Jeff, 

JBD> when the cars make contact, does the triadic
relation exist? In saying
that the triadic relation is degenerate, do you take that to imply it is
 reducible
 in all cases?

The essential aspect of Thirdness is a
mediating intention (goal or purpose) by some mind or quasi-mind. 
Peirce's most characteristic example is 'giving', which requires an
intention by the giver A to transfer ownership of some gift B to some
recipient C.

If A happens to put B on a table and C takes
it.  The transfer is completed, but there is no evidence of a mediating
intention.  You could represent that transfer by a triadic relation.  But
that triad is degenerate because it is equivalent to a conjunction of
dyads.

If you apply that principle to the collision of three
cars, we must ask whether there was any mind or quasi-mind that had some
intention, plan, or goal to cause that collision.   If so, any adequate
representation of the situation must contain at least one triadic
relation.  If not, it could be represented by a conjunction of
dyads.

John
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