From the mail:
I saw your blog post the other day titled Saying and Showing where you talked about Wittgenstein's exchange with Russell on 'things', along with his Kantian perspective. Toward the end you say this: "What goes for 'world' also goes for 'thing.' You can't count things. How many things on my desk? The question has no clear sense. It is not like asking how many pens are on my desk. So Wittgenstein is on to something. His nonsense is deep and important."
In fact, E. J. Lowe says something similar toward the beginning of his book The Possibility of Metaphysics. However, I have never entirely understood the motivation behind this claim. It seems to me that, as a matter of fact, a man *can* count the number of things on his desk. There will certainly be very *many* things (the composite objects, their parts down to the atoms, and so forth), but what stops them from being *in principle* counted? [. . .]
Let's begin by clearing up an ambiguity. I can count the cats in my house; cats are things (in the very broad sense in which the term means the same as: object, entity, existent, being, item); and so one might think that one can count things. I'll grant that. But what we cannot do -- and this was my claim --is count things as things. I can sensibly ask how many cats, cat whiskers, unicorns, pachyderms, and bottles of tequila are presently in my house, and I can sensibly give the following answers: 2, <40, 0, 0, 1. What I cannot do is sensibly ask how many things or existents are in my house.
Why is this? Well, when I count Fs, what I am doing is counting instances of the concept F. To count I need a concept, a classificatory device. To count the spatulas in a drawer I have to have the concept spatula. I have to know what 'counts' as a spatula. I have to know WHAT a spatula is to know whether there are any and how many there are. I have to be able to identify a particular item as a spatula (as opposed to, say, a ladle) and I have to be able to re-identify it -- so that I don't count it twice. To count three spatulas and two ladles I need the concepts spatula and ladle. That makes five utensils. How many electrical appliances? Zero. In each of these cases, what we are counting are the instances of a concept.
How many utensils in the drawer? Five. How many entities? This question has no clear sense. The question presupposes that some definite answer is possible in terms of a finite or even a transfinite cardinal. But any answer given, whether 5 or 50 or aleph-nought will be arbitrary. Do we count the handle of the ladle as distinct from the rest of it? Is one ladle two entities? But of course, parts themselves have parts, and they have parts, etc. Suppose the ladle is ultimately composed of simple (indivisible) bits of matter. Suppose there are n such bits. In the region of space occupied by the ladle are there n entities or n + 1 entities? Is the whole ladle countably distinct from its parts? Or is the whole ladle just those parts? (Compare van Inwagen's denial of artifacts.) And what about the space occupied by the ladle? It is not nothing! So do we count it too when we count the entities in the drawer? And the time during which it exists?
And then there are properties and relations and relational properties and perhaps also property-instances. Do I count the properties of the spatula and the relations in which it stands to the other things in the drawer when I (try to) count the entities in the drawer?
Suppose in the drawer there is a triangular piece of mental. Now everything triangular is trilateral, and vice versa. And this is true as a matter of broadly-logical necessity. So, when I count (or try to count) the entities in the drawer, do I count triangularity and trilaterality as two properties or as one property?
From considerations like these one can see that the question How many entities? has no clear sense. We can give a sense to it, but that would involve the arbitrary imputation of conceptual content into 'entity.' Suppose I define:
X is an entity df= x is either a feral cat or a piece of cooked seaweed.
That 'definition' would allow me to count the entities in my house. And the answer is . . . (wait for it): zero.
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.
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.
Posted by: Alfredo | Monday, April 09, 2012 at 04:09 AM
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.
Posted by: John | Monday, April 09, 2012 at 06:51 AM
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.
Posted by: Bill Vallicella | Monday, April 09, 2012 at 02:20 PM
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!
Posted by: Bill Vallicella | Monday, April 09, 2012 at 02:42 PM
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.
Posted by: Bill Vallicella | Monday, April 09, 2012 at 03:14 PM
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.
Posted by: Alfredo | Monday, April 09, 2012 at 10:33 PM
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.
Posted by: Bill Vallicella | Tuesday, April 10, 2012 at 05:01 AM