On Vagueness

The various problems of vagueness1 can be brought into a common form that is something like the following:

For any concept/category X, either there is a strict boundary separating X and not-X or there is no such boundary. If there is no such boundary and there are some cases/examples that are neither completely/clearly X nor not-X, either there is a strict boundary between X and [not-X or neither X nor not-X] or there is no such boundary, and similarly for the boundaries between not-X and [X or neither X nor not-X]. We can repeat this process until either (1) we find a (strict/precise) partition of the space of possible X-candidates2 into degrees of X-ness; or (2) the process doesn't converge to anything, except as far as our limited resolution can meaningfully distinguish. In either case, it's hard to escape some notion of strict boundaries between degrees of concept membership.

The proper solution to is that the boundary between X and not-X (for any particular X) is often irrelevant. For a statement about X-ness to have meaningful implicative potential, it needs to be relevant for something else. If that something else is specified, much of the result's counterintuitiveness vanishes.

The end/purpose to which the judgment of X-ness is supposed to be relevant also modulates what should influence the judgment of X-ness. Discussions of the sorites paradox, for example, often implicitly assume that baldness is a property of the number of hair. This I question.

If one really wanted (and had the means to do so), one could take an adequately accurate emulation of a human mind,3 show to each several photos of the same person except modified so as to have a different number of hair, and then test what is the number of hair at which a person goes from "bald" to "not-bald" (according to that particular experimental subject).4

But here's what I predict5 we would find. We would find that the threshold depends on the experimental subject, the experimental object,6 the contingencies of the subject's (neuro)physiological7 state, the way in which the hair are being removed or added, etc. In short, the judgement bald/non-bald will turn out to be a function of not just the number of hair but of a bunch of other stuff.

Would it tell us something Important about the True™ meaning of the word "bald"? Of course not. Sure, in the limit of emulation we might be able to find a multidimensional surface separating bald heads from non-bald heads and we would also find a similar partition of the space if we allowed some non-zero number of in-between-ish categories.8 But this doesn't tell you much. An input-output table is a wrong model for this sort of situation.

A less wrong model for this sort of situation is: judgments of baldness are context-dependent and directed towards some possible uses (affordances). A characteristic9 feature of a meaningful judgment is that it has a high implicative potential. For example, the exact number of hair doesn't matter. What matters is whether this person looks sufficiently bald to be included in the category of bald people (for example, for the purpose of easy singling them out in a crowd), or whether this person's number of hair is abnormal given their health, age, sex, etc., or whether they recently shaved their head (because normally they would not be expected to be bald), etc.

The true name of a concept often is not a sharp boundary is some low-level-of-abstraction feature space, but rather its intended use.

Footnotes

  1. See, e.g., SEP on vagueness and the Sorites paradox. ↩

  2. Here, "X-candidates" being examples/cases for which it makes sense to ask "Is this thing X or not-X?". ↩

  3. Or use a redaction machine. ↩

  4. To the extent that humans behave somewhat stochastically in these settings, the experimenter can obviously include that as well; although as far as I know, human behavior is surprisingly deterministic (citation needed but see e.g. here). ↩

  5. Although I don't expect this prediction to be verifiable, at least not with humans. ↩

  6. "Experimental object" meaning the person whose head (or rather whose head's image) is being modified to determine the threshold of baldness. ↩

  7. Or whatever is the equivalent of physiology in a whole brain emulation. ↩

  8. Personally, I am inclined to think that it usually makes most sense to include exactly one in-between-ish category (e.g. "neither bald, nor non-bald"). ↩

  9. The characteristic? ↩