[Inquiry] Re: Utter Indetermination -- Discussion

[Jon Awbrey]

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UI.  Discussion Note 6

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JA = Jon Awbrey
KM = Kirsti Määttänen

Re: UI-DIS 5.  http://stderr.org/pipermail/inquiry/2005-October/003116.html
In: UI-DIS.    http://stderr.org/pipermail/inquiry/2005-October/thread.html#3092

Kirsti, Peirce List,

I just now (Tuesday morning) got your message from Sunday night,
so there might be some problem with the Peirce List deliveries.

JA: You seem to have assumed that determination falls under the category
    of secondness, that is, the category of 2-adic relations.  Perhaps
    this arises from taking determination only in its causal sense --
    I can but guess about that -- but I see no justification in
    Peirce's writing for limiting his sense of determination
    to a purely 2-adic cause-effect relationship

KM: No, I was not taking determination in its causal sense.  I was
    considering how generality, vagueness, and determination are
    related in terms of Firstness, Secondness and Thirdness,
    taking Thirdness as Mediation (in a triad).  -- Which
    was prompted by your claim:

JA: Peirce is sometimes precise in his technical distinction between
    general and vague, and sometimes not -- as a general rule I think
    that we can regard "indeterminate" as the most general concept of
    the three, regarding "general" as "to be determined in extension"
    and "vague" as "to be determined in comprehension".

KM: So, I too do not see any justification for
    limiting determination to purely 2-adic
    cause-effect relationships.

Okay, that's a start.  I should say that I did not see any reason for
lining up vagueness, determination, generality with the categories in
the way that you did here:

KM: To my mind the adequate way to approach the three concepts
    is take the categories as a methodical starting point, and
    ask:  Do these three form a triad?  If so, how?

KM: To me the answer seems clear:

    Vagueness -- Firstness,

    Determination -- Secondness, and

    Generality -- Thirdness.

KM: So the relation of vagueness and determination is (or becomes) mediated
    by generality.  It is only within the triad involved in the second aspect,
    that of determination, that your distinction "extensively undetermined",
    "intensively undetermined" seems to me to apply as you claim. -- The general
    methodic rule being:  every angle of a triad involves a triad -- which then
    involves a triad and so forth.  And what is involved may be evolved, some time.
    What needs to be evolved depends on the questions posed.

Generally speaking, I do not see the use of the categories to be a method
for finding a unique one-to-one correspondence between every set of three
things that Peirce happens to mention, and the philosophical project that
tries to do just that is not implied by Peirce's method, so I do not take
it as automatic or given that there always has to be such correspondences.
Life is just not that simple.

As a general rule, one of the places where people commonly go astray
on these issues is in thinking that 3-adicities depend on 3-tomies.
This is not the case.  We can see this from considering the fact
that perfectly good 3-adic relations exist among three domains
that are all the same, in extension, L c X x X x X.  Indeed,
it is very possible to have sign relations of this form,
rendering it nonsensical to treat object, sign, interp
as a 3-tomy rather than as roles in a 3-adic relation.

I supplied links to a few texts from Peirce on the topic of
determination, with especial focus on its relationship to
generality and vagueness.  The linkage arises from the
relationship of general/individual to extension, and
the relationship of vague/definite to comprehension:

DET.  Determination
DET.  http://stderr.org/pipermail/inquiry/2004-December/thread.html#2197

ICE.  Information = Comprehension x Extension
ICE.  http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913
ICE.  http://forum.wolframscience.com/showthread.php?threadid=609
ICE.  http://forum.wolframscience.com/printthread.php?threadid=609

Many of the ideas that we find in the "New Elements" can
be seen evolving in a much earlier series of manuscripts
that Peirce wrote on the subject of "Time And Thought".
I collected most of these here:

JITL.  Just In Time Logic
JITL.  http://stderr.org/pipermail/inquiry/2003-August/thread.html#712
JITL.  http://stderr.org/pipermail/inquiry/2005-April/thread.html#2542

The place where Peirce first mentions these subjects
in the "New Elements" paper is I believe about here:

KS-Sep.  http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063
KS 1.    http://stderr.org/pipermail/inquiry/2005-September/003063.html
KS 2.    http://stderr.org/pipermail/inquiry/2005-September/003065.html
KS-Oct.  http://stderr.org/pipermail/inquiry/2005-October/thread.html#3075
KS 3.    http://stderr.org/pipermail/inquiry/2005-October/003075.html
KS 4.    http://stderr.org/pipermail/inquiry/2005-October/003090.html

He proceeds from here to recapitulate, in fairly short order
considering the span of years, but in a somewhat winding way
considering the length of the preface before us, most of the
major points of his earliest treatments of these same topics.

I have the impression that actually reading a few of these texts --
I am a slow enough typist that I already did so as I typed them --
might afford a more fruitful basis for further discussion than
any host of a priori categorics.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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