Re: SUO: Re: Analogy
Jon,
Slides are extremely abbreviated summaries, which are
open to many interpretations. I frequently reuse the same
slides because they enable me to revise my talk without the
trouble of revising my slides.
>Well, then your slide summary is just a little misleading.
>I took Dedre's course in analogies and mental models back
>in 1985-86. Peirce's notion of mathematical formulas and
>logical graphs is that they are partly iconic, not, say,
>as much as venn diagrams, though, but partly indexical,
>and also partly symbolic. Only the iconic aspect is
>analogical.
I agree.
> The trickiest part of structure-mapping,
>which the rest of us call a "morphism", is the same
>as with GPS -- the way NOT to climb a hill is to
>do it in the syntactic space instead of in the
>space of objective referents. In a similar
>way, syntactic analogies are some of the
>worst kind -- what you want is analogies
>that respect the structure of objects.
Indeed. Your only hope in the value of a morphism is in the
iconicity of the structures that are being mapped. If the
structures don't have any real similarity to the actual
referents, you won't get anything useful out of the morphism.
But if they do, then the mapping can tell you something useful.
John