SUO: Re: Theory of Inquiry, Types of Inference, Types of Signs
- To: Arisbe <arisbe@stderr.org>, SemioCom <semiocom@listbot.com>, Standardize Unto Others <standard-upper-ontology@ieee.org>
- Subject: SUO: Re: Theory of Inquiry, Types of Inference, Types of Signs
- From: Jon Awbrey <jawbrey@oakland.edu>
- Date: Sun, 20 May 2001 00:08:01 -0400
- CC: Cathy Legg <cathy@coombs.anu.edu.au>, Arien Malec <arien_malec@yahoo.com>, David Low <low@cdi.com.au>, David Whitten <whitten@NETCOM.COM>, John F Sowa <sowa@bestweb.net>, Jean-Marc Orliaguet <jmo@medialab.chalmers.se>
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- Reply-To: Jon Awbrey <jawbrey@oakland.edu>
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Theory of Inquiry, Types of Inference, Types of Signs
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Inquiry SIG,
This continues the series of discussions that arose
in the Peirce Forum last year, as I recall, incited
by some complimentary remarks that Chomsky makes in
connection with discussing hypothesis formation and
Peirce's problem of "giving a rule to abduction".
In this episode, the three-way connection among Peirce's
Three Categories, the Three Types of Inference, and the
Three Types of Signs engaged the attention of the party.
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Note 4
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Subj: Re: Arguments and the Categories
Date: Thu, 11 May 2000 01:30:01 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: Peirce Discussion Forum <peirce-l@lyris.acs.ttu.edu>
Arien Malec wrote:
AM: In being forced, by Jean-Marc's helpful criticism, to defend my
incidental description of abduction as corresponding to iconicity,
I have taken a closer look at what Peirce has to say about the
relationship between the categories in the only place, so far
as I know, in the CP were Peirce discusses the relationship:
the Minute Logic (ripped and scattered throughout the CP,
but the directly relevant sections form the first part
of the second volume of the CP, and especially 2.95-97).
It would be relevant and important to the discussions
relating arguments and the categories to present what
Peirce has to say about them. To the extent possible,
this is a presentation, summarization, and interpretation
of what Peirce himself has to say, rather than an exposition
of my own views on the matter.
David Low wrote:
DL: Another place to look is in MS 312 (1903), published in Ann Turrisi's
'Pragmatism as a Principle and Method of Right Reasoning'. A passage
of special interest is on p.276 where Peirce says:
| And as to the connection between the three categories and the
| three modes of inference ... Abduction, or the suggestion of
| an explanatory theory, is inference though 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.
DL: This, it seems to me, reaffirms his opinion of 1867 (CP 1.559):
| In an argument, the premisses form a representation of the
| conclusion, because they indicate the interpretant of the
| argument, or representation representing it to represent
| its object. The premisses may afford a likeness, index,
| or symbol of the conclusion. In deductive argument, the
| conclusion is represented by the premisses as by a general
| sign under which it is contained. In hypotheses, something
| like the conclusion is proved, that is, the premisses form a
| likeness of the conclusion. Take for example, the following
| argument:
|
| M is, for instance, p1, p2, p3, and p4;
| S is p1, p2, p3, and p4:
| Therefore S is M.
|
| Here the first premiss amounts to this, that 'p1, p2, p3, and p4'
| is a likeness of M, and thus the premisses are or represent a
| likeness of the conclusion. That it is different with induction
| another example will show.
|
| s1, s2, s3, and s4 are taken as samples of the collection M;
| s1, s2, s3, and s4 are P:
| Therefore All M is P.
|
| Hence the first premiss amounts to saying that
| 's1, s2, s3, and s4' is an index of M. Hence
| the premisses are an index of the conclusion.
DL: There is also a passage in MS 315 (1903) that is pertinent:
| I have already explained to you briefly what these three
| modes of inference, Deduction, Induction, and Abduction
| are. I ought to say that when I described induction
| as the experimental testing of a hypothesis, I was
| not thinking of experimentation in the narrow sense
| in which it is confined to cases in which we ourselves
| deliberately create the peculiar conditions under which we
| desire to study a phenomenon. I mean to extend it to every
| case in which, having ascertained by deduction that a theory
| would lead us to anticipate under certain circumstances phenomena
| contrary to what we should expect if the theory were 'not' true,
| we examine the cases of that sort to see how far those predictions
| are borne out. (p. 249).
DL: In this extended sense of induction, Peirce says we can still
be reasoning retroductively (cf. CP 8.231), and thus we would
have the assurance of an icon. If we return to the phenomena
and then find how nearly the consequences agree with the actual
facts, we then move to induction (cf. CP 8.233). So, a part of
the process of arriving at the hypothesis to be tested against
the external is first, precision, then dissociation, then
discrimination (e.g., MS 645). These stages, Peirce says,
take place before phenomenological enquiry, but if we were
to apply the categories to these prephenomenological, or perhaps
I should say 'mathematical' stages, I think precision would have
the assurance of an icon, dissociation the assurance of an index,
and discrimination the assurance of a symbol. Note, however, that
the inductive stage of the prephenomenological investigation is not
tested against the phenomenological world, thus the logic of abduction
cannot interfere with or limit the phenomenological logic of induction.
DL: This thread began with Chomsky I recall, and I suppose from
the little I know about what he said that I would agree that
the number of possible permutations in language are infinite,
but that is true only until we bump the prephenomenological
up against the phenomenological.
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David,
Allow me to diagram some of these forms of arguments, so that everybody can
plainly see some of the reasons why Peirce says a few of the things he does.
Abduction to a Case:
M is, for instance, P^1, P^2, P^3, and P^4;
S is P^1, P^2, P^3, and P^4:
Therefore S is M.
Here the first premiss amounts to this,
that "P^1, P^2, P^3, and P^4" is a likeness of M,
and thus the premisses are or represent a likeness
of the conclusion.
Peirce's analysis of this pattern of abductive argument
can be understood according to the following paraphrase:
Fact: S => P^1, S => P^2, S => P^3, S => P^4.
Rule: M => P^1, M => P^2, M => P^3, M => P^4.
---------------------------------------------------
Case: S => M.
When X => each of A, B, C, D, ...
then X => the Greatest Lower Bound (GLB) of A, B, C, D, ..., which is to say,
then X => the Logical Conjunction, A & B & C & D, to give it a nickneme, "N",
then X => N.
Most succinctly, the argument can be summarized as follows:
Where N = P^1 & P^2 & P^3 & P^4:
Fact: S => N.
Rule: M => N.
----------------
Case: S => M.
In this abduction, it is the GLB or the Conjunction
of the ostensible predicates that is the operative
predicate of the argument, in other words, the one
that is common to both the Fact and the Rule.
Finally, the reason why one can say that N is an iconic sign
of the object M is that N can be taken to denote M by virtue
of the qualities that they share, namely, P^1, P^2, P^3, P^4.
The situation can be diagrammed as follows:
| P^1 P^2 P^3 P^4
| o o o o
| \* \ / */|
| \ * \ / * / |
| \ * \ / * / |
| \ * \ / * / |
| \ *\ /* / |
| o N o |
| | | * | |
| | | * | |
| | | | |
| | | | * |
| | | | * |
| o | o M
| \ | / *
| \ | / *
| \ | / *
| \ | / *
| \|/*
| o
| S
|
| Figure 3. Abduction to the Case S => M
I will put off the example of Induction to a Rule until tommorrow,
as this requires a bit of extra work, mainly by way of digging up
the supplementary texts that are necessary to explain one or two
peculiarities of Peirce's language, as he was wont to use it in
the 1860's.
Until Then,
Jon Awbrey
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