Syllogistic Poems

mathematics, mathematical logics, Aristotelian syllogisms
hyphenation

Among manuals of logic written after the spread of the ars nova the oldest which has been printed so far is the Introductiones in Logicam or Summulae of William of Shyreswood.1 This little work, which comprises only seventy-five pages in the modern printed text, was composed by an Englishman in the first half of the thirteenth century and probably at Paris. It is divided into six parts which deal respectively with propositions, predicables, syllogisms, dialectical topics, proprietates terminorum, and fallacies.

  • 1Edited by M. Grabmann in Sitzungsberichtz der Bayerischen Akademie, Phil.-Hist. Abteilung, 1937, Heft to. His introduction contains information about the author and the manuscript (Bibliothéque Nationals, Cod. Lat. 16617, formerly Codex Sorbonnensis 1797.)

In the part on propositions it is said that for the truth of a conjunctive proposition (copulativa) it is necessary that both of its parts should be true, while for the truth of a disjunctive proposition it is enough that one of its parts should be true and for the truth of a conditional proposition quod cum sit antecedens sit consequens. The relations of the quantifiers, omnis, quidam, and nullus, and the ways in which they can be combined with non are also discussed here, and the results of the discussion are summarized in the mnemonic verses

Aequivalent omnis, nullus-non, non-aliquis-non.
Nullus, non-aliquis, omnis-non aequiparantur.
Quidam, non-nullus, non-omnis-non sociantur.
Quidam-non, non-nullus-non, non-omnis adhaerent.2

  • 2In the third and fourth lines of Grabmann’s printed text, p. 39, ullus appears instead of nullus.

[…] In the part of syllogisms the famous mnemonic verses Barbara celarent make their first appearance, and in the form:

Barbara celarent sarii ferio baralipton
Celantes dabitis fapesmo frisesomorum;
Cesare campestres festino baroco; darapti
Felapton disamis datisi bocardo ferison.

A new and corrected version of poem:

Barbara, Celarent, Darii, Ferioque prioris
Cesare, Camestres, Festino, Baroco secundae
Tertia grande sonans recitat Darapti, Felapton
Disamis, Datisi, Bocardo, Ferison. Quartae
Sunt Bamalip, Calames, Dimatis, Fesapo, Fresison.

Here each word is to be taken as the formula of a valid mood and interpreted according to the following rules: the first three vowels indicate the quantity and quality of the three propositions which go to make a syllogism, a standing for the universal affirmative, e for the universal negative, i for the particular affirmative, and o for the particular negative; the initial consonant of each formula after the first four indicates that the mood is to be reduced to that mood among the first four which has the same initial; s appearing immediately after a vowel indicates that the corresponding proposition is to be converted simply during reduction, while p in the same position indicates that the proposition is to be converted partially or per accidens, and m between the first two vowels of a formula indicates that the premisses are to be transposed; c appearing after one of the first two vowels indicates that the corresponding premiss is to be replaced by the negative of the conclusion for the purpose of a reduction per impossibile. The verses, as given here, have the defect that the division of lines does not correspond exactly to the division of figures, and many later authors have exercised their ingenuity in suggesting improvements. In spite of his interest in modality and his acquaintance with the Prior Analytics William makes no attempt to deal with modal syllogisms.


First Figure: L, M, S.

1.1. If every M is L and every S is M, then every S is L (Barbara).
2.2. If no M is L and every S is M, then no S is L (Celarent).
1.3. If every M is L and some S is M, then some S is L (Darii).
1.4. If no M is L and some S is M, then some S is not L (Ferio).

Second Figure: M, L, S.

2.1. If no L is M and every S is 11.I, then no S is L (Cesare).
2.2. If every L is M and no S is M, then no S is L (Camestres).
2.3. If no L is M and some S is M, then some S is not L (Festino).
2.4. If every L is M and some S is not M, then some S is not L (Baroco).

Third Figure: L, S, M.

3.1. If every M is L and every M is S, then some S is L (Darapti).
3.2. If no M is L and every M is S, then some S is not L (Felapton).
3.3. If some M is L and every M is S, then some S is L (Disamis).
3.4. If every M is L and some M is S, then some S is L (Datisi).
3.5. If some M is not L and every M is S, then some S is not L (Bocardo).
3.6. If no M is L and some M is S, then some S is not L (Ferison).
Source

Kneale, W.—Kneale, M.: The Development of Logic. Oxford: The Clarendon Press, 1962.