Re: Categorical Aspects of Abduction, Deduction, Induction

Peircers,

Gary brings us evidence that Peirce continued to find favor with his "original opinion"
about the "connections" of the three categories with the principal types of signs and
the principal types of inference, even when all the second guessing and third guessing
had settled down, and yet leaves the question undecided in his own mind at that time.

Working from the understanding that all semiotic phenomena are irreducibly triadic,
taking "irreducibile" in the strictest sense of the word, specific reasons must be
given for assigning any number less than 3 to the arity of any aspect or component
of a semiotic species, for example, a type of sign relation or a type of inference,
in effect, exhibiting an approximate reduction in some looser sense of "reduction".

There are plenty of examples in Peirce's early work where he demonstrates the form
of reasoning that he uses to make these categorical associations and connections,
and I had intended to go hunt a few of these up, but the niche of the web where
I last copied them out is down right now, so I will have to try again later.

Regards,

Jon

CL = Cathy Legg
GR = Gary Richmond

CL: I don't see how one might interpret induction as secondness though.
     Though a *misplaced* induction may well lead to the secondness of
     surprise due to error.

GR: And yet that's exactly how Peirce saw it for most of his career
     (with the brief lapse mentioned in my earlier  post and commented
     on by him in the 1903 Harvard Lectures on Pragmatism). There he wrote:

CSP: Abduction, or the suggestion of an explanatory theory, is inference through an Icon,
      and is thus connected with Firstness;  Induction, or trying how things will act, is
      inference through an Index, and is thus connected with Secondness;  Deduction, or
      recognition of the relations of general ideas, is inference through a Symbol, and
      is thus connected with Thirdness. ... [My] connection of Abduction with Firstness,
      Induction with Secondness, and Deduction with Thirdness was confirmed by my finding
      no essential subdivisions of Abduction; that Induction split, at once, into the
      Sampling of Collections, and the Sampling of Qualities.

      CSP, ''Pragmatism as a Principle and Method of Right Thinking :
      The 1903 Harvard Lectures on Pragmatism'', Turrisi (ed.), 276-277.

GR: Shortly after this he comments on his brief period of "confusion" in the matter.

CSP: [In] the book called ''Studies in Logic by Members of the Johns Hopkins University'',
      while I stated the rationale of induction pretty well, I confused Abduction with
      the Second kind of Induction, that is the induction of qualities.  Subsequently,
      writing in the seventh volume of the Monist, sensible of the error of that book
      but not quite understanding in what it consisted I stated the rationale of Induction
      in a manner more suitable to Abduction, and still later in lectures here in Cambridge
      I represented Induction to be connected with the third category and Deduction with the
      Second" [op. cit., 277].

GR: [You can also read the entire deleted section by googling
     "At the time I first published this division of inference"
     and 'Peirce'.]

GR: So, as he sees here, for those few years Peirce was "confused" about
     these categorial associations. In that sense Peirce is certainly at least
     partially at fault in creating a confusion in the minds of many a thinker
     about the categorial associations of the three inference patterns.  Still,
     he continues in that section by stating:

GR: "At present [that is, in 1903] I am somewhat disposed to revert to my
     original opinion" yet adds that he "will leave the question undecided."
     Still, after 1903 he never associates deduction with anything but thirdness,
     nor induction with anything but 2ns.

GR: I myself have never been able to think of deduction as anything but thirdness,
     nor induction as anything but 2ns, and I think that I mainly have stuck to that
     way of thinking because when, in methodeutic, Peirce employs the three categories
     together in consideration of a "complete inquiry" — as he does, for example, very
     late in life in *The Neglected Argument for the Reality of God* in the section the
     CP editors titled "The Three Stages of Inquiry" [CP 6.468–6.473; also, EP 2:440–442] —
     he *explicitly* associates abduction (here, 'retroduction' of the hypothesis) with 1ns,
     deduction (of the retroduction's implications for the purposes of devising tests of it)
     with 3ns, and induction (as the inductive testing once devised) with 2ns.

GR: But again, as these particular categorial associations apparently proved confusing
     even for Peirce, constituting one of the very few tricategorial matters in which
     he changed his mind (and, then, back again!), I too will at least try to leave
     the question undecided (for now).

-- 

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