By Karl Durr

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Extra resources for Propositional Logic of Boethius

Example text

626). Following Boethius’ text, we will speak of the first and second subclasses ; the first subclass consists of those sentences which Boethius calls non-homogenous sentences (propositiones non- FIFTH CLASS OF PROPOSITIONAL FORMS 49 aequimodi), and the second those which he calls homogenous sentences (propositiones aequimodij (Cf. , p. 626). The following eight propositional forms belong to the first subclass of the first class: (29) et cpqcNpr et cpqcNpNr et cpNqcNpr et cpNqcNpNr et cNpqcpr et cNpqcpNr et cNpNqcpr et cNpNqcpNr (Cf.

Supra, p. 35), we note that formula (a) of 5 24 follows if “q” is replaced by the expression “q 3 r”. As B result of these considerations, we see that inference scheme (5) may be termed correct if the system of material implication is used as metascience. q

I n agreement with the text, we will also order the classes of propositional forms and the classes of inference schemes, so that we can, for example, speak of the first class of propositional forms and of the first class of inference schemes. It will be noticed that since we have, on the one hand, ordered the elements of the classes and, on the other hand, the classes 32 ANALYSIS OF “DE SYLLOGISM0 HYPOTHETICO” themselves, it is easily possible to order all the elements of all the classes. 8 21.

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