Path: utzoo!utgpu!news-server.csri.toronto.edu!rutgers!att!linac!midway!midway.uchicago.edu!mitchell From: mitchell@tartarus.uchicago.edu (Mitchell Marks) Newsgroups: comp.ai Subject: Medieval coined words for valid syllogisms (was Re: K. T. Fann's thesis on abduction.) Message-ID: Date: 11 May 91 21:33:16 GMT References: <8409@uceng.UC.EDU> Sender: news@midway.uchicago.edu (NewsMistress) Organization: University of Chicago Computer Science Lines: 82 In-Reply-To: rar@saturn.ads.com's message of 10 May 91 23: 15:41 GMT >>>>> "RAR" == Bob Riemenschneider 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?