mitchell@tartarus.uchicago.edu (Mitchell Marks) (05/12/91)
>>>>> "RAR" == Bob Riemenschneider <rar@saturn.ads.com> writes:
RAR> "Barbara" refers to the following (valid) mode of the syllogism:
RAR> All A's are B's
RAR> All B's are C's
RAR> ---------------
RAR> All A's are C's
To be over-fussy for a moment, you might want to reverse the order of
the premises, to get this into "standard form". "All Bs are Cs"
contains the major term (C), and is thus the major premise (in that
technical sense), and is "supposed" to come first. The point of this
standardization is so that you can look at where the two occurrences
of the middle term (B) come, and see that this syllogism is in the
"First Figure". (Certainly the way RAR has given it is the way we
intuitively prefer to list it today.) Writing M for the Middle Term,
P for the Major Term (the Predicate of the conclusion), and S for the
Minor Term (the Subject of the conclusion), the four figures arrange
the terms in the premises thus:
First Second Third Fourth
M...P P...M M...P P...M
S...M S...M M...S M...S
RAR> In teaching "classical logic", vowels `A', `E', `I', and `O' are
RAR> associated the "All", "No", "Some", and "Some not" of the
RAR> Aristotelean square of opposition. Then consonants are added to
RAR> the vowel triplets corresponding to valid modes, making names
RAR> (e.g., "AAA" -> "bArbArA") which are used as a mnemonic.
Adding the consonants indeed makes the vowel-triplets into
pronouncable coined-words, which can be used as a mnemonic. While
some of the consonants have solely that function, others carry
additional meaning. In particular, the initial consonant is always
significant.
The theory is that you just accept the syllogisms of the first figure,
by intuition or demonstrations; then any syllogism in a later figure
can be reduced to, or proved or derived from, a first-figure
syllogism. The initial consonant tells which first-figure syllogism
to use, and sometimes internal consonants indicate how to go about the
reduction. Internal N, R, L, and T are filler, internal C, M, S, and P
guide the reduction. For example, the fourth-figure syllogism
BRAMANTIP should be derived from BARBARA, with its major premise
_M_utated into the minor premise of the BARBARA, and with its
conclusion converted _P_er accidens into the conclusion of the
BARBARA. Happily, I forget what those mean.
RAR> Nobody seems to learn them all --
For some reason I didn't and don't really understand, in an
introductory undergraduate logic sequence I took once we had to
memorize the whole list of coined words. I still recite it to myself
now and then, as a sort of left-brain mantra. There are different
versions of the list, depending on whether you explicitly list
syllogisms that can be derived from others by immediate inference,
e.g. strengthening a premise or weakening the conclusion. Thus my
list includes CELARENT but not CELARONT, but other versions include
CELARONT. [Note that there's an underlying assumption that none of
the sets are empty, so that immediate inferences are valid which would
not be under modern understandings of quantification -- from A (all)
to I (some), and from E (none) to O (some not).]
Here's the version of the list that rattles out of my head when you
shake it right:
First Second Third Fourth
BARBARA BAROCO BOCARDO BRAMANTIP
CELARENT CAMESTRES DARAPTI CAMENES
DARII CESARE DATISI DIMARIS
FERIO FESTINO DISAMIS FESAPO
FELAPTON FRESISON
FERISON
RAR> [...] but somehow "Barbara" alone has survived as common logical
RAR> parlance.
Sometimes you can find a quiet mock-citation to the prominent logician
Barbara Celarent.
--
Mitch Marks mitchell@cs.UChicago.EDU
...and who am I to argue with my subconscious?