Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Irreducibly Plural Predication: ‘They are Surrounding the Building’

Let's think about the perfectly ordinary and obviously intelligible sentence,

1. They are surrounding the building.

I borrow the example from Thomas McKay, Plural Predication (Oxford 2006), p. 29.  They could be demonstrators.  And unless some of them have very long arms, there is no way that any one of them could satisfy the predicate, 'is surrounding the building.'  So it is obvious that (1) cannot be analyzed in terms of 'Al is surrounding the building & Bill is surrounding the building & Carl is surrounding the building & . . . .'  It cannot be analyzed in the way one could analyze 'They are demonstrators.'  The latter is susceptible of a distributive reading; (1) is not.  For example, 'Al is a demonstrator & Bill is a demonstrator & Carl is a demonstrator & . . . .'  So although 'They are demonstrators' is a plural predication, it is not an irreducibly plural predication.  It reduces to a conjunction of singular predications.

How about a relational reading?  'Sam and Dave met'  cannot be understood in terms of 'Sam met & Dave met.'  You have to bring in a dyadic relation: Msd.  McKay argues that this sort of approach cannot work for examples like (1).  I'll assume he is right for the space of this post.

McKay also rejects set-theoretical, mereological, and other forms of singularism.  Accordingly we cannot take 'they' in (1) to refer to some one single thing over and above individual persons whether this single thing be a set or a mereological sum, or anything else.  If sets are abstract entities (i.e., causally inert and nonspatial), then it is clear that no set can surround a building.  It is not clear to me that no other sort of whole could serve as the logical subject of the predicate 'is surrounding the building.'  But for present purposes, I will just assume that singularism is out.

The idea, then, is that in some cases, (1) being an example, predication is irreducibly plural.  In such predications, there is no one single item which is the logical subject of the predication. I am having some trouble deciding whether this is a coherent notion.  I have the inchoate sense that, in that case, we wouldn't know what we are talking about.  Let's try to make this inchoate sense less inchoate.

Suppose one and the same building is being surrounded by some Commies and some Nazis.  Bill assertively utters a token of (1) thereby referring to the Commies.  (Bill intends to refer to the Commies and succeeeds in so referring using a token of (1).)  Peter assertively utters a token of (1) thereby referring to the Nazis.  Mike assertively utters a token of (1) thereby referring to both the Commies and the Nazis.  Bill and Peter and Mike at the same time and in the same context are referring to three different groups using tokens of the same sentence-type.  We may even assume that the three use exactly the same type of sweeping arm gesture to draw attention to the people surrounding the building.

But how is it possible that Bill, Peter, and Mike are referring to three different groups if there are no groups?  Whatever a group is, and it needn't be an abstract entity, it is a single item distinct from its members, though of course not wholly distinct from them inasmuch as it cannot exist without its members existing.  But if there are no groups, and there are just the demonstrators, then 'they' in (1) has no definite reference as used by Bill, Peter, and Mike.

What my example shows is that 'they' in (1), if it is taken to be an irreducibly plural referring term, cannot be taken to refer to all of the demonstrators, for it could just as easily be taken to refer to some of them (the Commies) or some others of them (the Nazis).  'They' therefore has no definite reference.  Lacking a definite reference, the sentence of which it is a part lacks a definite sense.  But if (1) lacks a definite sense or meaning, then there is no point in attempting an analysis of that meaning.

So what are we talking about when we utter (1) in the context described?  If it is just assumed that 'they' in (1) refers to all the demonstrators, then it is being assumed that there is some unifying feature that makes it precisely them who are being referred to, the feature of being a demonstrator, say.  But then how could there fail to be a 'collective entity' corresponding to this feature?  It might not be a set (as defined by standard set theory); it mght not be a sum (as defined by standard mereology); but there would have to be some one single collective entity distinct from the demonstrators.

I don't believe I am expressing "singularist prejudice" here.  I am not just assuming that there cannot be irreducibly plural predication.  I gave an argument, the Bill-Peter-Mike argument, for the incoherence of irreducibly plural predication.  That 'they' in (1) could have a definite reference without there being anything at all that collects the individual persons I find incoherent. 

A similar problem arises with

2. Demonstrators are surrounding the building.

It doesn't mean that each is surrounding the building, nor does it mean that some set is surrounding the building.  (2) looks to be an irreducibly plural predication:  the demonstrators are surrounding the building.  But again we can ask: all of them or only some of them?  Either way, (2) could be true.

