Misleading language and ontology

Question

Does natural language suggest a different ontological status to different things? I have noticed in our natural language we like to pluralise things sometimes in a way I disagree with. For example, a 'metre' is defined as a certain length, which to me suggests that a length is not really a class of any kind, to say 'a metre' or 'two metres' is incorrect, it is one length.

We do the same with numbers, there is apparently only one number 10 yet we often talk about 'tens' or discuss how many '5s' must be added to get 15.

Are these examples of a somewhat ontologically incorrect view of their objects through natural language? Is there any way of solving this other than using entirely logical languages where classes and their members must be vividly made distinct from one another.

We might use 'a' before a word to describe a member of the 'class' that word defines and it can be very very difficult to see what the type is, what the class is and what the tokens /members are, as it can denote all three. There is 'a cat' there is the class 'cat' and the type 'cat' however there is the type 'green' yet a token of green is not 'a green'.

Answer 1

Yes, natural language does suggest a different ontological status to different things. That observation led to the development of analytic philosophy, which analyses language to identify and correct illusions, particularly in metaphysics and ontology, that are created by ordinary grammar.

One distinction that has been made is between “count nouns” which are for things that can be counted and “mass nouns” that identify things that cannot be counted. “Table”, “Tree” and “Dog” are examples of the former and “Water”, “Sand” and “Stone” are examples of the latter. Some nouns seem to identify a physical object, but don’t. So, before they were understood, “Sky” and “Rainbow” were thought to identify physical objects, but now we know that the colours are just the effect of the sun’s light scattered by the atmosphere or by rain.

“Length” is a bit more complicated, because it is the noun corresponding to an adjective – “long” which gets its meaning by being the opposite of “short”. In the same way, the noun “Redness” corresponds to the adjective “red”, which is a property of physical objects and “anger” corresponds to “angry” which is an emotion. Grammar might lead us to believe that all these nouns must identify some physical object, but they clearly don’t. The word for this process is nominalization.

“Long” and “short” are really vague. When we want more precision, we need to invent something else. When we hold our hands apart to show how long the fish I nearly caught was, we are comparing the length of the fish to the distance between my hands. When I want to know how far it is to the next town, I can count my steps (and “step”, of course, is a count noun, but for an event, not for a physical object, but each step has a certain length). So by counting steps, we get a number for the distance, with all the conveniences that brings.

“Metre” depends on the same trick, except that it is a fraction of the distance round the earth, so it is possible to measure distances and lengths more accurately than by counting steps, which vary, not only in the same person, but also between people. So you are right. A metre is one length and two metres is a different length – twice as long as one metre. But it isn’t incorrect, because behind it, there is a process that defines a standard measure and how to use it.

You are also right that there is only one number 10 yet we often talk about 'tens' or discuss how many '5s' must be added to get 15. (I’m not going to get into the philosophy of mathematics, which is very complicated.) For present purposes, it is best to think of 10s and 5s as temporary nouns for any group of (countable) objects. In the same way, we say that there are 1,000 metres in a kilometre and so on. Then you have to add 5+5+5 to get 15, which is we say that 3 times 5 is 15.

As you can see, there are many cases of an ontologically incorrect view of their objects in natural language. I can’t think of another way of sorting out the misleading ontological implications of ordinary grammar in language than analysing and clarifying the relevant words. At one time, it was thought that formal logic was the best way to do that, but now it is recognized that it is best to rely on informal logic of the kind used in this answer.

This is often very difficult, which is what makes it fun. In your examples, “there is the class 'cat' and the type 'cat' however there is the type 'green' yet a token of green is not 'a green'”. The problem is that you are trying to use the type-token distinction where it does not apply. Colours are defined by reference to samples (each of us has our own), not by types, and the process of colour matching, which is quite different from what makes a token a token of its type. I suggest that the important difference between the class of cats and the type (as you call it) “cat” is that the class has members which satisfy a definition – again a different process from the type-token distinction.

Answer 2

Multiset theory is perhaps relevant; whereas {a, a} reduces to a singleton set in normal set theory, in the multiset context we would keep track of a's "multiplicity" in the baroque containment field (2, in this case, so {a, a, a} has an a-multiplicity of 3, or {a, b, b} has an a-multiplicity of 1 and a b-multiplicity of 2).

Types and tokens (not exactly the same thing as types and their satisfiers in type theory) are such that we might talk about the type of a metered length having two tokens composed as a two-meter length. (There's also the local question of "occurrences" of types; the type/token article discusses this.) In a related vein, trope theory has the "piling" problem:

Consider a particular red rose. Given trope theory, this rose is red because it is partly constituted by a redness-trope. But what is to prevent more than one—even indefinitely many—exactly similar red-tropes from partly constituting this rose? Given [sui generis, as opposed to spatiotemporal, individuation]: nothing. It is however far from clear how one could empirically detect that the rose has more than one redness trope, just like it is not clear how one could empirically detect how many redness tropes it has, provided it has more than one. This is primarily because it is far from clear how having more than one redness trope could make a causal difference in the world. But if piling makes no empirical/causal difference, then given a (plausible) Eleatic principle, the possibility of piling is empty, which means that [sui generis individuation] ought to be rejected (Armstrong 1978: 86; cf. also Simons 1994: 558; Schaffer 2001: 254, fn. 11).

In defense of [sui generis individuation], its proponents now point to a special case of piling, called ‘pyramiding’ (an example being a 5 kg object consisting of five 1 kg tropes). Pyramiding does seem genuinely possible. Yet, if piling is ruled out, so is pyramiding (Ehring 2011: 87ff.; cf. also Armstrong 1997: 64f.; Daly 1997: 155). According to Schaffer, this is fine. For, although admittedly not quite as objectionable as other types of piling (which he calls ‘stacking’), pyramiding faces a serious problem with predication: if admitted, it will be true of the 5 kg object that “It has the property of weighing 1 kg” (Schaffer 2001: 254). Against this, Ehring has pointed out that to say of the 5 kg object that “It has the property of weighing 1 kg” is at most pragmatically odd, and that, even if this oddness is regarded as unacceptable, to avoid it would not require the considerable complication of one’s theory of predication imagined by Schaffer (Ehring 2011: 88–91).