Jon A., list,
When criticizing a long post or a series of posts, it's good to quote
the words, or at least typical instances of the words, with which one
disagrees or which at any rate occasioned one's criticism. That is what
I had in mind in saying that your criticism was "precise in itself yet
too vague in application."
Now, it's occurred to me what part of the discussion may have occasioned
your criticism of discussing the categories as if they were
non-relational essences.
At some point, I mentioned that the _/case/_ in which an abductive
inference concludes may be something such as "all whales are mammals"
which in most contexts one would call a rule. I wrote:
Ergo /Case:/ (Plausibly) all whales are mammals.
The "case" there is itself a new rule.
[End quote]
In the course of a reply, you commented:
With ref to your last, one of the reasons that I like that early
example of Peirce's about Wisdom and Charity is that it makes plain
that the designations Case, Fact (Result), Rule are relational roles
not ontological properties of premisses. This is of course analogous
to and probably derivative of the corresponding situation with
Object, Sign, and Interpretant roles.
[End quote
http://permalink.gmane.org/gmane.science.philosophy.peirce/18778 ]
So in your later criticism it would have helped if you had specifically
referred back to it and to another example or two (if any) of the kind
of thing that you were discussing.
It is true that always taking rule, case, result in a strictly
ontological sense will lead to problems. What there seem to be,
nevertheless, are some sort of affinities between the logical roles in
categorical syllogisms and the things that fulfill them, a tendency, in
the practices of inference, for the 'rule' in a syllogism to be a real
rule, etc. The tendency perhaps reflects people's tendency to get
involved in interplays of inference modes, where they reason about
generals, singulars, and qualities. The interplay of inference modes is
_/normal/_ at the methodeutical level, the crowning level of logic, in
Peirce's system. That's my off-the-cuff defense of the idea of
affinities as opposed to a sheer lack of relationship between
syllogistic role and ontological category.
Let me give two examples of where confinement to one of those three
(generals, singulars, qualities) seems to limit invertibility.
1. Confinement to singulars.
/Rule:/ The Morning Star is the Evening Star.
(Make "the Evening Star" seem more like a predicate by replacing it with
"the same as the Evening Star", and so on - a kind of a strategem of
which Peirce avails himself somewhere in another context, as I recall)
/Case:/ The Planet Venus is the Morning Star.
Ergo /Result:/ The Planet Venus is the Evening Star.
Well, one could call any of the two propositions premisses and the
remaining one the conclusion, and the result would still be deductive;
there's no way to invert them into inductions or abductions. So the
invertibilities need that not all three of rule, case, result be
singular propositions.
2. Confinement to mathematicals (very general).
Mathematics deals with extremely general things; insofar as they are
purely hypothetical, they seem like pure possibilities, and are arguably
Firsts; yet the qualities of feeling in pure math are so subdued as to
be barely noticeable (Peirce says that somewhere). Some of math's
generals serve relatively as singulars, such as individual numbers (I'm
thinking vaguely, not referencing set theory, etc.) Mostly we think of
mathematicals as extremely general. Now, it is not clear to me how to
present a mathematical induction as a categorical syllogism, with
subject, middle, and predicate, and still have it arrive clearly at its
thesis as the conclusion. Now, natural numbers are so defined that they
are well-ordered; other than that, they are our "beans" here. Now let us
suppose that a _/ripe number/_ is defined as a natural number with a
certain property R. The thesis to be proved is that every natural number
is a ripe number.
*Heredity:* /Middle:/ Each ripe number is /Predicate:/ succeeded by a
ripe number (this is concluded in a separate proof).
*Base case:* /Subject:/ The first natural number is /Middle:/ a ripe
number (this is concluded in a separate proof).
*Ergo:* /Subject:/ The first natural number is /Predicate:/ succeeded by
a ripe number.
I don't see how to get that form to state the intended thesis which it
nevertheless proves, that every natural number is a ripe number. Maybe
there's some other way to do it, I don't know. At least, when one
inverts it, the resulting inference is non-deductive.
But if, as in the usual mathematical induction, the thesis _/were/_ the
explicit conclusion, and if the two premisses retained their form above
(also usual except for the uses of the terms 'Middle', 'Predicate',
etc.), then all three inversions would be deductive.
Best, Ben
On 5/13/2016 2:12 PM, Jon Awbrey wrote:
Peircers,
As the weekend of this auspicious day looms I find myself
still struggling to maintain a hold on a thread of signal
in a maze of confusion and distraction. My retrospective
of the week, month, decade, and last half century appears
to be doing me good, but it's going to be very slow going.
I'm just now catching up to Ben's last remarks and lately
realized I don't know what he means by my criticism being
“precise in itself yet too vague in application”, so I'll
go back and look at that exchange again. I can't do much
more at this point than add a few items to my list of blog
rewrites for whatever improvement of clarity or refreshment
of memory they might bring.
Regards,
Jon
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
