Handbook of the History of Logic: - Fordham University Faculty

The Latin Tradition of Logic to 1100 13
work.
Boethius puts forward his fullest and most influential answer in his second
commentary. Even here, he is one sense loyal to the Porphyrian project, since
he turns to one of Porphyry’s preferred sources, the great Peripatetic philosopher
Alexander of Aphrodisias, from whom he says he has taken his position (cf. [De
Libera, 1999]). He begins with a powerful argument [Boethius, 1906, 161:14–164:2]
which claims to show that universals do not exist, and any enquiry into them is
pointless. The first premiss resumes Porphyry’s first question:
1. Either genera and species exist (sunt atque subsistunt) or they are formed
by the intellect, in thought alone.
He then argues against the truth of the first disjunct of (1): -
2. Everything that exists is one in number.
3. Nothing that is common to many at the same time can be one in number.
4. Genera and species are common to many at the same time.
5. Genera and species do not exist. (2,3,4)
It follows, therefore, that
6. Genera and species are formed in the intellect, in thought alone. (1,5; disjunctive
syllogism)
But to hold (6), Boethius goes on to show, apparently entails a drastic conclusion
for the enquirer. Some thoughts — call them ‘corresponding thoughts’ —
correspond to how their object is in reality, some do not.
7. If the thoughts that, by (6), are genera and species are corresponding thoughts,
then genera and species exist in reality in the way they are thought.
8. Genera and species do not exist in reality in the way they are thought. (5)
9. Genera and species are not corresponding thoughts. (7, 8; modus tollens)
10. Thoughts that are not corresponding are empty and false.
11. All enquiry into universals should cease.
Boethius does not, of course, agree with this argument, but one of the remarkable
feature of his answer is that he accepts every stage of this argument up to
(9). He simply denies (10), and therefore (11); the opponent’s argument, in the
main, goes through, but without its sting. Boethius denies (10) by appealing to
the idea of (mathematical) abstraction. He explains [Boethius, 1966, 164:12–14]
that when one thing is abstracted from another ‘the thing is indeed not as the
thought is, but the thought is not however at all false.’ For example, a line cannot