Medieval logicians on ‘and’, Part 1

Another item on my todo list reads “24. Med Log on &”. So much research time and effort is put into the conditional, or the consequence, and also into negation, while other propositional connectives are relatively little discussed, at least, not in any focused way. So it occurred to me one day, “I wonder if we’d find anything interesting by surveying what medieval logicians have to say about ‘and'”, having a vague recollection of William of Sherwood’s discussion of the sentence “Pepper is sold here and in Paris” in the context of one of the lesser-discussed types of supposition.

So I’m going to start a series of posts where I collect what various medieval authors have to say about ‘and’, as a means of seeing whether they say anything unusual or interesting.

In the Introductiones Montane Minores (de Rijk, ed., Logica Modernorum, pp. 7-71), a reportatio on the lectures of Alberic of Paris dating around 1130 (de Rijk 1966, p. 56), hypothetical propositions are divided into simple and composite, simple ones being those which do not have hypothetical propositions as parts (simplex est illa que non habet aliquam ypotheticam partem sui, LM, p. 40), and composite ones being ones which do. The author considers whether, on such definitions, sentences such as

If every man is an animal and every man is a substance, and Socrates is a man, and [sic] Socrates is a substance (si omnis homo est animal et omne animal est substantia, et Socrates est homo et Socrates est substantia) (p. 40)

are complex or simple: It isn’t complex because the parts are all categorical, not hypothetical, but it isn’t simple, because it has more than two predicatives; we will not dwell on these matters but turn to the division of composite hypotheticals. They are of two type: connexa and disiuncta. Disjunctive hypotheticals are ones using aut or vel, while “connexive” hypotheticals are formed with si, cum, quando, quotiens, or the like (p. 41). There seems to be no place for reasoning according to conjunction in the Montane Minores — something which should not be considered especially surprising considering the treatise’s date and its firm roots in the logica vetus (de Rijk, 1966, p. 9).

It’s my intention to work through all the treatises in LM looking at what they have to say about conjunction, and then move on to 13th-century treatises on supposition and syncategorematic terms. After that, 14th-century treatises on consequences are the way to go.


de Rijk, L.M. 1966. “Some New Evidence on Twelfth Century Logic”, Vivarium 4: 1-57.
de Rijk, L.M. 1967. Logica Modernorum volume 2, part 2. (Assen: Van Gorcum & Comp.)

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3 Responses to Medieval logicians on ‘and’, Part 1

  1. Pingback: Medieval logicians on ‘and’, Part 2 | Medieval Logic & Semantics

  2. Pingback: Medieval logicians on ‘and’, Part 3 | Medieval Logic & Semantics

  3. I don’t think the et…et… in the consequent is an error. When used in pairs, the term can function in the way the English ‘both…and…’ does. Alternatively, the punctuation could be altered to place the comma before the final ‘et’, which can take on the semantic function of ‘then’ (cf. the English ‘she could go outside in that weather and catch a cold’.).


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