Discussion Forum—A Way with Words, a fun radio show and podcast about language

We often think of words as having concrete meanings. What most words actually have is a denotative compass (a range of possible meanings). The denotative compass is what you find when you look up an entry in a dictionary. In phonetic languages, words import additional meaning cues from their situational environments. So the meanings of categorical pairs can be quite elastic as they move across shifting points of reference. Let's take the example of categorizing a 9-year-old girl.

Is she a woman? Well she's not a woman in the sense of women as distinguished from girls, (maturity reference) but she is a "woman" in the sense of women as distinguished from men (gender reference).

Okay, so she can be a "woman" but not a "man?"

Actually…she's not a "man" in the sense of men as distinguished from women, (gender reference) but she could be a "man" in the sense of men as distinguished from animals (genus reference)…though some might argue this use of man is fading.

Okay, so she can be a "woman"…and maybe a "man," but not an "animal?"

Actually…she's not an "animal" in the sense of animals as distinguished from men, (genus reference) but she's an "animal" in the sense of animals as distinguished from plants (kingdom reference)

Reference-dependent meanings are common and can alter the domain of inclusion in a categorical pair. In the distinction between a fruit and vegetable, for example, tomatoes, squashes, peppers and eggplants are vegetables in the culinary sense (produce with a low sugar content), but fruits in the botanical sense (the ripened seed-containing ovaries of flowers).

One thing to be aware of in parsing distinctions of meaning is the difference between domain-exclusive and domain-inclusive (hierarchical association) comparisons. "What's the difference between an apple and an orange?" is a different kind of question than "what's the difference between a citrus and an orange?" I would argue that your second example is domain-exclusive: no sword is a knife and no knife is a sword. Your third example might be considered domain-inclusive, at least by members of the general public: all daggers are knives, but most knives are not daggers. The notion of jargon, also comes into play here, though. I suppose weapons mavens might make a distinction between point tools used for stabbing and edge tools used for slicing. That would make "knife" and "dagger" domain-exclusive for the lexicon of that particular interest group. Even so, the two are not cleanly disjunct categories as there are certainly examples of daggers/knives that have a cutting edge as well as a stabbing point. The difference between a shrub and a tree is one of those cases where there is a clear distinction at the poles of the domain, but a gray area in the middle that is rather subjective. A blueberry is certainly a shrub. A redwood is certainly a tree. California toyon, the plant you honor with your log-on name, is an example of a plant that might morph from one to the other over its lifetime. Botanically speaking, there is no distinction between a small tree and a large shrub. One of the main reasons biologists so often use scientific nomenclature is to avoid the classification slop that comes from vernacular idioms.
The difference between a sword and a knife is similarly based on scale and probably contains intermediate versions that don't fall neatly into either category.

However, I don't know of a term that would fit the placeholder that would help the two debaters understand the pointless nature of their argument. Is there such a term?

I don't know of any term in linguistics that fits this. This seems to me, though, to have more to do with philosophy than linguistics, and in particular, it has certain implications for inductive logic and nominalism — the branch of metaphysics that questions the existence of abstractions and universals. Since the time of classical Greek philosophers, human knowledge has been divided into two basic realms: things that have been discovered and things that have been invented. Categories are not spatiotemporal entities that have been discovered and whose existence outside the human brain can be empirically confirmed. They are abstract concepts invented by humans, and they have been legislated into being through the use of language. Since categorization is a language-based construct to begin with, we have to question whether the supposed existence of discrete categories has any real merit at all. Tools do not have a unique category into which they fit; multiple categories may prove apt. This leads to a lot of begging-the-question and contemplation of circular argument. The categories were created through language and yet language is an imperfect classifier of what it created.
See also, problem of induction: "http://en.wikipedia.org/wiki/Problem_of_induction"