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Saturday, January 19, 2013

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Dr. Vallicella,

Here's the passage with his commentary (More Kinds of Being, pp. 3-4):

"I distinguish between the following four uses of 'is' as a copula. [lists 1-4, as quoted above] I do not, however, claim that all of these uses of 'is' are equally fundamental from a logical point of view. I regard the 'is' of attribution as being logically redundant, a relatively superficial feature of the English language. As for the 'is' of constitution, I suspect that it, too, is not logically irreducible, although I shall commit myself to no definitive analysis of constitution statements in this study. But the other two uses of 'is' so far mentioned I do consider to be logically primitive, even if for some purposes the 'is' of identity may effectively be defined in terms of the 'is' of instantiation. [Next paragraph]. Now, this still leaves one other important use of 'is' to which I have not yet alluded: the 'is' of existence [as quoted above]. I take this use of 'is' also to be logically primitive, but I do not follow current orthodoxy in identifying its role with that played in symbolic logic by the so-called (but in my view misnamed) existential quantifier, '∃'.

So, you are correct: Lowe does not refer to all five uses of 'is' as a copula. Just the first four. Apologies for the sloppiness!

Bill, I'd be reluctant to accept that 'Max is black' contains an existence assertion. For if so I think we lose the possibility of proof by reductio ad absurdum. We need to be able to separate out existence assertion from property possession assertion. The former can then be abandoned in the face of contradiction, 'Px & ~Px', in the latter. I don't see how this can be possible if the 'Px' itself contains an existence assertion.

David,

You may well be right. It would be helpful if you could provide us with an RAA proof as illustration.

I'm not sure if it is relevant, but one can assert a conditional without asserting its antececedent or consequent. One can assert that if Max is black then he is colored without asserting that Max is black or that he is colored.

Bill, apologies for the earlier terseness. I am getting over the flu and consequent chest infection. I have put up a rather longer exposition here.

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