Thanks for the outline, Ben. I agree with it all - and liked the 'extension of
a rule'..
Edwina
----- Original Message -----
From: Benjamin Udell
To: peirce-l@list.iupui.edu
Sent: Monday, April 25, 2016 3:50 PM
Subject: Re: [PEIRCE-L] Is CP 5.189 a syllogism?
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
To: peirce-l@list.iupui.edu
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, <kirst...@saunalahti.fi > 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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