Edwina,
Well, yes, abductive inference, when formed like a categorical syllogism
by juggling Barbara as Peirce did repeatedly through the years, is
deductively invalid.
Peirce did not hold that hypothesis (abductive inference) always
involves creating a new rule.
Many of Peirce's examples of abductive inference involve merely the
extension of a known rule to cover a surprising case. The beans example
is classic, from 1878 in "Deduction, Induction, and Hypothesis".
All the beans from this bag are white.
These beans are white.
∴ these beans are from this bag.
https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=472#v=onepage&q&f=false
Even in later years, Peirce did not hold that all abduction involves
creating a new rule. What it always involves is a new conception, new to
the case.
[....] The mind seeks to bring the facts, as modified by the new
discovery, into order; that is, to form a general conception
embracing them. In some cases, it does this by an act of
_/generalization/ _. In other cases, no new law is suggested, but
only a peculiar state of facts that will "explain" the surprising
phenomenon; and a law already known is recognized as applicable to t
he suggested hypothesis, so that the phenomenon, under that
assumption, would not be surprising, but quite likely, or even would
be a necessary result. This synthesis suggesting a new conception or
hypothesis, is the Abduction. [....]
(From "Syllabus", 1903, EP 2:287
http://www.commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-some
)
A question is, how to distinguish abduction of a new rule from
induction? Note his emphasis on the word "/generalization/ ". Peirce
through the years uses the word "generalization" in special sense; he
means a kind of selective generalization. My guess is that the
generalization that he mentions above is the generalization of a
hypothetical explanation to a whole class of cases on the grounds that
the explanation (e.g. some hidden mechanism) happens to make sense only
if it happens in a whole class of cases. Say, somebody who has never
heard of rainfall guessing from wet grass that it happens whenever water
falls there from the sky.
In any case, since abduction does not always involve a new rule, we are
not forced to treat "all beans from that bag are black" as a
hypothetical new rule. Instead, it can be a case where, in Peirce's
words, "a law already known is recognized as applicable to the suggested
hypothesis". I did mention the middle - beans from that bag - twice,
albeit one of the times I put it between parentheses.
Best, Ben
On 4/25/2016 2:56 PM, Edwina Taborsky wrote:
Ben:
Hmm.
First, I agree with your description of the 5.189 as a 'modus ponens'
and also, the caution about a deductively invalid 'affirmation of the
consequent'.
To repeat 5.189
The surprising fact, C, is observed;
But if A were true, C would be a matter of course,
Hence, there is reason to suspect that A is true'.
1) But - your attempt to turn it into a regular syllogism...I'm not
sure. The point of the hypothesis is to *create* a new rule, a
universal. Your new rule is 'all the beans from that bag are black'.
But you have assumed it as necessary rather than hypothetical. AND..
Your example has the middle term used only once. Has to be used twice.
So- your example doesn't work as a valid syllogism.
2) If I try to use the same terms, in the 5.189 format - it won't work
either:
The surprising fact, black beans, is observed.
But if it's a rule that ALL beans from these bags are black, then,
these beans being black would be a matter of course.
Therefore, there is reason to suspect that it's a rule that all beans
from these bags are black.
Now, if I put this into a syllogistic format:
ALL beans from these bags are black.
Some [surprise!] beans are black
Therefore, some beans are from that bag.
I've got three terms:
beans from these bags
some beans
black
Format: PM/SM/SP
And it's invalid. Fallacies of the undistributed middle and
undistributed major.
Edwina
----- Original Message -----
*From:* Benjamin Udell <mailto:[email protected]>
*To:* [email protected] <mailto:[email protected]>
*Sent:* Monday, April 25, 2016 2:17 PM
*Subject:* Re: [PEIRCE-L] Is CP 5.189 a syllogism?
Jerry R.,
I'd say that CP 5.189 is a "syllogism" in a broad sense admitted
by Peirce, though the broad senses are not usual senses nowadays.
Usually people mean a deductive categorical syllogism, in Barbara
and the rest.
To find the subject, middle, and predicate, one would have to
rephrase 5.189, whose form is akin to modus ponens and the
deductively invalid affirmation of the consequent. One has to put
it at least /somewhat/ into the form of a categorical syllogism;
the categorical syllogism is what has three terms, subject,
middle, and predicate, in its schemata.
So here's 5.189's form half-morphed into the black beans example.
These beans are (oddly) black.
But if these beans were from that bag, then it would be a matter
of course for them to be black (since all the beans from that bag
are black).
Ergo (plausibly), these beans are from that bag.
The subject is these beans.
The middle is beans from that bag.
The predicate is black.
Best, Ben
On 4/25/2016 1:28 PM, Jerry Rhee wrote:
Thanks Ben, Kirsti and list...
So, would you say that CP 5.189 qualifies as syllogism, i.e., is
it "hypothesis" based on what you know of what Peirce said on
Aristotle? Why or why not?
What's the predicate, subject and middle term?
Thanks,
Jerry R
On Mon, Apr 25, 2016 at 12:19 PM, <[email protected]
<mailto:[email protected]> > wrote:
CSP was thoroughly familiar with Aristotle, both his syllogisms
and their context in those times. It may be good to remember
that Aristotle's works, along all others, were translated into
Latin by the time we call the new age.
Translations always involve interpretation. Thus what has passed
on into modern logic & philosophy as 'Aristotelian syllogism' I
find gravely misunderstood. - Basics of Western math had
changed, via Arab influence. The birth of albegra (al-jabr) had
taken place.
Ben is putting the discussion into right tracts in introducing
CSP's entries on the topic.
Kirsti
Benjamin Udell kirjoitti 25.4.2016 19:16:
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