I disagree with your view that Peirce never had a coherent theory of the interpretants’. I find his outlines clear and coherent and are all through his writings- in that it is logical and obvious that the triad includes not merely a single interpretant but several - and these several are basic and functional. That is- the notion of not merely one but three Interpretants is, I feel, basic to the Peircena semiosis....
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Example from page 9 of "Confronting context effects in intelligence analysis" by Keith Devlin. The actual sentences that were spoken are in BOLD. And the context is in italics. Without the context, it's impossible to determine the interpretant of the sentence.
HUSBAND: Dana succeeded in putting a penny in a parking meter today without
being picked up.
This afternoon as I was bringing Dana, our four-year-old son, home from the
nursery school, he succeeded in reaching high enough to put a penny in a parking
meter when we parked in a meter zone, whereas before he has always had to be
picked up to reach that high.
WIFE: Did you take him to the record store?
Since he put a penny in a meter that means that you stopped while he was with
you. I know that you stopped at the record store either on the way to get him or
on the way back. Was it on the way back, so that he was with you or did you stop
there on the way to get him and somewhere else on the way back.
HUSBAND: No, to the shoe repair shop.
No, I stopped at the record store on the way to get him and stopped at the shoe
repair shop on the way home when he was with me.
WIFE: What for?
I know of one reason why you might have stopped at the shoe repair shop. Why did
you in fact?
HUSBAND: I got some new shoe laces for my shoes.
As you will remember I broke a shoe lace on one of my brown Oxfords the other
day so I stopped to get some new laces.
WIFE: Your loafers need new heels badly.
Something else you could have gotten that I was thinking of. You could have taken
in your black loafers which need heels badly. You’d better get them taken care of
pretty soon.
A number of things are obvious about this particular exercise. First, the original
conversation is remarkably everyday and mundane, and concerns an extremely
restricted domain of family activity. Second, the degree of detail given in the subsequent
‘explanations’ or ‘elaborations’ of what each person said seems quite arbitrary.
It is easy to imagine repeating the exercise over again, this time providing still further
explanation. And then it could be repeated a third time. Then a fourth. And so on,
and so on, and so on. Apart from boredom or frustration, there does not seem to be
any obvious stopping point.