[FRIAM] Motives - Was Abduction

[lrudolph at meganet.net]

Nick writes, in relevant part:

> I am not sure what monads and monism have to do with each other, other
> than that they share a linguistic root.  Honest.  I have trouble seeing
> the connection.
...
> I don't have much of a grip on MonADism.  As I understand monads, they
> are irreduceable "atoms" of existence.  They have no innards.

The "monads" of category theory did not arise under that name, and they
absolutely have "innards".  Why Saunders MacLane renamed them (as I just
learned by checking Wikipedia) that is probably known to many, but not to
me; as an instance of the "working mathematician" to whom his book
"Categories for the Working Mathematician" was purportedly addressed (J.
Frank Adams has a reference in one of his books to "Categories for the
Idle Mathematician"), I have a long experience of observing category
theorists' whimsy (e.g., Peter Freyd's "kittygory" for a "small category",
Peter Johnstone's "pointless topology", etc., etc.), and I suspect that
MacLane was mostly indulging in that rather than riffing on antique
philosophy.  Certainly the word is short and snappy, and that's sufficient
to explain why it caught on.

To the extent that it can be useful and accurate to describe some bit of
mathematics (or a name for that bit of mathematics) by applying to it the
term "metaphor" borrowed from rhetoric, it will almost always be MORE
useful and MORE accurate (if harder for Nick to deal with) to apply to it
another term borrowed from rhetoric, "conceit". Consulting Wikipedia, I
find that "modern literary criticism", damn its collective eyes, has
redefined that good old word for its own malign ends.  What *I* mean by it
is (I find by consulting the rather pre-modern Princeton Encyclopedia of
Poetry and Poetics) a generalization away from literature of the
"metaphysical conceit" (as contrasted with the "Petrarchian conceit"; and
named for the Metaphysical Poets, not for William James's coterie): "An
intricate [...] metaphor [...] in which the [...] qualities or functions
of the described entity are presented by means of a vehicle which shares
no physical features with the entity" (of course the "physical features"
business is not part of *my* meaning).

That is, a conceit is a metaphor that pays serious attention to the
multi-level *structures* and *functions* involved on both sides of the
trope.  A simple metaphor need have no innards; a conceit can be
jam-packed with them, but not arbitrarily jam-packed.  (The part of the
preceding sentence before the semi-colon is itself a pretty simple
metaphor.  The part after the semi-colon at least tends towards conceit. 
If I started to distinguish different kinds and functions of innards that
bodies can have--bones, muscles, vital and less-vital organs, etc.--and
likewise to distinguish different substructures that metaphors can have,
along with functions that they perform in the service of metaphorical
communication, and THEN set up a correspondence between the bodily innards
and the metaphorical substructures that "respected" their respective
functions...that would be a conceit.  Which I don't intend to work on any
further at the moment.)

The category-theorists among us may think I'm describing morphisms etc.
etc.  If they do, then they're committing metaphor (or thinking that I
am).  If they go further, and try to make sense about rhetorical
activities by applying category theory, then they're committing conceit.

Enough for now.

Lee