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The Hatfields and the McCoys: A Challenge to Reists and Extreme Nominalists
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6 responses to “The Hatfields and the McCoys: A Challenge to Reists and Extreme Nominalists”
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“it cannot be any individual Hatfield that is 100 strong. This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate ‘100 strong.’”
I wonder if a compulsion to posit *another entity* or type of entity over and above the hundred hatfields, comes from a rejection of the intelligibility of what is called ‘plural quantification’ (the grasp of which, I mainly have from reading the Stanford encyclopedia article).
https://plato.stanford.edu/entries/plural-quant/
Although I will note that the logical structure of ‘The Hatfields are mean’ is different from the ‘The Hatfields are a hundred strong’ . The Hatfields are mean is analyzable as saying that each Hatfield is mean. Not so for the ascription of number, as you note. I believe the argument for there not being anything in addition to each Hatfield making it the case that there are a hundred hatfields, begins by claiming that you don’t anything but a single Hatfield to make it the case that there is one Hatfield.
One is a number, after all. I believe we should be consistent about what makes it true that there is one Hatfield, and what makes it true for greater numbers of Hatfields. -
Suppose the McCoys slaughter the Hatfields to the point where are are only two left, Gomer and Goober. You would say that the McCoys outnumber the Hatfields, but they don’t outnumber each of the two. But then they kill Gomer leaving only one Hatfield, Goober. Wouldn’t you still say both:
a) The McCoys outnumber the Hatfields
but
b) The McCoys do not outnumber each Hatfield.
So your claim, though reasonable, is not rationally coercive. I can still reasonably insist on a distinction between set and members even in this case where the set is a singleton with exactly one member. {Goober} is not identical to Goober. -
I somewhat overstated the case with respect to plural quantification. I won’t go into all the details, but I’ll just say there’s a bit of debate about whether plural quantification should be understood as ‘ontologically innocent’. George Boolos who helped popularize plural quantification as an interpretation of monadic second order logic thought of it as ontologically innocent though (not requiring sets, for instance). A primitive notion of ‘plural reference’ is used for the notion of referring to multiple objects at once.
I certainly don’t mind sets of objects. But I also don’t see a singleton set as being needed to make true there being one Hatfield — is the empty set needed to make true there being *zero* Hatfields?
There’s a line from Kant he uses in a different context which comes to my mind (I’m appropriating it in a way where the correct interpretation does not matter). That line is ‘a whole of representation is not the representation of a whole’. When I read this line I understood it this way: considering multiple things together is different from considering those multiple things as part of, as constituting one thing.
Your example with the McCoys and Hatfields is interesting, I will respond again about it if I can think of a good paraphrase or analysis. -
>>A primitive notion of ‘plural reference’<< Doesn't introducing plural reference as a primitive notion just beg the question?
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We’ve been through this before. If there are two Hatfields, there is at least one Hatfield, and at least another. That means two things. Not two things and a third thing.
I think you want to say that ‘these two Hatfields’ refers to a single thing, different from either one of the two. Not so. The term refers to two things, not one. -
Imagine the Hatfields master their bloody impulses, and slaughter only 27 McCoys.
What, then, are we to make of this:
There are 73 McCoys, and the number of McCoys is prime.
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