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

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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).
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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).
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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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