Dear Friends:
A couple of days ago I posed some questions about the role and nature of
ancillary generalizations in inference. Professor Verbeek made some
interesting observations about my questions. His comments provoked a
further thought or two on my part, which I thought I would pass on.
In my original message I said, in part, the following:
> One may add more to this picture by supposing that evidence -- ancillary evidence -- may support such generalizations,
> ancillary hypotheses, warrants, or what have you, and that a series of inference may thus look like something like this:
>
> primary evidence -------------->| r ---------------->| s -------------->| t and so on
>
> |________________| |__________| |____________|
> H-1 H-2 H-3
>
> ^ ^ ^
> | | |
> | | |
>
> ancillary evidence #1 ancillary e-2 ancillary e-3
>
Professor Verbeek's comments made me ponder more carefully how a
hypothesis or generalization such as H-1 or H-2 might make an inference
such as "r ------> s" uncertain.
****
Several preliminary observations:
First, "primary evidence ------->| r -----------| s ------------> t" is
a chain of inferences.
Note: Clearly, I do not follow the convention that the
direction of an arc must run from the proposition in issue to
evidence of the proposition in issue.
Second, "r" and "s" are propositions rather than events. Hence, it is
logically possile for r to be the basis for an inference of s
regatrdless of the temporal sequence of r and s.
Third, a common example in the law of the sort of chain inferences I
have in mind here is:
D's escape from the clutches of the law ---> D's belief in
his guilt ---> D's guilt
****
My original questions focused on the nature of ancillary generalizations
in a chain of inferences such as the above.
Professor Verbeek's comments made me think that the the following are
some distinct possibilities explaining why, e.g., s is uncertain given r
(but Professor Verbeek does not deserve any blame for any of my errors
here):
(i) H-1 or H-2 describes a stochastic process.
(ii) H-1 or H-2 is deterministic but the decision maker is uncertain
which of two or more deterministic hypotheses applies.
(iia) H-1 or H-2 is deterministic but the decision maker is
uncertain of the validity of his inference or induction of
some deterministic hypothesis, principle, or generalization;
i.e., e.g., (s)he is uncertain whether a proposed
deterministic generalization is in fact the best explanation
for some set of data (such as ancillary evidence #1 or #2).
(iii) H-1 or H-2 consists of a combination of (i) & (ii) above.
(iv) H-1 or H-2 is a generalization that uses fuzzy (or rough?) sets and
either the membership of r or s in some generalization is not complete
or the concepts used in the generalization are rough.
(v) H-1 or H-2 involves some combination of (i), (ii) & (iv).
(vi) H-1 or H-2 involves inchoate or tacit principles.
(vii) H-1 or H-2 involves some combination of (a) principle(s)
describing a stocahstic process (b) one or more known and applicable
deterministic generelizations, (c) uncertainty about which of two or
more alternative deterministic generalizations applies, (d) fuzzy or
rough generalizations, and (e) inchoate, tacit, common sense, or "folk"
generalizations or principles.
Best regards,
Peter T.
*********************************************************
Tillers' Dynamic Evidence Site
--with "frames":
http://www.tiac.net/users/tillers/index.html
--sans "frames":
http://www.tiac.net/users/tillers/home.html
**********************************************************
Peter Tillers, Professor of Law
Benjamin N. Cardozo School of Law, Yeshiva University
55 Fifth Avenue, New York, New York 10003, U.S.A.
(212) 790-0334; FAX (212) 790-0205
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Dear Friends:
A couple of days ago I posed some questions about the role and nature of ancillary generalizations in inference. Professor Verbeek made some interesting observations about my questions. His comments provoked a further thought or two on my part, which I thought I would pass on.
In my original message I said, in part, the following:
One may add more to this picture by supposing that evidence -- ancillary evidence -- may support such generalizations, ancillary hypotheses, warrants, or what have you, and that a series of inference may thus look like something like this: primary evidence -------------->| r ---------------->| s -------------->| t and so on |________________| |__________| |____________| H-1 H-2 H-3 ^ ^ ^ | | | | | | ancillary evidence #1 ancillary e-2 ancillary e-3
Professor Verbeek's comments made me ponder more carefully how a hypothesis or generalization such as H-1 or H-2 might make an inference such as "r ------> s" uncertain.
****
Several preliminary observations:
First, "primary evidence ------->| r -----------| s ------------> t" is a chain of inferences.
Note: Clearly, I do not follow the convention that the direction of an arc must run from the proposition in issue to evidence of the proposition in issue.Second, "r" and "s" are propositions rather than events. Hence, it is logically possile for r to be the basis for an inference of s regatrdless of the temporal sequence of r and s.
Third, a common example in the law of the sort of chain inferences I have in mind here is:
D's escape from the clutches of the law ---> D's belief in his guilt ---> D's guilt****
My original questions focused on the nature of ancillary generalizations in a chain of inferences such as the above.
Professor Verbeek's comments made me think that the the following are some distinct possibilities explaining why, e.g., s is uncertain given r (but Professor Verbeek does not deserve any blame for any of my errors here):
(i) H-1 or H-2 describes a stochastic process.
(ii) H-1 or H-2 is deterministic but the decision maker is uncertain which of two or more deterministic hypotheses applies.
(iia) H-1 or H-2 is deterministic but the decision maker is uncertain of the validity of his inference or induction of some deterministic hypothesis, principle, or generalization; i.e., e.g., (s)he is uncertain whether a proposed deterministic generalization is in fact the best explanation for some set of data (such as ancillary evidence #1 or #2).(iii) H-1 or H-2 consists of a combination of (i) & (ii) above.
(iv) H-1 or H-2 is a generalization that uses fuzzy (or rough?) sets and either the membership of r or s in some generalization is not complete or the concepts used in the generalization are rough.
(v) H-1 or H-2 involves some combination of (i), (ii) & (iv).
(vi) H-1 or H-2 involves inchoate or tacit principles.
(vii) H-1 or H-2 involves some combination of (a) principle(s) describing
a stocahstic process (b) one or more known and applicable deterministic
generelizations, (c) uncertainty about which of two or more alternative
deterministic generalizations applies, (d) fuzzy or rough generalizations,
and (e) inchoate, tacit, common sense, or "folk" generalizations or principles.
Best regards,
Peter T.
*********************************************************
Tillers' Dynamic Evidence Site**********************************************************--with "frames": http://www.tiac.net/users/tillers/index.html
--sans "frames": http://www.tiac.net/users/tillers/home.html