal, some work well enough. 

I'm not sure if that was metaphorically or allegorical or simply an analogy.  :)