2023-11-08

The Figures of the Syllogism

As described by Petrus Hispanius.

I	Barbara	all M is P; all S is M: all S is P
I	Celarent	no M is P; all S is M: no S is P
I	Darii	all M is P; some S is M: some S is P
I	Ferio	no M is P; some S is M: some S is not P

II	Cesare	no P is M; all S is M: no S is P
II	Camestres	all P is m; no S is M: no S is P
II	Festino	no P is M; some S is M: some S is not P
II	Baroko Fakofo	all P is M; some s is not M: some S is not P

III	Darapti	all M is P; all M is S: some S is P
III	Disamis	some M is P; all M is S: some S is P
III	Datisi	all M is P; some M is S: some S is P
III	Felapton	no M is P; all M is S: some S is not P
III	Bocardo Dokamok	some M is not P; all M is S: some S is not P
III	Ferison	no M is P: some M is S: some S is not P

IV	Bramantip	all P is M; all M is S: some S is P
IV	Camenes	all P is M; no M is S: no S is P
IV	Dimaris	some P is M; all M is S: some S is P
IV	Fesapo	no P is M; all M is S: some S is not P
IV	Fresison	no P is M; some M is S: some S is not P

The vowels indicate the type of statements:
A - Universal affirmative
E - Universal negative
I - Particular affirmative
O - Particular negative

Conversions of II, III, IV to corresponding I:
S - simple
P - per accidens
M - transpose premises
N - reductio ad absurdum

Daniel Seely Gregory's "Practical logic: or, The art of thinking" (1881) says: "The initial consonant, B, C, D or F, in the last three Figures indicates the mood in the first Figure to which the syllogism reduces. Thus, a syllogism in the mood Cesare, reduces to Celarent. The inserted consonants, s, p, k, f, m, indicate the various processes in reduction. S indicates that the proposition symbolized by the vowel preceding it is to be converted simply; p, by limitation or per acciden; k, by contraposition; f, by infinitation or obversion. The letter m (mutari) indicates that the premises of the preceding judgment are to be transposed. The p in Bramantip shows that, after converting simply, the premises warrant a universal conclusion. The other consonants, b, d, l, n, r, t, are not significant, but are inserted for the sake of euphony, or of the metre in the mnemonic hexameters invented, to keep the moods and figures in mind, by Petrus Hispanus, who died in 1277 as Pope John XXII."

(The lecture by R. J. Kilcullen of Macquarie University on the Abbreviatio Montana is no longer online.)

Another useful classification.