Jerry,

JFS
In his late writings on the logic of pragmatism, he emphasized the
multiple cycles of observations, induction, abduction, deduction,
testing (actions) and repeat.

JLRC> Do you have specific citations?

I wish that Peirce had used the word 'cycle' and had drawn a diagram
similar to the one I frequently use.  See the attached soup1.jpg.

I pieced together passages from many of Peirce's writings about
induction, abduction, and deduction to construct that cycle.
There are many such comments scattered all through his writings.
(His lectures on pragmatism in EP vol. 2 contain many of them.)

Following is a passage (CP 5.171) that mentions all four arrows of the
cycle:  abduction, deduction, testing (action), and induction:
Abduction merely suggests that something may be. Its only justification
is that from its suggestion deduction can draw a prediction which can
be tested by induction, and that, if we are ever to learn anything or
to understand phenomena at all, it must be by abduction that this is
to be brought about.

See Section 7, pp. 26 to 34, of http://jfsowa.com/pubs/signproc.pdf .
Diagram 7 (p. 31) is soup1.jpg.  On page 32, I use that diagram to
explain Peirce's point "truth can be nothing more nor less than the
last result to which the following out of this method would ultimately
carry us." (EP 2.379-380)

That passage implies a cycle.  Peirce's lectures on pragmatism would
have been much clearer if he had drawn such a cycle.

John
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