In 1878 "Deduction, Induction, and Hypothesis," W 3:323–338;
EP 1:186–199; CP 2.619–644, Peirce wrote near its start:
But, because all inference may be reduced in some way to /Barbara,/
it does not follow that this is the most appropriate form in which
to represent every kind of inference. On the contrary, to show the
distinctive characters of different sorts of inference, they must
clearly be exhibited in different forms peculiar to each. /Barbara/
particularly typifies deductive reasoning; and so long as the is is
taken literally, no inductive reasoning can be put into this form.
/Barbara/ is, in fact, nothing but the application of a rule. The
so-called major premise lays down this rule; as, for example, /All
men are mortal./ The other or minor premise states a case under the
rule; as, /Enoch was a man./ The conclusion applies the rule to the
case and states the result: /Enoch is mortal./ All deduction is of
this character; it is merely the application of general rules to
particular cases.
[End quote]
Meanwhile, in "On the Natural Classification of Arguments," (1867), from
which I quoted in a previous message, Peirce shows how to reduce some
moods to others, but I'm unsure whether he shows how to reduce them all
to Barbara.
Best, Ben
On 10/28/2015 1:14 PM, Benjamin Udell wrote:
"On the Natural Classification of Arguments" 1867 W 2:42, CP 2:506
The first figure is the fundamental or typical one, and Barbara is
the typical mood.
On 10/28/2015 12:45 PM, Benjamin Udell wrote:
Here's one place where Peirce says that /Barbara/ is not enough:
"Relatives (logic of)" in Baldwin's _Dictionary of Philosophy and
Psychology_, New York: Macmillan, 1902, DPP 2:447-450; CP 3.636-643
http://www.gnusystems.ca/BaldwinPeirce.htm#Relatives
[....] Since Kant, especially, it has been customary to say that
deduction only elicits what was implicitly thought in the
premisses; and the famous distinction of analytical and
synthetical judgments is based upon that notion. But the logic of
relatives shows that this is not the case in any other sense than
one which reduces it to an empty form of words. Matter entirely
foreign to the premisses may appear in the conclusion. Moreover,
so far is it from being true, as Kant would have it, that all
reasoning is reasoning in _/Barbara/_, that that inference itself
is discovered by the microscope of relatives to be resolvable
into more than half a dozen distinct steps. In minor points the
doctrines of ordinary logic are so constantly modified or
reversed that it is no exaggeration to say that deductive logic
is completely metamorphosed by the study of relatives.
[End quote]
Best, Ben
On 10/28/2015 12:17 PM, Christina Da Silva wrote:
I am finishing up a masters that focuses on Medieval Islamic
philosophy, and this list has been an inestimably useful resource
for me, so thank you to all who post here. I am now trying to find
the source for some information I have in my notes, and my hope is
that someone on the list can help me.
Here is my question: where does Peirce suggest that all syllogisms
may be reduced to Barbara, and where does he later renounce this idea?
Thank you,
Christina da Silva
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