Matias, Jon, list,
Jon is quite right. Don't get hung up on Peirce's remark on the
ampliative-explicative distinction as applied to deduction.
SIDE NOTE: I'm getting a bit rusty. In a previous post I said Peirce
never discussed nontriviality or depth in their later sense, but that
was my bad editing; he discussed them by discussing theorematic
deductions; I meant that he didn't call them by such words as
"nontrivial" and "deep". I should add that it's kind of interesting that
Gilman discussed some deductive categorical-syllogistic conclusions (all
corollarial) as being, in effect, _/less/_corollarial than others.
END OF SIDE NOTE.
The following, with various links to texts, is about *Peirce's
terminology*, maybe helpfully to Matias and lurkers.
By "ampliative" Peirce USUALLY meant "non-deductive" and there several
passages of his across the years that show it.
Peirce usually made a distinction between "ampliative" and "deductive"
rather than between "ampliative" and "explicative", since some
deductions are too vacuous to be called "explicative".
The English words "explicative" and "ampliative" were used by writers
before "analytic" and "synthetic" to translate Kant's division of
conclusions. Peirce regarded mathematical reasoning as based on
hypotheses and did not hold with Kant's idea of the synthetic a priori,
an idea strongly associated with the use of the English words "analytic"
and "synthetic" in logic.
The following are gathered from my notes. I place underlines and
asterisks around italicized and bolded text respectively because the IU
peirce-l archive's list-serv program is designed to sadistically refuse,
among other things, to render visually bold tags, italic tags, and other
simple HTML markup. I checked the online archive texts' markup and the
italic tags, bold tags, etc., are there, but they don't change the
appearance of the text. Or maybe the owner (IUPUI) has to pay extra for
such "amenities".
**Peirce *1883**:*
We are thus led to divide all probable reasoning into deductive and
ampliative, and further to divide ampliative reasoning into
induction and hypothesis. [….]
—Page 143
https://books.google.com/books?id=xq8RAAAAYAAJ&pg=RA3-PA143
<https://books.google.com/books?id=xq8RAAAAYAAJ&pg=RA3-PA143> in “A
Theory of Probable Inference”
https://www.google.com/books/edition/Studies_in_Logic/xq8RAAAAYAAJ?gbpv=1&pg=PA126
<https://www.google.com/books/edition/Studies_in_Logic/xq8RAAAAYAAJ?gbpv=1&pg=PA126>
in_Studies in Logic_.
**Peirce 1889–91**:
***ampliative*** (am*/′/* pli-ạ̄-tiv) […] Enlarging; increasing;
synthetic. Applied — (/a/) In _/logic/,_ to a modal expression causing
an ampliation (see _/ampliation/,_ 3); thus, the word _/may/_ in “Some
man may be Antichrist” is an _/ampliative/_ term. (/b/) In the _/Kantian
philosophy/,_ to a judgment whose predicate is not contained in the
definition of the subject: more commonly termed by Kant a _/synthetic/_
judgment. [“Ampliative judgment” in this sense is Archbishop Thomson’s
translation of Kant’s word /Erweiterungsurtheil/, translated by Prof.
Max Müller “expanding judgment.”]
No subject, perhaps, in modern speculation has excited an intenser
interest or more vehement controversy than Kant’s famous distinction
of analytic and synthetic judgments, or, as I think they might with
far less of ambiguity be denominated, explicative and _/ampliative/_
judgments. _/Sir W. Hamilton./_//
— _Century Dictionary_, p. 187
https://archive.org/stream/centurydictipt100whituoft#page/187/mode/1up ,
in Part 1: A – Appet., 1889–91, of Volume 1 of 6, and identically nd
identically on p. 187
https://books.google.com/books?id=dHsxAQAAMAAJ&pg=PA187&dq=ampliation
<https://books.google.com/books?id=dHsxAQAAMAAJ&pg=PA187&dq=ampliation>
in Volume 1 of 12, 1911 edition . The brackets around the sentence
mentioning Archbishop Thomson are in the originals.
Peirce also opposes “explicative inference” and “ampliative inference”
to each other in his long definition of inference
https://archive.org/details/centurydictipt1100whituoft/page/3081/mode/1up
in CD. Note that _/explicative inference/_ there amounts to non-vacuous
deductive inference.
[….] **Explicative inference,** an inference which consists in the
observation of new relations between the parts of a mental diagram
(see above) constructed without addition to the facts contained in
the premises. It infers no more than is strictly involved in the
facts contained in the premises, which it thus unfolds or
explicates. This is the opposite of _/ampliative inference,/_ in
which, in endeavoring to frame a representation, not merely of the
facts contained in the premises, but also of the way in which they
have come to present themselves, we are led to add to the facts
directly observed. [….]
**Peirce1892**: Peirce treats “non-deductive” and “ampliative” as
alternate labels for the same kinds of inference, as follows in “The
Doctrine of Necessity Examined”
http://www.iupui.edu/~arisbe/menu/library/bycsp/necessity/necessity.htm
, § II, 2nd paragraph:
[….] Non-deductive or ampliative inference is of three kinds:
induction, hypothesis, and analogy. If there be any other modes,
they must be extremely unusual and highly complicated, and may be
assumed with little doubt to be of the same nature as those
enumerated. For induction, hypothesis, and analogy, as far as their
ampliative character goes, that is, so far as they conclude
something not implied in the premises, depend upon one principle and
involve the same procedure. All are essentially inferences from
sampling. [….]
Note: Throughout the years, Peirce usually regarded analogy as a
combination of induction and hypothetical inference. Also, in later
years, he didn't regard abduction as essentially an inference from sampling.
Best, Ben
On 8/22/2023 11:11 PM, Jon Alan Schmidt wrote:
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