So the phrase ‘these two things’ actually refers to three things? Makes no sense to me.
BV: Perhaps it makes no sense to you because you think that 'thing' can only mean 'material thing.' We agree that 'these two shoes' refers to exactly two shoes, each of which is a material thing, and that there is no third material thing of which they are members. So if that is what our nominalist means when he denies that the two shoes form a plurality, then we agree.
Here is a slightly more complicated example. You have a bolt B and a nut N that fits the bolt, i.e., N can be screwed onto B. Now there is clearly a difference between B, N unconnected and B, N connected. But even here I will grant that there is no third material thing wholly distinct from B and wholly distinct from N when B, N are connected. There is no third material thing 'over and above' the connected bolt and nut. Here is exactly what you have and no material third thing in addition:
Disagreement may begin to set in when I point out that the weight of the object depicted above is strictly greater that the weights of the bolt and the nut taken separately. The total weight is additive such that if the nut weighs 2 ounces and the bolt 16 ounces, then the weight of the object depicted is equal to 2 + 16 = 18 ounces. The predicate '___weighs 18 ounces' is not true of the nut, and it is not true of the bolt, and it is not true of any material third thing 'over and above' the object depicted, and this for the simple reason that there is no such third material thing.
So what is the predicate '___ weighs 18 ounces' true of? I say that it is true of the plurality the sole members of which are N and B. I am not further specifying the nature of this plurality. Thus I am not saying that it is a mathematical set, nor am I saying that it is a mereological sum. I am saying that there is a distinction to be made between a plurality of items and the items.
Note that if our nominalist were to say that a plurality is exhausted by, or reduces to, its members, then will have given up the game by his use of 'its.' So he has to somehow avoid that locution.
Our nominalist will grant that the predicate '___weighs 18 ounces' is not true of the nut, not true of the bolt, and not true of any third material thing wholly distinct from the bolt and the nut. But he might say that it is not true of anything. The predicate is flatus vocis, a mere word, phrase or sound to which nothing extramental and extralinguistic corresponds. I reject this view. It implies that the nut threaded onto the bolt has in objective reality no weight that is the sum of the objective weights of the nut and bolt taken separately.
Our nominalist seems committed to an intolerable linguistic idealism. Suppose all language users were to cease to exist. It would remain that case that the weight of our nut-bolt combo would equal 18 ounces. It would remain the case that Earth is spheroid in shape and has exactly one natural satellite.
But why is he a nominalist in the first place? Is it because he thinks that only material particulars exist? If that is true then of course there cannot be a plurality of two material particulars. Hilary Putnam: "Nominalists must at heart be materialists . . . otherwise their scruples are unintelligible." (Phil Papers, vol. I, 338)
Is he a nominalist because he is an empiricist who thinks that only sensible particulars exist? I see the nut, I see the bolt, I see the nut threaded onto the bolt; but I don't see any plurality of material particulars. Is our man restricting what exists to that which is empirically detectable via our senses and their instrumental extensions (e.g., microscopes, telescopes, etc.)?
Is he both a materialist and an empiricist? How do those two positions cohere?
