truncation cannot be what that creates this narrowing since there’s a preexisting split between the full meaning and the narrowed one.
Right. Basically, truncation just reveals an existing split. (Whether that is within the same lexeme, or across two, or whatever, I don't know, and the technical details would depend on your theory. This is very interesting evidence to consider though!!)
In other words, truncation doesn’t involve a new meaning just like a suffixation does (for example).
Not in these cases. There are a few instances of so-called "subtractive morphology" in languages, where for example removing the final consonant from a noun might create the plural form. So truncation
can be productive with a consistent meaning, but that's not the case here, and in fact that is very, very rare cross-linguistically. (I'm not sure that more than a handful of uncontroversial examples have been identified, since what I've seen in textbooks/handbooks/overviews is just a few of the same examples cited over and over again. Maybe it's not quite so rare, but it's certainly unusual, and not known in Europe I don't think.)
That leads to consider truncation as an operation of subset selection
Well, it depends on whether that set was properly formed in the first place. It does result in a subset of the meanings, but I just phrased it that way for explanatory purposes. Instead, my hypothesis would be that there are two things in parallel and that truncation simply highlights that they are distinct. Imagine two identical twins who you cannot easily tell apart. But then one gets a very short haircut, and suddenly you can see that they were clearly distinct individuals the whole time even though it was hard to see that.
An alternative possibility would be that truncation actually
changes the meaning (by narrowing it), but I find that less likely. I imagine the narrowing has already occurred at least through frequency in usage, and that the truncation instead highlights that, rather than creating it.
You might argue that the act of truncation is what triggers the split, sort of mixing the two ideas. There was a split ready to be triggered (because speakers are aware of distinct uses/senses), but it wasn't really "split" yet, not until something (truncation) came along to trigger it.
I'm not entirely sure how to determine which theory is correct. But the reason I'm leaning toward the "already split" interpretation is that theories often underestimate the amount of memorization we have done as speakers. Syntactic chunking ("How are you?" is not productively generated each time from a tree structure), or frequency statistics are examples of things that fall outside of generative theories but are part of our 'competence' (knowledge) of the language. Even if we COULD still say it's a single lexeme from a minimal theoretical account, I don't know that we SHOULD, because we already have memorized a lot (including different senses of the 'same lexeme' in this case). So why not just let that be the explanation? Theoreticians don't seem to like relying on performance to explain competence, but it's actually non-minimal to not refer to givens like memory-- they come for free, rather than positing something else additional to explain the data in a theory!
I tend to think that the initial form and the truncated one represent two different lexemes. I have the impression it’s your opinion too.
Not quite. I would say that first there are two "twin" lexemes (or a "complex lexeme" if you prefer). Then one of those becomes optionally truncated, leaving the other behind. Again, refer to the haircut metaphor above.
I'll give a concrete example:
Stage 0: Referee refers to anyone who makes decisions, references, etc. "One who refers."
Stage 1: Referee has several meanings. Speakers know that, and can probably list the meanings without much thought.
Stage 2: Referee in the sense of "sports official" is a particularly common usage/meaning, and for many individuals this is the main meaning with the others considered secondary.
Stage 3: "Ref" enters as a truncated form of the sense in Stage 2.
Now I would say that around Stage 2 (not Stage 3!) the lexeme has split (either internally or externally-- that's a question that must be embedded within a theory).
The issue remains how to describe the semantic relation between the two lexemes.
That's an issue however we analyze this data. Clearly there are similar (but distinct) lexemes at some point. And that's a theoretical question that can have very different answers. I don't have one in particular to suggest here. Whether "lexemes" are even proper constructs on a cognitive level is a good question-- are they really distinct nodes in a network or some sort, or are they just related information dispersed on that network? etc.
I think the hypothesis of synonymy is defendable if we consider that a full semantic equivalence is not necessary. A partial equivalence is sufficient for two lexemes to be synonymous. I admit that leads to other issues.
Many other issues. In fact, I don't know that then "synonymy" would have any value as a theoretical concept, since you're just saying "some lexemes are similar", but not that they are actually somehow tied together.
What's the definition of vagueness that you use ? Because to me a lexeme is vague when its extension can’t be discrete by nature, like the extension of young. I may be wrong, semantic ambiguity is not really my specialism.
There is a distinction between two concepts:
Vagueness/specificity: how narrowly defined something is, and how easily it can apply to different usage.
Ambiguity: when there are multiple but distinct senses for words, which could be listed.
Those two terms are often used interchangeably, but they should not be confused. They are also not related to other non-technical senses of the same words (such as "vague" meaning "intangible").
So a word is vague when it can refer to many different things. Lots of things can be "good" for example, because there is a wide range of usage for "good"-- a "good person", a "good book", a "good idea", and so forth. Note that we cannot very easily identify clearly different meanings, and they all seem to be on a continuum (or various continuums).
On the other hand, a word is ambiguous when it can refer to distinct different things, and when those different things can be listed out, with relatively clear boundaries. For example, that's how I would interpret your original examples of French
manifestation. They are still related ideas, but they are distinct-- it is possible to identify which one.
One test for vagueness vs. ambiguity is whether you can ask "Which one?"-- if so, it's ambiguous. If not, it's vague.