Presumably (2) means that all the demonstrators are surrounding the building, both the Commies and the Nazis in terms of our earlier example.  But (2) cannot mean that all the demonstrators are surrounding the building if the predication is irreducibly plural. For if the reference of 'demonstrators' in (2) is purely plural, absolutely plural, then it is indeterminate with respect to all or some.  For the reference to be determinate, for (2) to mean that all the demonstrators are surrounding thre building, a 'collective entity' of some sort must be brought into the analysis.  I grant, however, that it cannot be a mathematical set.

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11 responses to “Irreducibly Plural Predication: ‘They are Surrounding the Building’”

  1. Quinn Avatar
    Quinn

    It has always sounded funny to me to ask what a particular word refers to. Words do not refer to anything. Human beings use words to refer to things. Referring is a kind of speech act, or an integral part of some speech act; referring is not a property of words, or something words do. Strictly speaking, words don’t do anything.
    Do you agree? Does that help?

    Reply
  2. Philoponus Avatar
    Philoponus

    Bill,
    How about this. As is fairly common in ordinary language, (1) and (2) are compressed compound statements. (2) asserts (a) demonstrators are standing around (adjacent to) the building, and (b) the positions of these demonstrators could be roughly said to encircle or surround the building. (a) clearly reduces to a series of singular predication. (b) is a relational statement that says if we plot the position of each demonstrator on a 2D grid, a simplest point-to-point line thorough their positions may be said (roughly) to encircle the hotel. We have a mixed quantification over people and their positions, to be sure, but no mysterious groups or abstractions (unless we want to posit them).

    Reply
  3. Bill Vallicella Avatar
    Bill Vallicella

    Quinn,
    I agree with you that a word, by itself, does not refer to anything. We refer to things using words. But it doesn’t follow that one cannot study sentence meaning in abstraction from speakers. For example, one doesn’t have to bring in speakers to study the logical difference between
    1. They come from many different countries
    and
    2. They are old enough to vote.
    (1) obviously does not mean that each of the persons referred to comes from many different countries. (2), however, does mean that each of the persons referred to is old enough to vote. Since ‘they’ in (1) cannot refer to any person, we can sensibly ask what it does refer to.
    To accommodate your point, I merely have to spell out the last sentence as follows: Since ‘they’ in (1) cannot be used by a speaker to refer to any person, we can sensibly ask what a speaker is referring to when he uses ‘they’ as it figures in (1).
    So your point, though correct, does not help resolve the issue under discussion.

    Reply
  4. Bill Vallicella Avatar
    Bill Vallicella

    Phil,
    If you are free tomorrow afternoon at 3 you should join us at Peter’s place. I bought a case of Fat Tire at Costco this afternoon.
    So you think that (2) — Demonstrators are surrounding the building — can be analyzed using the resources of standard predicate logic with ordinary distributive predication and
    relations along these lines:
    (i) Each demonstrator occupies a position near the building
    and
    (ii) The positions of the demonstrators are so related that they are connectable by line segments which form a polygon that approximates a circle around the building.
    That makes sense, but McKay has an argument against relational approaches like this. Above, I just assumed that relationism is out in order to raise the question whether irreducibly plural predication makes sense.
    McKay’s approach to a sentence like (2) is to reject both singularism and relationism in favor of irreducible plural predication.
    I should write a separate post on why he rejects relationism.

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  5. William Avatar
    William

    >>If you are free tomorrow afternoon at 3 you should join us at Peter’s place. I bought a case of Fat Tire at Costco this afternoon.
    This sounds great. I take it ‘Fat Tire’ is a beer rather than a bicycle.
    On irreducibly plural predication, how about
    (*) Alice and Bob and Carol surrounded the tree.
    You have none of the problems that you seemed to have with ‘they’, and the predicate
    — and — and — surrounded the tree
    seems to be irreducibly plural. For that matter
    — loves —
    is irreducibly double. What’s the problem?
    I wish I was there having a beer with you. We have just had a barbecue here in London and there is some white wine in the freezer.

