Temporalis — the logic of ‘While’
Medieval logicians generally accepted a distinction between atomic and molecular propositions. Molecular propositions are formed from atomic (or simple) propositions by means of propositional connectives. Propositions thus formed were also known as hypotheticals, a term which was applied not only to implicational statements, but also to the other kinds of molecular propositions such as conjunctions, disjunctions etc. In the Middle Ages, however, there was little agreement as to which connectives should be taken into consideration within logical studies. Thus the number of propositional connectives was not fixed in general. William of Ockham [EL, p.198] suggested that there were at least five: conditionalis, i.e. implication (in a broad sense), copulativa, i.e. conjunction, disiunctiva, i.e. disjunction, and temporalis and causalis. Temporalis will be discussed below. With respect to causalis, we may mention two of the many examples put forth by Paul of Venice (c. 1369-1429) in his Logica Magna:
Because you are a man you are not a donkey [II, 3, 27e] Because the sun is this light is [II, 3,29e]
KeywordsTemporal Logic Atomic Proposition Valid Consequence Temporal Proposition Scholastic Tradition
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