skhadye@uceng.UC.EDU (Shankar P. Khadye) (05/11/91)
Hello netters, I am reading Fann's thesis on Peirce's theory of abduction. In it, Fann has referred to Barbara, as in - " ... can be reduced to Barbara." and so on. Can anybody elaborate on it? Thanks. ......Shankar P. Khadye
rar@saturn.ads.com (Bob Riemenschneider) (05/11/91)
"Barbara" refers to the following (valid) mode of the syllogism:
All A's are B's
All B's are C's
---------------
All A's are C's
In teaching "classical logic", vowels `A', `E', `I', and `O' are
associated the "All", "No", "Some", and "Some not" of the Aristotelean
square of opposition. Then consonants are added to the vowel triplets
corresponding to valid modes, making names (e.g., "AAA" -> "bArbArA")
which are used as a mnemonic. Nobody seems to learn them all -- or
worry much about the theory of the syllogism for that matter -- these
days, but somehow "Barbara" alone has survived as common logical
parlance.
-- rarscotp@csc2.essex.ac.uk (Scott P D) (05/12/91)
In article <8409@uceng.UC.EDU> skhadye@uceng.UC.EDU (Shankar P. Khadye) writes: >I am reading Fann's thesis on Peirce's theory of abduction. In it, >Fann has referred to Barbara, as in - " ... can be reduced to Barbara." >and so on. Can anybody elaborate on it? It comes from a medieval mnemonic poem devised to help one remember which syllogisms are valid. It is of course in Latin and goes as follows:- Barbara celarent darii ferio baralipton Celantes dabitis fapesmo frisesomorum; Cesare camestres festino baroco; darapti Felapton disamis datisi bocardo ferison. Every word in the poem corresponds to a valid syllogism. The rules for interpreting the mnemonic are themselves quite complicated. A partial explanation is given in Delong's "A Profile of Mathematical Logic", which was also my source for the full text of the poem (not all mnemonics are easy to remember!). However you probably only want to know which syllogism 'Barbara' denotes. It is simply If every Y is Z And every X is Y Then every X is Z Paul Scott, Dept Computer Science, University of Essex, Colchester, UK.
hah@ztivax.UUCP (Dr. Hans Hellendoorn) (05/24/91)
In article <8409@uceng.UC.EDU> skhadye@uceng.UC.EDU (Shankar P. Khadye) writes: >I am reading Fann's thesis on Peirce's theory of abduction. In it, >Fann has referred to Barbara, as in - " ... can be reduced to Barbara." >and so on. Can anybody elaborate on it? > > ......Shankar P. Khadye I can advise you to read the book of Jan Lukasiewisz, "Aristotle's Syllogistic - from the standpoint of modern formal logic", Oxford, Clarendon Press, 1951. The Barbara is the most simple and well known syllogism, like All man are mortal, All Greeks are men, therefore All Greeks are mortal. These are three A-sentences, therefore bArbArA. There are E, I and O sentences too, forming moods like the Fesapo: All B is A No C is B therefore Some A is not C, like the Fresison: Some B is A No C is B therefore Some A is not C, and the well known Datisi, written in a style that better corresponds to Aristotle's original texts: A belongs to all B C belongs to some B therefore A belongs to some C A recent contribution on the field of syllogisms that I found most interesting is from a Soviet scientist: S.V. Chesnokov, "The Effect of Semantic Freedom in the Logic of Natural Language", Fuzzy Sets and Systems 22(1987)121-154. Hans Hellendoorn