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The work of John Sowa and Arun Majumdar should also be of interest – Analogical Reasoning at http://www.jfsowa.com/pubs/analog.htm
Cheers,
Richard
Thanks, Richard. This paper from 2003 addresses the modes of analogy, explicitly Simile (likeness) and less obviously Metaphor (equivalence, i.e. effect) which duality may be seen as class and type. Reinforces that notion that analogical reasoning is about how we perceive and conceive, not necessarily what’s out there.
Curt,
Have you considered this one:
Conceptual Mathematics: A First Introduction to Categories
By F. William Lawvere, Stephen H. Schanuel
Cheers,
Richard