Can Things Be Counted?

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7 responses to “Can Things Be Counted?”

1. 

   Alfredo

   April 9, 2012

   Thank you for the thoughtful response Dr. Vallicella. Here are some of my worries. I have to confess that I am somewhat confused by your argument, but this may simply be a failure on my part to understand. I will try to explain. The meat of your response starts in your third paragraph I think. You pose the question:
   “How many utensils in the drawer? Five. How many entities? This question has no clear sense.”
   So it seems here you are arguing that the question of how many entities there are is simply not well-formed. (Yet surely, if there are no more entities in the drawer, then there are exactly five?) But you say further on to anyone who tries to answer the question that his answer “will be arbitrary.” So now, with the introduction of talk of arbitrariness, it seems the problem is really one of vagueness about when something counts as a thing and when it does not.
   You then present us with many examples of these apparently vague cases. Each of your examples in this paragraph seems to be related to the question of composition. For instance, to take just one quote, you ask, “Is the whole ladle countably distinct from its parts? Or is the whole ladle just those parts?” I think there is a dilemma here though.
   First, your questions here seem to be ones about objects. Now either the terms ‘object’ and ‘thing’ are equivalent, or they are not. If they are not, then your argument from vagueness does not affect our ability to count things, but rather our ability to count objects. On the other hand, if the terms are equivalent then the person who holds to the view where we can count things qua things has a good answer. He will first ask the special composition question in terms of objects: When is it that some plurality of objects composes another object? The nihilist of course says a plurality of objects never composes another object, and the universalist says a plurality of objects always composes another object. The point is not about who is correct, but rather that if we can give a well-formed, cut and dry answer in this way, then your argument from vagueness doesn’t go through. So, either your argument from vagueness does not apply to the countability of things, or your argument from vagueness is not sound.
   With regard to the space, you answer the question yourself. It is not nothing, therefore it is something. But if we’re counting things, then of course we would count it. I think similar considerations can be given for the various other examples you give. Thus, it is not entirely clear that the question of “how many entities?” lacks sense. Even if it did, if I am understanding your argument correctly as being one from vagueness, then I’m not sure your argument would prove it, since the vagueness of a predicate certainly does not imply its meaninglessness. You then lay out a clear argument:
   “To count is to count the instances of a concept. Existence is not a concept that has instances. Therefore, one cannot count existents as existents.”
   But it seems to me the second premise, that existence is not a concept with instances, is precisely what someone who holds to the contrary belief will deny. According to this person, there is a single, univocal sense of ‘being’, or ‘thing’, which is satisfied by absolutely everything. I think Peter van Inwagen’s paper “Being, Existence, and Ontological Commitment” sets this view forth with admirable clarity, particularly in sections titled “Thesis 3” and “Thesis 4.”
   Thanks again for your thoughts. If you have further comments I would like to hear them.

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2. 

   John

   April 9, 2012

   A few comments. From Dr. Vallicella’s claim that the question “How many entities?” is not well-formed, it does not follow that the problem is one of vagueness. Nor does it follow with the additional claim that any answer to the question will be arbitrary. Compare Carnap’s claim that questions asked external to any linguistic framework are not well-formed. One might say that any answer to such a question will also be arbitrary. It does not follow that the problem there is a problem of vagueness. At any rate, I doubt Carnap would have thought it was a problem of vagueness as to which things count as numbers. I’m not even sure what that would be. Problems of vagueness arise due to the sorites-susceptibility of terms. Dr. Vallicella’s claim is not that the word ‘entity’ is susceptible to the sorites paradox. In sum, questions can be ill-formed, and answers to ill-formed questions can be arbitrary, without the problem being a matter of vagueness. This is important because one criticism you offer of Dr. Vallicella is that “the vagueness of a predicate certainly does not imply its meaninglessness”. That’s true, but Dr. Vallicella is not saying that any predicates are vague in the sense required for your claim to be true. You seem to equivocate here on ‘vagueness’.
   Second, Dr. Vallicella clearly takes ‘entity’ to be equivalent to ‘object’, ‘thing’, and other related terms (e.g., ‘existent’ and ‘item’). So he would clearly opt for the second horn of your dilemma. There you say that we can count things qua things by answering van Inwagen’s Special Composition Question – this will allow us to know that the number of things in the world is n (if nihilism is true) or 2^n-1 (if universalism is true). One question here: what if some restricted answer in between nihilism and universalism is true? Will counting things qua things be as easily done? A more important point here, though, is that you’re assuming that what van Inwagen calls a Series-style answer to the Special Composition Question is false. If such an answer were correct, we could not count things, but only things falling under more specific kinds.
   This relates to a more general point. It seems to me that one can believe that there is a single, univocal sense of ‘being’ while simultaneously denying that we can count things qua things or, indeed, quantify over everything. Amie Thomasson in her “Answerable and Unanswerable Questions” seems to affirm that there is a single, univocal sense of ‘being’ while at the same time maintaining that we cannot count things qua things. Likewise, Lowe maintains that it is impossible to employ an absolutely unrestricted quantifier, but that we must always quantify in some restricted fashion. But I do not think it follows from Lowe’s point – or Thomasson’s – that ‘being’ is equivocal. Endorsing an ontology of kinds, denying the possibility of unrestricted quantification, and so on, does not commit one to the equivocality of existence. It seems that to endorse the equivocality of existence is to endorse something like Heidegger’s notion of ways of being, a view which is admirably presented in Kris McDaniel’s 2009 paper “Ways of Being”. Endorsing an ontology of kinds and rejecting the idea that we can quantify in an absolutely unrestricted way does not imply that things enjoy different modes or ways of existence.
   Or so it seems to me.

