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Started by Geremia, May 31, 2016, 11:00:36 AM

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QuoteMedieval logicians memorized this most famous logic mnemonic:Barbara, Celarent, Darii, Ferio ← direct first figure Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum ← indirect first figure Cesare, Camestres, Festino, Baroco ← second figure Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison ← third figureThe 3 vowels of each name represent the 4 possibilities of the square of opposition: So Barbara is an AAA syllogism, e.g.:Every man is an animal.Every animal is a creature.∴ Every man is a creature.There is more to the mnemonic than this. Apparently the consonants in the names allow one to reduce the corresponding syllogism to that of a simpler figure.Are there any references that overview how to fully use all that is packed into this very elaborate, well-thought-out mnemonic?

QuoteExplanation of the MnemonicBrody, Boruch A. "Logical Terms, Glossary of." Encyclopedia of Philosophy. Ed. Donald M. Borchert. 2nd ed. Vol. 5. Detroit: Macmillan Reference USA, 2006. 533-560. Gale Virtual Reference Library. Web. 19 May 2016.:Quotemnemonic termsThe names that the medieval logicians introduced for the valid syllogisms. One such term is "Barbara." The key for these mnemonics is as follows: The three vowels respectively indicate the three constituent propositions of the syllogism as A, E, I, or O. For first-figure syllogisms the initial consonants are arbitrarily the first four consonants; for the other figures the initial consonants indicate to which of the first-figure syllogisms the syllogism in question may be reduced. Other consonants occurring in second-, third-, and fourth-figure mnemonics indicate the operation that must be performed on the proposition indicated by the preceding vowel in order to reduce the syllogism to a first-figure syllogism. The key for this is as follows: "s" indicates simple conversion, "p" indicates conversion per accidens, "m" indicates metathesis (interchanging of the premises), "k" indicates obversion, and "c" indicates convertio syllogism (that is, the syllogism is to be reduced indirectly). In mnemonic terms the only meaningless letters are "r," "t," "l," "n," and noninitial "b" and "d." More elaborate mnemonics have been devised for syllogisms in which two or more of the premises exhibit modality. See entry "Logic, Traditional."Mnemonic TermsName Figure Major Minor Conclusion premise premiseBarbara first A A ABaroco second A O OBocardo third O A OBramantip fourth A A ICamenes fourth A E ECamestres second A E ECelarent first E A ECesare second E A EDarapti third A A IDarii first A I IDatisi third A I IDimaris fourth I A IDisamis third I A IFelapton third E A OFerio first E I OFerison third E I OFesapo fourth E A OFestino second E I OFresison fourth E I OReductionSo, what are the different types of reduction mentioned above?simple conversionconversion per accidensmetathesis (interchanging the premises)obversionconvertio syllogism (indirect conversion)Quotereduction of syllogismsThe process whereby syllogisms in imperfect figures are expressed in the first figure. Reduction is direct when the original conclusion follows from premises in the first figure derived by conversion, obversion, etc., from premises in an imperfect figure. Reduction is indirect when a new syllogism is formed which establishes the validity of the original conclusion by showing the illegitimacy of its contradictory. See entry "Logic, Traditional."QuoteconversionIn traditional logic, a type of immediate inference in which from a given proposition another proposition is inferred that has as its subject the predicate of the original proposition and as its predicate the subject of the original proposition (the quality of the proposition being retained). The process of conversion yields an equivalent proposition only when the original proposition is an E- or I-proposition; when it is an A-proposition traditional logicians allowed for conversion per accidens (or by limitation)--that is, conversion plus a change in the quantity of the proposition from universal to particular. Thus, the E-proposition "No men are immortal" yields "No immortals are men," but the A-proposition "All men are mortal" can be converted only by limitation, yielding "Some mortals are men." The process of conversion yields no equivalent proposition if the original proposition is an O-proposition. See entry "Logic, Traditional."QuoteobversionIn traditional logic, a type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa. Obversion of a proposition yields an equivalent proposition when applied to all four types (A, E, I, and O) of propositions that traditional logicians considered. See entry "Logic, Traditional."

Quotemnemonic termsThe names that the medieval logicians introduced for the valid syllogisms. One such term is "Barbara." The key for these mnemonics is as follows: The three vowels respectively indicate the three constituent propositions of the syllogism as A, E, I, or O. For first-figure syllogisms the initial consonants are arbitrarily the first four consonants; for the other figures the initial consonants indicate to which of the first-figure syllogisms the syllogism in question may be reduced. Other consonants occurring in second-, third-, and fourth-figure mnemonics indicate the operation that must be performed on the proposition indicated by the preceding vowel in order to reduce the syllogism to a first-figure syllogism. The key for this is as follows: "s" indicates simple conversion, "p" indicates conversion per accidens, "m" indicates metathesis (interchanging of the premises), "k" indicates obversion, and "c" indicates convertio syllogism (that is, the syllogism is to be reduced indirectly). In mnemonic terms the only meaningless letters are "r," "t," "l," "n," and noninitial "b" and "d." More elaborate mnemonics have been devised for syllogisms in which two or more of the premises exhibit modality. See entry "Logic, Traditional."Mnemonic TermsName Figure Major Minor Conclusion premise premiseBarbara first A A ABaroco second A O OBocardo third O A OBramantip fourth A A ICamenes fourth A E ECamestres second A E ECelarent first E A ECesare second E A EDarapti third A A IDarii first A I IDatisi third A I IDimaris fourth I A IDisamis third I A IFelapton third E A OFerio first E I OFerison third E I OFesapo fourth E A OFestino second E I OFresison fourth E I O

Name Figure Major Minor Conclusion premise premiseBarbara first A A ABaroco second A O OBocardo third O A OBramantip fourth A A ICamenes fourth A E ECamestres second A E ECelarent first E A ECesare second E A EDarapti third A A IDarii first A I IDatisi third A I IDimaris fourth I A IDisamis third I A IFelapton third E A OFerio first E I OFerison third E I OFesapo fourth E A OFestino second E I OFresison fourth E I O

Quotereduction of syllogismsThe process whereby syllogisms in imperfect figures are expressed in the first figure. Reduction is direct when the original conclusion follows from premises in the first figure derived by conversion, obversion, etc., from premises in an imperfect figure. Reduction is indirect when a new syllogism is formed which establishes the validity of the original conclusion by showing the illegitimacy of its contradictory. See entry "Logic, Traditional."

QuoteconversionIn traditional logic, a type of immediate inference in which from a given proposition another proposition is inferred that has as its subject the predicate of the original proposition and as its predicate the subject of the original proposition (the quality of the proposition being retained). The process of conversion yields an equivalent proposition only when the original proposition is an E- or I-proposition; when it is an A-proposition traditional logicians allowed for conversion per accidens (or by limitation)--that is, conversion plus a change in the quantity of the proposition from universal to particular. Thus, the E-proposition "No men are immortal" yields "No immortals are men," but the A-proposition "All men are mortal" can be converted only by limitation, yielding "Some mortals are men." The process of conversion yields no equivalent proposition if the original proposition is an O-proposition. See entry "Logic, Traditional."

QuoteobversionIn traditional logic, a type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa. Obversion of a proposition yields an equivalent proposition when applied to all four types (A, E, I, and O) of propositions that traditional logicians considered. See entry "Logic, Traditional."