Jack KRC> At the risk of being pedantic, what is meant by
"mathematical" here?
That question is important for
understanding what Peirce meant in saying that Phaneroscopy depends on
mathematics. 
The simplest and clearest definition:  "Anything
that can be completely specified by a definition stated in any branch of
mathematics."  This definition is consistent with everything Peirce
wrote.  There are many statements by Peirce that say something very
similar to this, and nobody has found any statement by Peirce that is
inconsistent with it.
John
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