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3. 

   Bill Vallicella

   April 9, 2012

   As John points out, the question is not about vagueness. Consider these questions:
   1. How many bald people are in the pool?
   2. How many people are in the pool?
   3. How many mermaids are in the pool?
   4. How may entities are in the pool?
   The first question may not have a definite answer if there are one or more border-line bald people in the pool. I am not concerned above with vagueness.
   The second and third questions have definite answers in terms of a finite cardinal number.
   My point is that (4) has no definite answer because we have no idea what counts as an entity.

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4. 

   Bill Vallicella

   April 9, 2012

   I think we can avoid questions about composition as well.
   Suppose there is a drawer in which there are three spatulas and two ladles, making five utensils. Suppose, per impossibile, that each of these items is a simple. In this domain there is no material composition. How many entities in the drawer?
   That question has no definite answer. It is clear that there are five utensils, three spatulas, and two ladles. It is not clear how many entities there are in this domain. Do we count the properties of the utensils or not? If we do, then we get a different answer than if we do not.
   And if we count properties, do we count only monadic properties or also relational properties?
   Is it not now perfectly clear that one cannot count entities as entities?
   To put it aphoristically: you can’t count entities unless you know what counts as an entity!

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5. 

   Bill Vallicella

   April 9, 2012

   We agree (I hope!) that everything exists. That is not trivial since Meinongians deny it. But it certainly doesn’t follow from this that the question How many existents are there? makes sense.
   So it looks as if I agree with John, except for the bit about quantifying over everything.
   We can quantify over what exists and only over what exists. But it doesn’t follow that one can count what exists. John, do you agree with that?
   I reiterate one of my central points: Counting is relative to a concept. I can count the cats in my house because I know what it is to be a cat. But I can’t count existents because existing theings are not a kind of things as Aristotle says in the Prior Analytics. At 998b22 of the Metaphysics, Aristotle says that being is not a highest genus.

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6. 

   Alfredo

   April 9, 2012

   John and Dr. Vallicella
   Thank you for your comments. I find a lot of what you have to say compelling. This makes a lot of sense. I assumed that the reason Dr. Vallicella thought an answer to the question of how many entities there are would be arbitrary is because of some vagueness in the predicate, but you rightly point out that arbitrariness does not necessarily imply vagueness.
   The reason I was thinking a distinction might be made between ‘object’ and ‘thing’ here is due to Dr. Vallicella’s inclusion of relations and properties–platonic abstracta–which are at least in some sense not ‘objects.’ Certainly the special composition question does not deal with objects in this sense.
   This is very helpful. Thanks.

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7. 

   Bill Vallicella

   April 10, 2012

   You’re welcome, Alfredo. Thanks for the comments.
   So did I convince you that existents cannot be counted as existents?
   ‘Object,’ ‘thing,’ etc. are used in different ways by different people. There is no standard terminology and any attempt to enforce one would inevitably beg debatable questions. See http://maverickphilosopher.typepad.com/maverick_philosopher/2009/10/notes-on-philosophical-terminology-and-its-fluidity.html
   for details.

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