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.
On 30 Dec 2009, at 11:51, marc.geddes wrote:
> 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.
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