Nominalism Presupposes What it Denies

What makes a pair of shoes a pair and not just two physical artifacts? Nominalist answer: nothing in reality. Our resident nominalist tells us that it is our use of 'a pair' that imports a unity, conventional and linguistic in nature, a unity that does not exist in reality apart from our conventional importation. We are being told that out there in the world there are no ones-in-many, let alone any ones-over-many. If that is  right, then there are no sets. For a set is a one-over-many in this sense: it is one item distinct from its many members. (Let's not worry about the null set, which has no members and unit-sets or singletons which have exactly one member each. Here lies yet another rich source of aporiai, but one problem at a time.) 

If there are no sets, then there are neither finite sets nor infinite sets. There are just pluralities, and all grouping, collecting, subsuming under common rubrics, unifying, etc. is done in language by language-users. What I will try to show is that if you think carefully about all of this you will have to make distinctions that are inconsistent with nominalism. 

My aim is purely negative: to show that the nominalism of the resident nominalist is untenable. If you have read a good amount of what I have written you will recall that I am a solubility skeptic, which in this instance means that I am not endorsing any realist solution of the problem. I am not pushing an opposing theory. 

I will start with some data that I find 'Moorean,' i.e., rationally indisputable and pre-theoretical.  (Unfortunately, one man's datum is another man's theory.) The phrase 'a pair' has a sense that remains the same over time and space, a sense that is the same for all competent speakers of English whether here or abroad. The same holds for ein Paar in German, and similarly for all languages. The sense or meaning of an expression, whether word, phrase, sentence, etc. must be distinguished from the expression.  An expression is something physical and thus sensible. The sensible is that which is able to be sensed via one of our senses.  I hear the sound that conveys to me the meaning of 'cat,' say, or I see the marks on paper. Hearing and seeing are outer senses that somehow inform us or, more cautiously, purport to inform us of the existence and properties of physical or material things that exist whether or not we perceive them. But I don't hear or see the meaning conveyed to me by your utterance of  a sentence such 'The cats are asleep.' The sentence, being a physical particular, is sensible; the meaning is intelligible. That's just Latin for understandable. I hear the words you speak, and if all goes well, I understand their meaning or sense, thereby understanding the proposition you intend to convey to me, namely, that the cats are asleep. Note that while one can trip over sleeping cats, one cannot trip over that the cats are asleep.

There are two distinctions implicit in the above that need to be set forth clearly.  I argue that neither is compatible with nominalism

A. The distinction between the sense/meaning of a linguistic expression and the expression. Why must we make this distinction? (a) Because the same sense can be expressed at different times by the same person using the same expression. (b) Because the same sense can be expressed at the same and at different times by different people using the same expression. (c) Because the same sense can be expressed in different languages using different expressions by the same and different people at the same and at different times. For example the following sentences express, or rather can be used to express, the same sense (meaning, proposition):

The cat is black.
Il gatto è nero. 
Die Katze ist schwarz.
Kedi siyah.
Kočka je černá.

So the sense of a word or phrase or sentence is a one-in-many in that each tokening of the word or phrase expresses numerically the same sense.  A tokening, by definition, is the production of a token, in this case, a linguistic token.  One way a speaker can produce such a token is by uttering the word or phrase in question. Another way is by writing the word or phrase down on a piece of paper. (There are numerous other ways as well.)  This production of tokens therefore presupposes a further distinction:

B. The distinction between linguistic types and linguistic tokens. In the following array, how many words are there?

cat
cat
cat

Three or one? Is the same word depicted three times? Or are there three words? Either answer is as good as the other but they contradict each other. So we need to make a distinction: there are three tokens of the same type. We are forced by elementary exegesis of the data to make the type-token distinction.  If you don't make it, then you will not be able to answer my simple question: three words or one?

You see (using the optical transducers in your head, and not by any visio intellectualis) the three tokens. And note that the tokens you now see are not the tokens I saw when I wrote this entry. Those were different tokens of the same type, tokens which, at the time of your reading are wholly past. Linguistic tokens are in time, and in space, which is not obviously the case for linguistic types. I said: not obviously the case, not: obviously not the case.   You see the three tokens, but do you see the type of which they are the tokens? If you do, then you have powers I lack. And yet the tokens are tokens of a type. No type, no tokens. So types exist. How will our nominalist accommodate them? He cannot reduce types to sets of tokens since he eschews sets. No sets, no sets of linguistic tokens. Linguistic types are multiply instantiable. That makes them universals. But no nominalist accepts universals.  Nominalists hold that everything is a particular.  I grant that the rejection of sets and the rejection of universals are different rejections. But if one rejects sets because they are abstract objects, one ought also to reject universals for the same reason.

Now glance back at the first array. What we have there are five different sentence tokens from five different languages.  Each is both token - and type-distinct from the other four. 

To conclude, I present our nominalist with two challenges. The first is to give a nominalist account of linguistic types without either reducing them to sets or treating them as ones-in-many or ones-over-many. The second challenge is to explain the distinction between the sense or meaning of an expression, which is not physical/material and the expression which is.

Suppose he responds to the second challenge by embracing conceptualism according to which  meanings are mental.  Conceptualism is concept-nominalism, as D. M. Armstrong has maintained. My counterargument would be that the meaning/sense expressed by a tokening of 'The cats are asleep'  is objectively either true or false, and thus either true or false for all of us, not just for the speaker. Sentential meanings are not private mental contents.  Fregean Gedanken, for example, are not dependent for their existence or truth-value on languages or language-users.  

 

Comments

[oz]

>the first [challenge to the nominalist] is to give a nominalist account of linguistic types without either reducing them to sets or treating them as ones-in-many or ones-over-many.<

But the Ockhamist does adhere to a ‘one over many’ approach. Ockham:

For just as every word, howeversomuch common by convention, is truly and really singular and one in number because it is one thing and not several things, so an intention of the soul (intentio animae), signifying several things outside the mind, is truly and really singular and one in number, because it is one thing and not several things, though it signifies many things.

>The second challenge is to explain the distinction between the sense or meaning of an expression, which is not physical/material and the expression which is.

The Ockhamist would speak of signification of an expression, by means of which the expression can supposit for (i.e. denote) many things. You correctly point out that language is common to all, and will not work unless what the word signifies is the same for all. That is indeed a significant (!) challenge for nominalism (and any theory of meaning, not just Ockhamistic).

[BV]

Ockham hasn't met the first challenge. Yes, the word is one over against the many to which it refers, but what is needed in a one-in-many on the side of reality. As for the intentio animae, it won't cut the mustard for the reason given when I discussed the second challenge. Not only is it on the side of the subject and not on the side of reality, it is merely private and subjective, not intersubjective. 'The planets between Earth and Sun' has an objective, hence intersubjective meaning.

Is there are difference in reality between two shoes and a pair of shoes? Yes by my lights. If there are two shoes in my closet it does not follow that they make a pair. Hence the corresponding phrases cannot have the same reference.

And what about 'two shoes'? Neither shoe is two, so the subject of 'two' must be a third item.

[oz]

>And what about 'two shoes'? Neither shoe is two, so the subject of 'two' must be a third item.<

No! "There are two shoes" means the same as "there is a shoe and there is another shoe". If there is a third item implied by the first, there must be a third item implied by the second.

In which case "there is one thing and there is another thing, and there are no other things" is necessarily false. Which it isn't.