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.