Brentano held that a thought must have an object. Did he mean to qualify this by ‘existing object’? According to at least one important thing he said, he would not have drawn any distinction between ‘object’ and ‘existing object’. According to what is now called the Brentano-Venn analysis of propositions, every categorical proposition (one of the form ‘A is B’) is convertible with an existential proposition ‘An A-B exists’. He says, for example
The categorical proposition "Some man is sick", has the same meaning as the
existential proposition "A sick man exists" or "There is a sick man".
It follows from this that 'some hobbit is thought about by some man' is convertible with 'some hobbit thought by some man exists' or 'there is a hobbit thought about by some man'. I have more to say on the history of this here.
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