[From Bill Powers (2003.04.27.2113 MDT)]
It occurred to me that the view of analogies as relationships unnecessarily
confines us to one level of perception. I think we get analogies any time a
single higher-order perception can be perceived in significantly different
sets of lower-order perceptions. We say that two sets of lower perceptions
are analogous if we get from them the same higher-order perception.
Thus we cn have a scream which pierces the ears in a way analogous to the
piercing thrust of an epee. There can be a logical arrangement of tools on
a pegboard, analogous to the logic of their use. A person can follow a diet
"religiously," meaning in a way analogous to the way a devotee follows the
precepts of his sect.
This would imply that two statements that are paraphrases of each other are
also analogous in terms of their common meaning.