Last week I was in Bonn for the Time and Modality workshop in Bonn, where I gave a talk based on my paper, “The Logic of Where and While in the 13th and 14th Centuries”.
One of the definitions I quoted comes from the anonymous Ars Burana (c1200):
In temporali et causali: si antecedens est falsum et consequens verum, nugatoria est [AB, p. 191].
I translated nugatoria as “worthless”, and the question came up as to why a temporal proposition (something of the form “X while Y”) is worthless when X is false but Y is true. Is it nugatoria because it is invalid? Or is it invalid because it is nugatoria? Are these terms equivalent? Nugatoriness (I can coin a word if I want to) is not something you commonly see in later 13th century and 14th century logical treatises — indeed, I’m not sure I’ve come across it before. But the question made me think, and I wanted to see what else AB had to say about being nugatoria.
This definition of the truth and falsity of temporal and causal propositions comes in the section De propositione ypothetica eiusque speciebus, with the species considered being conditionals, temporals, locals, causals, copulatives, disjunctives, and adjunctives. Of these seven, no truth conditions are given for local propositions; truth and falsity conditions are given for conditionals; only truth conditions for copulatives, disjunctives, and adjunctives; and only the conditions of being nugatory are given for causals and temporals. This appears, as far as I can tell, to be the only occurrence of nugatoria in this treatise.
However, in searching for hints about nugatoriness in AB, I found a couple of other 13th-century examples of the term; these will make up a hopefully future part 2 post!
- Anonymous, Ars Burana, in Logica Modernorum, vol. II, part II, edited by L.M. de Rijk, Van Gorcum & Comp., 1967: 175-213.
- Uckelman, Sara L., “The Logic of Where and While in the 13th and 14th Centuries”, in Advances in Modal Logic vol. 11, edited by Lev Beklemishev, Stéphane Demri, András Máté, College Publications: 2016, 535-550.