[Inquiry] Re: Utter Indetermination -- Discussion

[Jon Awbrey]

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UI.  Discussion Note 10

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JA = Jon Awbrey
KM = Kirsti Määttänen

JA: Taking for granted the possibility that Peirce may have used words 
    like "determinate", "general", "vague", along with every other word 
    of the Anglish language, in more than one sense ...

KM: No objection to this.  Still, these concepts form a part in the conceptual
    system Peirce evolved.  My interest lies in understanding and using them as
    conceptual tools in the Peircean tool-box of concepts.  The categories and
    triadicity are then the keys for the tool-box ...

JA: I'll simply call to mind the contexts where
    he used "general" to mean ranging in extension
    and "vague" to mean ranging in comprehension (or
    intension) ...

KM: Well, you may do so if you wish.  But then you deliberately
    take a one-sided and skewed view on them, which I cannot see
    as a good starting point.  It is only after a good-enough grasp
    of them as Peircean concepts that one may do so, if and when one
    claims to proceed along Peircean paths.

I've already pointed you to the basic texts in Peirce's work where he
defines "general" and "vague" this way, and up till now I have always
thought that this is what most readers of Peirce have taken away from
their reading.  And I have pointed you to a collection of texts where
he says what he has in mind under the topic heading of "determination".
Texts along these lines can be multiplied at will.  Plus, they heve the
added benefit of explaining these terms in a way that reveals the sense
of their usual meanings in logic, mathematics, and philosophy generally.
This is important because we are talking about, and Peirce was very much
concerned to talk about, objective matters, and not the fantasies of this
or that individual, himself included.  I don't see what's 1-sided about that.
I know one place where he mentions "determination, generality, vagueness" in
that that order, in the passage that Clark Goble and I think Ben Udell recently
called to our attention, namely here:

| The purely formal conception that the three affections of
| terms, 'determination', 'generality', and 'vagueness', form
| a group dividing a category of what Kant calls "functions of
| judgment" will be passed by as unimportant by those who have
| yet to learn how important a part purely formal conceptions
| may play in philosophy.  Without stopping to discuss this,
| it may be pointed out that the "Quantity" of propositions
| in logic, that is, the distribution of the 'first' subject*,
| is either 'singular' (that is, determinate, which renders
| it substantially negligible in formal logic), or 'universal'
| (that is, general), or 'particular' (as the medieval logicians
| say, that is, vague or 'indefinite')^.  It is a curious fact that
| in the logic of relations it is the first and last quantifiers of
| a proposition that are of chief importance.  To affirm of anything
| that it is a horse is to yield to it 'every' essential character of
| a horse:  to deny of anything that it is a horse is vaguely to refuse
| to it 'some' one or more of those essential characters of the horse.
| There are, however, predicates that are unanalyzable in a given state
| of intelligence and experience.  These are, therefore, determinately
| affirmed or denied.  Thus, this same group of concepts reappears.
| Affirmation and denial are in themselves unaffected by these
| concepts, but it is to be remarked that there are cases in
| which we can have an apparently definite idea of a border
| line between affirmation and negation.  Thus, a point of
| a surface may be in a region of that surface, or out of
| it, or on its boundary.  This gives us an indirect and
| vague conception of an intermediacy between affirmation
| and denial in general, and consequently of an intermediate,
| or nascent state, between determination and indetermination.
| There must be a similar intermediacy between generality and
| vagueness.  Indeed, in an article in the seventh volume of
| 'The Monist'%, there lies just beneath the surface of what
| is explicitly said, the idea of an endless series of
| such 'intermediacies'.  We shall find below some
| application for these reflections.
|
|* Thus returning to the writer's original nomenclature, in despite
|  of 'Monist 7' [CP 3.532] where an obviously defective argument was
|  regarded as sufficient to determine a mere matter of terminology.
|  But the Quality of propositions is there regarded from a point
|  of view which seems extrinsic.  I have not had time, however,
|  to re-explore all the ramifications of this difficult question
|  by the aid of existential graphs, and the statement in the text
|  about the last quantifier may need modification.  [See 4.552 n.]
|
|^ [See CP 2.324.]
|
|% [See 3.527 ff.] ["The Logic of Relatives", 'Monist', 7, pp. 161-217 (1897)]
|
| C.S. Peirce, 'Collected Papers', CP 5.450, 'Essential Peirce', EP 2, 352-353.
|
| C.S. Peirce, "Issues of Pragmaticism", 'The Monist', 15, pp. 481-499 (1905).
| Reprinted, more or less, in these 2 places:  CP 5.438-463 and EP 2, 346-359.

Looking to the indicated section of Peirce's 1897 "Logic of Relatives",
we find him taking up once again the concept of a state of information,
the constraints that are placed on it by necessary reasoning, together
with the relation of the real world to the ideal world, specifically:
"the real world is a part of the ideal world" [Marginal Note, 1908].

Despite the added complexities of this 'fin de siecle' hypertext,
I do not see that it can possibly understood except on the basis
of how Peirce defined "general" and "vague" vis a vis extension
and comprehension, respectively.

Have to take a break here ...

Jon Awbrey

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