    Reply
  6. Bill Vallicella Avatar
    Bill Vallicella

    Fat Tire is technically an ale. An excellent brew made in Fort Collins, Colorado. I bought 24 12 oz bottles for $21.99 at Costco, a wholesale outlet. In a bar you would pay 400-500% more.
    I’m not following you. ‘…Loves—‘ is a two-place predicate. Plug the gaps and you get a sentence, e.g. ‘Alice loves Bob.’ But this sentence contains no plural referring devices. ‘Bob and Carol love Alice’ features the plural term ‘Bob and Carol.’ But this we can parse as ‘Bob loves Alice & Carol loves Alice.’
    What is in question, however, is whether there are irreducibly plural referring terms.
    You are welcome to join us anytime, though right now it’s a tad warm. There is a direct British Airways flight from London to Phoenix. The service is good, and I’ll pick you up at the airport.

    Reply
  7. William Avatar
    William

    >>What is in question, however, is whether there are irreducibly plural referring terms.
    I thought the question was whether there can be predication which is irreducibly plural. I take it we can always replace ‘they’ with a list of referring terms ‘a and b and c …’. Proof: for every ‘they’, there must be some true identity statement ‘they are a and b and c …’. For example ‘they are in love’. Who are ‘they’. Answer, Bob and Alice.
    The real question is whether we can take a plural referring term consisting of a list of singular terms ‘Bob and Alice and ..’ and replace the plural predicate with a list of singular predicates. For example, we can replace ‘Alice and Bob are American’ with ‘Alice is American and Bob is American’. But we can’t do the same with ‘Alice and Bob are in love’. This is not the same as ”Alice is in love and Bob is in love’.
    So I wonder if there is an analogy between irreducibly double predication, and irreducibly plural predication.
    >>You are welcome to join us anytime, though right now it’s a tad warm. There is a direct British Airways flight from London to Phoenix. The service is good, and I’ll pick you up at the airport.
    Well I would like to join you for the ale, and the warmth is only a bonus but I fear I would be a little late for the party. Have a good evening.

    Reply
  8. William Avatar
    William

    Are there not two questions here?
    (1) Are there predicates which are irreducibly polyadic? – E.g. ‘John loves Alice’. Clearly yes.
    (2) Are there predicates which can’t even be analysed in terms of relations between the singular terms?
    Does McKay argue for (2)? You mention above that he criticises the relational approach.

    Reply
  9. David Brightly Avatar
    David Brightly

    Bill,
    Do you not think that your argument re (1) reveals the ambiguities in the pronoun ‘they’ rather than any putative incoherence in the idea of an irreducibly plural predicate? Wouldn’t the argument go through just as well if we used a distributive predicate such as ‘— are badly dressed’?
    Likewise, with (2) ‘demonstrators’ is somewhat ambiguous. It can either be taken indefinitely as ‘some demonstrators are surrounding the building’, and the non-distributive plural sense in ‘surrounding’ tells us that ‘some’ here means ‘several’ rather than ‘at least one’. Or it can be taken definitely as ‘the demonstrators are surrounding the building’, where ‘the demonstrators’ refers to some previously identified or well-known persons, a, b, c…, and the meaning is the same as ‘a, b, c… are surrounding the building’. Does either of these resolutions of ‘demonstrators’ lead to an incoherent sentence?

    Reply
  10. Bill Vallicella Avatar
    Bill Vallicella

    Yes indeed there are two questions — and I thought you were conflating them.
    It is clear that ‘loves’ is, on the face of it, polyadic. But whether it is irreducibly polyadic is not so clear. In the spirit ff Plato, Aristotle, Leibniz and others, one could try to reduce relational propositions to conjunctions of monadic propositions.
    But the question before us is whether there are predications(e.g. ‘Those people have the building surrounded’) which cannot be understood with only the resources of standard logic.
    Yes, McKay argues for (2). Have you read his book or only corresponded with him?

    Reply
  11. Bill Vallicella Avatar
    Bill Vallicella

    Compare
    1. They are in love (with each other)
    2. They are Americans.
    Context: you see a man and a woman holding hands in a bar, etc. Obviously ‘they’ in (1) can be replaced by ‘Alice and Bob’ say. So the plural term ‘they’ in this context can be reduced to the plural term ‘Alice and Bob.’ The same goes for the ‘they’ in (2).
    But (2) means the same as ‘Alice is an American & Bob is an American’ while (1) does not mean ‘Alice is in love with each other & Bob is in love with each other.’
    So it APPEARS that the predication in (1) is irreducibly plural. The question is whether this is really the case, or whether (1) can be analyzed to dispel the appearance.

    Reply

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