Vagueness, definitions and translations

If we are to define a vague term, the definiens will need to be vague in exactly the same way as the definiendum is. But it is exceedingly improbable that the contextual profile of the vagueness of the definiens would exactly match the contextual profile of any complex definiendum that we could practically state, or maybe even that we could state in principle.

For instance, suppose we're trying to define "short". Now, "short" has a certain contextual vagueness profile which specifies, perhaps vaguely, in what context what lengths do and do not count as short and in what way, Either there is vagueness all the way up or at some level we get definiteness.

Suppose first that at some level we get definiteness. For simplicity, suppose it's after the first level of vagueness. Then for any context C, there will be precise lengths x₁ and x₂ such that anything shorter than x₁ is definitely short, anything of length between x₁ and x₂ is vaguely short, and anything longer than x₂ is definitely non-short. These precise lengths will be some exact real numbers determined by our actual linguistic practices—which things we've called "short" and which we haven't. It is exceedingly unlikely that we could construct a definiendum which will make the definitely/vaguely/definitely-not transitions in exactly the same spot. Suppose, for instance, we define "is short" as "has small length." Well, small will have its own vagueness profile, defined by a different set of social practices. It is exceedingly unlikely that this vagueness profile would exactly correspond to that of "is short", so that the exact point of transition between being definitely short and vaguely short should be the point of transition between being definitely of small length and being vaguely of small length.

Suppose now that we have vagueness all the way up. Then we're going to have arbitrarily long predications like "a is vaguely definitely vaguely vaguely vaguely definitely definitely vaguely definitely short." And which such predications apply to which objects will be determined by our complex linguistic practices surrounding "is short". It is, again, exceedingly unlikely that our complex linguistic practices surrounding some other term, like "has small length" would in every context match those of "is short".

For exactly the same reason, except when the users of one language self-consciously use a term as an exact translation of a term used by another language, it is exceedingly unlikely that we could find an exact simple translation of a vague term from one language to another, and for the same reasons as above, a complex translation is also unlikely. For we would have to exactly match the vagueness profile, and since the social practices underlying the different languages are subtly and unsubtly different, it is very unlikely we would succeed.

It may be worse than that. It may well be that no two people have the same vagueness profile in their homophonic terms, except when both defer in their usage to exactly the same community. And they rarely do.

In practice, when translating and giving dictionary definitions, we are satisfied with significant similarity between vagueness profiles.

More on conjunctive characterization

In an earlier post, I had argued that there is something generally fishy about conjunctive characterizations of non-stipulative concepts, such as defining a murder as an act that is both a killing and morally wrong. Natural concepts just don't have conjunctive analyses, and so one can typically find counterexamples to conjunctive analyses simply by looking at cases where the conjuncts are coincidentally satisfied (e.g., something might be a killing but be morally wrong for a reason independent of its being a killing, such as because it is also an instance of promise-breaking, and this does not make it a murder). In a post on prosblogion today, I use this fact to refute a particular argument against Molinism.

What I want to offer here is two hypotheses about why conjunctive definitions sound so plausible to us. The first hypothesis, stated in the prosblogion post, is is that conjunctive claims often carry an implicature of relevant connection between conjuncts. If someone tells me that he went to the store and bought a pound of butter, I assume that he bought the pound of butter at that store (order matters here: "I bought a pound of butter and went to the store" carries an implicature that the pound of butter was not bought at that store; in that case, the connection is a negative one). If I am told that Fred intended to meet George and Fred did meet George, I tend to assume that Fred intentionally met George, though that does not strictly follow.

The second hypothesis is that our minds are designed for finding connections. When we read a set of statements, or see a bunch of evidence, we tacitly assume a relation between them. It is not a matter of implicature, because the phenomenon is more than just a linguistic one. I see an open garbage can, and I smell a stink. I assume that what I see and what I smell are the same thing. Often this is justified. But this habit of mentally inserting connections can be pernicious. When we see a bunch of conjoined statements, it is our natural reaction to imagine a situation where they are co-satisfied in a related way. It was the genius of Gettier to show us that in philosophically evaluating a conjunctive characterization we need to look at cases of unrelated co-satisfaction.

At the same time, it may be that some conjunctive characterizations are close to the truth—to get the truth, all we need to add is that the conditions are satisfied in relevantly related ways. It could be that knowledge will be justified true belief once we understand that it must be justified, true and believed in relevantly related ways. (I wonder if what counts as relevantly related might be contextual.) Of course this is not satisfying to the philosopher—we want to make explicit the relevant relation, but perhaps this just cannot be done.