Saturday, February 19, 2011

Ockham and Brentano-equivalence

I talked about 'Brentano equivalence' a few times, e.g. here. It is the thesis that "some A-B exists" is convertible with "some A is B", and is closely connected with the thesis that existence is not a predicate. Something very similar can be found in Ockham's Summa Logicae, Book III, part 2, chapter 26. Parallel Latin-English below. Note that the similarity is not exact - Brentano also held that 'every A is B' is equivalent to the negative 'no A is not B', or to 'not: something that is A and not-B exists'. Ockham, by contrast, agreed with Aristotle that 'every A is B' is affirmative, and that it implies the particular 'some A is B'.

On the confusion about the 'existential import' of the universal proposition, I have a piece here.

Si autem propositio dubitabilis in qua praedicatur esse exsistere per propositionem de inesse vel de possibili habeat pro subiecto nomen connotativum vel respectivum vel negativum vel unum compositum ex multis nominibus, quandoque potest demonstrari, quandoque non.Now if there is a dubitable proposition in which existential being is predicated by an assertoric or de possibili proposition, and the proposition has for a subject a connotative, relative, or negative name, or one composed from many names, sometimes it can be demonstrated and sometimes it cannot.
Talis enim propositio semper aequivalet uni propositioni in qua praedicatur passio de subiecto, saltem large sumendo passionem. Sicut ista proposito ‘eclipsis est’ aequivalet isti ‘aliquid eclipsatur’; et ista ‘calefactivum est’ aequivalet isti ‘aliquid est calefactivum’; et ista ‘habens tres angulos aequales duobus rectis’ aequivalet isti ‘aliquid est habens tres angulos aequales duobus rectis’.For such a proposition is always equivalent to a single proposition in which an affection is predicated of a subject, at least when we take "affection" broadly. Thus the proposition, "An eclipse exists" is equivalent to "Something is eclipsed"; and "A heatable thing exists," is equivalent "Something is heatable"; and "Something having three angles equal to two right angles exists," is equivalent to "Something is a thing having three angles equal to two right angles."

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