Gary R., list,
I got careless in my previous message.
I said that "There is /F/, ergo anything is /F/" ("∃/F/∴∀/F/") would be
abductive; however, in a stipulatedly non-empty universe, its conclusion
entails its premiss, and so for my part I would rather call it inductive
than abductive, at least in the "usual" universes. A better candidate
for a toy example of an abduction to a rule would be "There is /FG/,
ergo anything /F/ is /G/" ("∃/FG/∴∀(/F/→/G/)"). These are silly
examples, but I like the idea of being able to sort out even the
simplest inference schemata into deductive, inductive, and abductive, in
terms of entailment relations between the premiss set and the
conclusion. In the second example, "∀(/F/→/G/)" is arguably a selective
generalization of "∃/FG/".
Also in considering the beans example, I forgot that it's just one way
of instancing Barbara and its inversions. After all, Barbara is named
for its vowels as a mnemonic for the universality and affirmativity of
its propositions - AAA. So, in a universe in which mammals are not
_/defined/_ as warm-blooded air-breathing live-young-bearers:
/Result:/ All whales are warm-blooded, breathe air, and bear live young.
/Rule:/ All mammals are warm-blooded, breathe air, and bear live young.
Ergo /Case:/ (Plausibly) all whales are mammals.
The "case" there is itself a new rule. I'm not sure whether that's an
example of what Peirce means by abductive generalization, but there it is.
Best, Ben
On 4/28/2016 3:10 PM, Benjamin Udell wrote:
Hi, Gary,
I agree with most of what you say, only I don't see hypothesization of
a rule in the beans example. On the other hand, Peirce is explicit
about hypothesizing a new general (or rule) in the 1903 quote.
[....] 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
the suggested hypothesis [....]
(From "Syllabus", 1903, EP 2:287
http://www.commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-some
)
Moreover, Peirce in a draft circa 1896 (CP 1.74) said "Kepler shows
his keen logical sense in detailing the whole process by which he
finally arrived at the true orbit. This is the greatest piece of
Retroductive reasoning ever performed." Clearly, Kepler was looking
for a rule, not merely for a special circumstance, to explain an orbit.
The problem, which has been nagging at me for a while (and I have read
too little of the secondary literature), is how to distinguish, in a
reasonably simple way, such abductive inference from induction?
Now, by "generalization" Peirce usually meant what many would call
_/selective/_ generalization. That's his hint to us there.
I've tried to think in terms of the hypothesizing of a hidden special
circumstance, e.g., a hidden mechanism, that would have to happen by a
new rule in order to make sense at all. But, how much of this hidden
special circumstance does one really need to conceive of, in order to
conceive of a new rule? I've also wondered whether it's a matter of
considering rules as special circumstances at some level of
abstraction, likewise as one may consider integers as singulars at
some level of abstraction, in an abstract universe of discourse.
But complications make me distrustful in questions of elementary
distinctions among inference modes. Remembering Peirce's idea of
selective generalization as a hint, it occurs to me that maybe it's a
matter of a need to select among the characteristics to extend. That's
where some guessing comes in. That is, Kepler's math may represent a
character of the appearance of orbits, but the orbits actually
observed at that time might be accounted for in other ways, and
Kepler's math might conceivably have worked just by accident up till
then. Well, in Kepler's case, his ultimate solutions could hardly
plausibly have worked just by coincidence, but there are plenty of
cases where a mathematical model fits the past by accident and turns
out to lack predictive value.
So, in the schema for abductive inference to a rule, maybe there
should be a premissual admission of characters that seemed salient,
not all of which are extended by inference to the whole. That very
selection may amount to an idea new to the case. Moreover, some of the
characters may be formulated (e.g., mathematically) in a new way, the
idea new to the case. Still, doubts nag at me. These may be patterns
of abductive inference, but my sense is that one needs to be able to
distinguish abductive inference (to a rule) from induction even in
ridiculously crude cases.
