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Overcoming Bias Commenter's avatar

Addendum:

I think this makes my idea crystal clear:

Analogies are *mappings* between knowledge domains; and there are varying *degrees* of mapping accuracy - ranging from a totally inaccurate mapping (a totally bad analogy) to a perfect mapping (Bayes, causal modelling).

In the limit that the mapping approaches perfect accuracy, the accuracy of analogical reasoning approaches Bayesian Induction/Causal modelling. This shows that Bayesian reasoning is merely a special case of analogical reasoning.

Eliezer keeps critisizing analogies because the mappings are inaccurate (missing info, mixed with some errors), but this is actually a strength of analogies!

Here's why: Imperfect mappings are what enable us to slide between different knowledge domains (to slide back and forth across concept space). Bayesian reasoning can only be applied to perfectly defined domains; true, Bayes is perfectly accurate, but Bayes cannot let us slide across concept space to explore new ill-defined domains (cross domain reasoning)

In summary there's a trade-off, the perfect accuracy of Bayesian reasoning at one end of the scale, but confined to narrow, precisely defined domains, and at the other end of the scale, the freedom of analogical reasoning to connect different domains (cross domain reasoning), but with some inaccuracy in the mappings.

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Overcoming Bias Commenter's avatar

I'm not sure that the examples you give are really any different from analogies Robin.

I wonder if all valid reasoning is actually analogy formation in disguise. It may just be the case that some analogies are much more sophisticated than others. What EY dismisses as 'surface similarities' is really only a criticism of the limitations of bad analogies, not of analogy formation per se.

Lemma:

(1) All valid reasoning can only proceed by manipulating concepts that are already known to us (i.e. concepts that are already in our mind)

(2) To reason about new domains or extend the applicability of known reasoning methods, new concepts must be derived, or old concepts extended.

(3) From (1), in order to move from old/known concepts to new/extended concepts in an understandable way, (2) must involve a mapping between new/extended concepts and old/known concepts

(4) Any such mapping relies on similarities between old/known concepts and new/extended concepts

(5) Mapping of similarities between things is analogy formation

(6) From (5), all valid reasoning is analogy formation

Types of analogies:

(a) Surface similarities (mostly bad analogies): Looking at structuralsimilarities (similarities in the way things appear)

(b) Functional similarities (better analogies): Looking at similarities in the way things act/are used. (Hypothesis: This is entirely equivalent to causal modeling/Bayesian Induction!)

(c) Semantic similarities (deep analogies): Looks at similarities in the meanings (high-level representations)of concepts (Hypothesis: This is equivalent to ontology creation and merging - interfaces/mapping between ontological categories)

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