By Roger Bishop Jones, for The Grice Club
Grice's definition of an interpretation of Q (VIII A of Vacuous Names) is ambiguous in what it says about the domain of an interpretation.
The domain is a set of correlates, some of which may be unit sets the element of which is a designatum.
Grice tells us that there need not be any such unit sets, but does not say explicitly that there may be no other correlates.
He does tell us that he has in mind that there will be exactly one non-designating correlate, the empty set, but he does not place this as a requirement, so the significance of his having this in mind is unclear.
There are three possibilities concerning the number of non-designating correlates in an interpretation, that there are none, exactly one, or more than one.
There are a number of possible positions in relation to the definition of an interpretation, insofar as that definition constrains the non-designata.
The most obvious are:
1. no constraint
2. there must be at least one
3. there must be exactly one
Of course there are other possibilities, but I propose to discuss just these three.
From a literal reading of Grice in this section I would take the first.
However, from the fact that he explicitly allows there to be no designata but does not explicitly say this for non-designating correlates, we might infer that he intends but does not state that there will be at least one non-designating correlate.
Alternatively we might take the case he "had in mind" more presciptively and work with item 3.
These are significant semantically, of course.
Allowing interpretations with no designata will create problems with descriptions if these were to be introduced into Q, for one would then have no correlate available for an unsatisfiable description.
It also effects a matter which Grice later discusses, which is whether certain existential claims are valid, notably the claim that there is something which does not exist.
This (or something similar) Grice later claims to be valid, and this is evidence against 1 in favour of 2 or 3.
Item 2, though the one perhaps preferred by Grice, has the disadvantage that all non-designating terms have the same correlate, and will therefore be equal in a sense of equality which satisfies the universal law of reflexivity of identity.
Do we want Pegasus and Sherlock Holmes to be identical?
Are there other passages in Vacuous Names or elsewhere which are relevant to this issue?
Is the above analysis of this issue good as far as it went?
Roger Jones
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Yes, it is very good. There are passages in "Vacuous Names". Recall that he says that he does NOT want to say that
ReplyDelete"Bellerophon is identical with Pegasus".
This he calls an uninteresting weak notion of identity (I would refer to = as identity rather than equality, incidentally -- philosophers' jargon!).
In the INTERESTING notion of weak identity he favours, Bellerophon is NOT identical with Pegasus (but, granted, he grants this would involve introduction of 'it is believed that'.
In Jones's case, "Sherlock Holmes" is believed to be a detective created by this Scots novelist. Pegasus is believed to be a winged horse, rather.
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Some of the things Grice says ARE confusing (if not confused!). I personally would never had spent 10 minutes of my life to create a system to justify the clever remark, "Someone isn't at the party". I.e. Marmaduke Bloggs.
On my reading of "Vacuous Names", I took the gist to be 'negation' --. The examples he uses SEEM to involve negation.
There IS something about 'descriptions' in the last but one section of "Vacuous Names". Grice wants to be less strict with descriptions. His example, as I recall:
"Mr. Spurgeon's haberdasher is not bald"
Someone isn't bald -- i.e. the haberdasher to Mr. Spurgeon.
So, he is indeed fighting FOR (rather than against) the unrestricted application of E. G. (existential generalisation) and U. I. (universal instantiation).
Most of what he says about 'names' rather goes over my head, because when I read Grice's "Vacuous Names" I had already read Quine's "On what there is" and Quine had convinced me that "Pegasus does not exist" boils down to "~Ex. PEGASUSx" -- there's no such thing that pegasizes. Or something. But I'll reconsider Grice's wording of the non-designating correlates. There is a fascinating sequence in "Reply to Richards" (part of it online) about the null-set. Since it relates, I may copy and paste in special post, right now.