The idea of induction is that of inference from a part or fragment of
a system to the whole. Yet it is possible to state any inference to a
rule without any reference to a positively granted larger whole. If I
conclude that, for any /F/, /F/ is /G/ , then I have not asserted or
entailed in the conclusion the existence of a whole or even of a part
of the population of /F/ 's. Induction and testing, however, do need a
positively granted larger whole to test. When one abduces to a rule,
it may simply be that one "attenuates" one's focus to the rule itself,
the rule as embodying a kind of real necessity, and _/that/_ rule,
taken as itself real, indefinitely projectable across a population not
yet contemplated, etc., is what is new to the case. So, the
implausibly crude ampliative inference "There is /F/, ergo anything is
/F/" ("∃/F/∴∀/F/") would be abductive, not inductive (in a
stipulatedly one-object universe, it would be a reversible deduction).
Well, I've been pottering around with these ideas for a while and I
haven't gotten much farther.
Best, Ben
On 4/27/2016 12:42 PM, Gary Richmond wrote:
Ben, list,
You gave Peircean examples whereas the rule (or law) is /already
known/ either before or after the surprising fact. This seems all
well and good to me for certain types of abductions, say, those
involved in sleuthing, Sherlock Holmes style.
But what of those inquiries in which the rule (law) is /not/ known,
/but is exactly the hypothesis/ of the inquirer? This is to say that
scientists sometimes come to uncover laws hitherto unkown or
unrecognized (such as those hypothesized by Newton, Darwin, Einstein,
Planck, etc.)
I have sometimes thought that in /that/ context--that is, of someone
hypothesizing a law /not/ previously known--that, modifying the 1878
bean example you gave:
Suppose I enter a room and there find a number of bags,
containing different kinds of beans. On the table there is a
handful of white beans; and, after some searching, I find one of
the bags contains white beans only. I at once infer as a
probability, or a fair guess, that this handful was taken out of
that bag. This sort of inference is called _/making an
hypothesis/ _. It is the inference of a _/case/ _ from a _/rule/
_ and _/result/ _. (CSP)
the situation might look something like this (although I'm not sure
that any bean example will quite do for this purpose.
Suppose I enter a room and find a large number of bags which I
know to contain different kinds of beans. Near one bag I find a
handful of white beans (the surprising fact) and I make the
supposition (the hypothesis) that /that/ particular bag of beans
is all white. I examine the bag of beans (make my experiment) and
find that the bag in question does indeed contain only white
beans (the rule). (GR)
Well, it may turn out that I know beans about abduction, but it does
seem to me that the scientifically most fruitful and significant
hypotheses are those where the law (rule) is /not/ know in advance
and is only supposed by the scientist, again, exactly /as the
hypothesis/ .
Peirce gives an example of that kind of hypothesis, one which is,
shall we say, /fresh/ at the time (the rule or law not being
previously known):
Fossils are found; say, remains like those of fishes, but far in
the interior of the country. To explain the phenomenon we suppose
the sea once washed over the land (CP 2.625).
Now suppose that a historian of the region in which those fish
fossils were found, himself finding documents showing that a large
caravan of traders had brought large quantities of dried fish into
that region, pooh-poohs my /sea washing over the land/ hypothesis,
which I have already imagined (for some good reasons) to have
happened in other parts of the world as well. Thus, as other
investigators find many other places, including deserts, etc.,
containing many fish fossils where there was no possibility of any
fish trade occurring, my hypothesis takes hold and is in time
accepted quite generally by the scientific community.
(Another, not unrelated example, would be that of continental drift.)
It seems to me that Peirce intended to cover both kinds of hypotheses
even in his bean illustrations as he offers examples of both (the
fossil example is preceded by what I referred to above as a sleuthing
type of example). Any help which you or others can offer towards
clarifying this matter--of someone hypothesizing a rule or law not
previously known--would be appreciated.
Best,
Gary R
Gary Richmond
*Gary Richmond
Philosophy and Critical Thinking
Communication Studies
LaGuardia College of the City University of New York
C 745
718 482-5690 <tel:718%20482-5690> *
On Tue, Apr 26, 2016 at 11:49 AM, Benjamin Udell wrote:
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