Medieval logicians on ‘and’, Part 2

In this post I continue my tour through what medieval logicians have to say about ‘and’ or conjunction (here is Part 1).

Roger Bacon in the Art and Science of Logic [1] introduces a distinction between when ‘and’ is used to conjoin two things “in a third” and when it is used to conjoin two things “under a third” [par. 169]. An example of the first is “Socrates and Plato run”. The second way of conjoining is further distinguished according to whether the two things conjoined are equally principle in the third, or whether one is principle and the other is secondary. An example of the first is “my body and my soul are an animal” or “two and three are five”, while an example of the second is “I would prefer to be set free and be with Christ” or “This one eats bread and wine”.

When ‘and’ conjoins things in a third, then it is “properly conjunctive”. When ‘and’ conjoins two equally principle things under a third, then it is “taken in a united sense”, and when it conjoins something principle and something secondary, it is “taken in an associative sense”. In the associative sense, ‘and’ has “the same force as ‘with'”. However, ‘with’ can be used both associatively, such as when “Socrates runs with Plato”, and conjunctively, such as when “Socrates [together] with Plato run”.

‘And’ can be used to conjoin terms and to conjoin propositions. When it conjoins terms, then the result will be a categorical proposition, and the conjoined terms can appear as either the subject, the predicate, or both, as in the examples “Socrates and Plato run”, “Five are two and three”, and “Socrates and Plato know grammar and music” [par. 170]. Interestingly, against the views of others, Bacon rejects that a conjunction of two propositions is a hypothetical proposition, because “the force of a conditional proposition is not understood to be actually in a conjunctive one”, and in this way conjunctions differ from disjunctions, as “a disjunctive proposition, as previously stated ([par. 157]), has the actual force of a conditional one since it can be resolved absolutely into a conditional one”. As a result, Bacon concludes that, strictly speaking, “a conjunctive proposition will be neither a hypothetical nor a categorical proposition” [par. 170].

This consequence raises interesting questions regarding the quality and the quantity of conjunctive propositions. If the conjunction is one of propositions then it “has no quantity because it does not have a subject and predicate as its parts, but only propositions” [par. 171]; it does, however, have a quality depending on whether or not the entire conjunction is negated:

[A conjunctive proposition] is not said to be affirmative or negative from an affirmation or negation of one or both of its parts, but when the whole conjunctive proposition and the conjunction itself is denied, as in “It is not the case that Socrates and Plato run” and “It is not the case that Socrates runs and Plato argues” [par. 174].

If the proposition is, however, categorical, and the conjunction of terms occurs in the subject, the proposition will be universal in quantity even though

singular terms are taken in the subject, because each of those terms is not the subject but the whole made up of them, which can be understood as having universally and according to its understanding the concept of a quantitative whole [par. 172].

One of the things that I am interested in seeing through doing these surveys is how and when ‘and’ developed into a fully-fledged logical connective. We saw in the Montanes Minores from 1130 that there was really no space available for conjunctive reasoning of any type. Here, a little over a century later (Bacon was writing in the 1240s and 1250s) we see conjunctions being admitted, but they are still not afforded the same full status that categoricals and (true) hypotheticals are given. I hadn’t realized before looking more closely at Bacon that he gave the categorical/hypothetical distinction but admitted well-formed propositions which were neither. Now I’m curious to see what William of Sherwood, Lambert of Auxerre, and Peter of Spain have to say on the matter, or if Bacon’s views are unusual for the middle of the 13th century.


[1] Bacon, Roger. Art and Science of Logic, trans. Thomas S. Maloney, (PIMS 2009).

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2 Responses to Medieval logicians on ‘and’, Part 2

  1. Ezra Keshet says:

    Makes me wonder whether Latin (or any contemporary vernacular) had conditional conjunctions, things like “You make one more sound and you’re grounded for a week”….


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

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