David Brightly asks whether there is really any problem with Van Inwagen’s position that Sherlock Holmes ‘holds’ the property of being a detective rather than ‘having’ such a property. Surely there is. Inwagen’s position is inconsistent with the three main theses he puts forward in the paper. First, he holds that certain kinds of statements about fiction are true. For example, ‘There is a fictional character who, for every novel, either appears in that novel or is a model for a character who does’, or just ‘there are fictional characters’. Second, he holds that ‘there is’ is equivalent to ‘there exists’. Thus, it is true that fictional characters exist. Finally, there is a simple correspondence between the predicate calculus and ordinary language. For example, ‘There are fictional characters’ translates to ‘for some x, fictional_character(x)’ and back.

This is inconsistent with his position that ‘Sherlock Holmes does not exist’ is true, and that he holds, but does not have, the property of being a detective. If it is possible to translate between ordinary language and predicate calculus and back, it follows that any valid inference in predicate calculus is also valid for the corresponding ordinary language statements, and conversely, and that anything true we can say about the predicate calculus statements, is true of the ordinary language ones. So take ‘Some fictional characters are detectives’, which Inwagen (presumably) holds to be true. Thus at least one fictional character is a detective, and thus has, rather than holds that property. Furthermore, if the corresponding predicate calculus statement ‘Ex, fictional_character(x) & detective(x)’ is true, there must be at least one object a in the domain such that fictional_character(a) & detective(a). For example a = sherlock Holmes. But the predicate detective() expresses the property of having, not holding the property of being a detective, so Inwagen’s claim that Holmes (or whatever x satisfies the predicate) does not have that property, is false.

Furthermore, Inwagen holds that 'All fictional characters exist’ is true, and clearly holds that Sherlock Holmes is a fictional character. And he holds that these can be simply translated into predicate calculus, so – according to him - the following are true.

(x) fictional_character(x) implies exist(x)

fictional_character(Holmes)

But these together imply exist(Holmes). This translates back into ‘Holmes exists’, and so his claim that ‘Holmes exists’ is false is contradictory.

## 5 comments:

It certainly looks as if PVI's position is inconsistent. Though he makes the exemplifies/encodes (has/holds) distinction between two modes of predication, he seems not to draw the distinction between concrete and abstract, which allows us to say that Sherlock exists but is not concrete.

1. Zalta writes 'Fs' to denote 's exemplifies F', eg, 'Sherlock is fictional' and 'sD' to denote 's encodes D', eg, 'Sherlock is a detective' understood as 'Sherlock encodes the property of being a detective'. 'sD' and '~Ds' are not inconsistent propositions.

2. to derive 'concrete(s)' (which is inconsistent with 'abstract(s)') we would have to start from '∀x. Fictional(x)-->concrete(x)'. But this last would be denied.

A last point: why would PVI or anyone introduce an existence predicate into

classicalpredicate calculus? If it means the same as '∃' it's surely redundant, being true everywhere, so that '∀x. Fx-->exists(x)' is true for any predicate term F. The answer would appear to be that it seems to enable us to regiment 'S does not exist' as '~exists(s)'. But from this we immediately deduce the rather paradoxical '∃x.~exists(x)'. This way surely madness lies. Either we take the NFL route accepting that some names simply do not refer, or we take the abstract object route. On one route we depart from classical predicate calculus. On the other we stay classical but get weird objects. Or is there a third possibility?>>A last point: why would PVI or anyone introduce an existence predicate into classical predicate calculus?

That was my embellishment. PVI believes that 'there is' means the same as 'there exists', so I introduced 'exist()'. There's no prohibition against this. (At least I don't think so).

>>The answer would appear to be that it seems to enable us to regiment 'S does not exist' as '~exists(s)'. But from this we immediately deduce the rather paradoxical '∃x.~exists(x)'.

Yes quite. There is no obvious translation from the commonplace 'Holmes does not exist' into the predicate calculus. But PVI's whole argument, and basis of his position, is that there always is such an easy translation.

>>Either we take the NFL route accepting that some names simply do not refer,

This is essentially Sainsbury's position.

>>or we take the abstract object route. On one route we depart from classical predicate calculus. On the other we stay classical but get weird objects. Or is there a third possibility?

Yes: my route, which is that proper names are descriptive, signifying 'haecceity'. I've already indicated how this would be possible in the posts about Aeneas. A proper name simply signifies whatever you were talking about before - whatever that is.

Can we take a closer look, then, at the Ockhamist theory of proper names? One implication appears to be that, for understanding and deciding the truth of a set of sentences, eg, the Dido and Aeneas story, we can do without the notion of reference altogether. The story can be thought of as a pattern or template or specification with blank spaces or empty slots. The pattern is to be offered up to the world and if we can find objects that fit the slots then the story is true. Names serve merely to label the slots and convey what relations between the slot occupiers are to hold. There is a strong whiff of circularity here which will need to be addressed. Basically, the pattern matching has to be done non-linguistically. But the upshot appears to be that the finding of the objects that satisfy the story is what makes them the referents of the names, under the usual understanding of 'reference'. So we had things backwards all along. This makes some sense to me but it doesn't seem to gel with your 'proper names are descriptive, signifying 'haecceity''. Could you expand on that?

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