Singular Concepts and Singular Negative Existentials

A re-post  from 15 May 2012. Reproduced verbatim.

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London Ed seems to be suggesting that we need irreducibly singular concepts (properties, propositional functions) if we are properly to analyze grammatically singular negative existence statements such as

1. Vulcan does not exist.

But why do we need to take 'Vulcan' to express a singular concept or haecceity property?  Why isn't the following an adequate analysis:

1A. The concept Small, intra-Mercurial planet whose existence explains the peculiarities of Mercury's orbit is not instantiated.

Note that the concept picked out by the italicized phrase is general, not singular.  It is general even though only one individual instantiates it if any does.  The fact that different individuals instantiate it at different possible worlds suffices to make the concept general, not irreducibly singular.

Comments

[Tom Tillett]

I have followed your posts about singular concepts with great interest. I would answer this particular question as follows: Because 'Vulcan' refers to an individual, distinct planet inside the orbit of Mercury that, per 1, does not exist. It is therefore a possible planet, not actual. 'Vulcan' no less than 'Socrates' is innately singular as this planet and no other, and does not become general just because you can refer to it as small anymore than Socrates becomes general because you can describe him as ugly. Similarly, I would argue that the fact that 'different individuals instantiate' in 'different possible worlds' does not make Vulcan or Socrates general. It just means that for them both, alternative possibilities are near infinite. Which is kind of the thing about possibilities, as opposed to actualities.