Recently I’ve been working on a paper looking at temporal and local propositions in the 13th and 14th C. Originally, it was to be just the 13th C, and just Roger Bacon, William of Sherwood, Peter of Spain, and Lambert of Auxerre — until I found out that only Bacon and Lambert discuss them, and two authors isn’t as good as four. So I cast around for some other 13th C treatises, and ended up looking through all the treatises in the Logica Modernorum that mention temporal propositions.
Most of them discussed temporal propositions only cursorily, so I was quite excited when I found that the Tractatus Anagnini (TA) [LM, pp. 215-332], dating around 1200 [LM, p. 42], actually gave three methods of proof involving temporal propositions — something none of the other texts I looked at did. This would’ve made an awesome addition to my paper, so I translated them, stuck them in, and continued my merry way until the time came to actually analyse them formally. Long story short: temporal propositions in TA are not discussed in that paper. I ended up excising them completely, but I don’t want them to entirely disappear, so this post is an attempt to look more closely at some of the difficulties this text throws up.
In TA, hypothetical propositions are divided into four kinds: copulative (i.e., conjunctive), temporal, disjunctive, and conditional [LM, p. 251]; temporal propositions are not further defined, except via the three methods of proof. The entire discussion is quite short, so I quote it here:
Temporalis tribus modis probatur: secundum antecedens, secundem consequens, secundum utrumque. Secundum antecedens hoc modo:
‘quando hoc est animal, ipsum est homo.
ergo quando aliquid est homo, ipsum est animal’.
Secundum consequens hoc modo:
‘quando aliquid est asinus, idem est gramaticum et musicum
ergo aliquid est asinus, quando idem est gramaticum et musicum’
Probatur etiam temporalis secundum copulativam hoc modo:
‘Socrates iacet <et> Socrates vadit ad ecclesiam
ergo quando Socrates iacet, Socrates vadit ad acclesiam’.
Generaliter autem omnis temporalis vera cuius utraque pars est vera [LM, p. 252]
A temporal [proposition] is proved in three ways: according to the antecedent, according to the consequent, [and] according to both. According to antecedent in this way:
‘When this is an animal, it itself is a man. Therefore when something is a man, it itself is an animal.’
According to consequent in this way:
‘When something is a donkey, that same thing is grammatical and musical. Therefore something is a donkey, when that same thing is grammatical and musical.’
In addition, a temporal [proposition] is proved copulatively in this way:
‘Socrates lies and Socrates walks to the church. Therefore when Socrates lies, Socrates walks to the church.’
These rules are unclear or underspecified in a variety of ways. A first point of unclarity: The antecedent and the consequent of a temporal proposition are never defined, and it isn’t entirely clear from the examples. The structure of the first two rules are:
When p, q
When q, p
When p, q
p, when q
In the first, ‘when’ appears in the first proposition (; in the second, ‘when’ is moved to the second proposition. So perhaps we can say that the first proposition is the antecedent and the second the consequent, and that these rules are differentiated on the basis of whether, from a temporal proposition (in some sort of canonical form?), the temporal adverb in the inferred conclusion is attached to the antecedent or the consequent.
Setting aside the question of how to understand the names of the rules, it isn’t entirely clear whether these two rules say anything different: “p, when q” and “When q, p” are equivalent natural-language statements in English, and I don’t know of any grounds on which to call them non-equivalent in Latin. If they are equivalent, the first two rules differ only in syntactic structure, but together they have an important consequence: They allow us to move from ‘p when q’ to ‘q when p’; i.e., temporal propositions are symmetric. If this is a correct interpretation, TA’s ‘when’ doesn’t function like ‘when’ does, generally, in English: For if Plato reads when Socrates sleeps, this has the implication that Socrates’s sleeping is a subinterval of Plato’s reading, but if Plato’s reading extends beyond Socrates’s sleeping, it won’t follow that Socrates sleeps when Plato reads.
The third rule seems to say that a temporal proposition can be inferred from a conjunction. If the author of TA really means this, then his account of temporals differs from all of the other 13th- and 14th-C accounts that I’ve considered, all of whom say that a conjunction can be inferred from a temporal proposition but not vice versa.
As it stands, all three rules are incredibly strange things to say about ‘when’, none of which are corroborated in any other 13th- or 14th-C text that I’ve looked at.