zero as grammatical number?

[priscianic]

But we don't have an example of negative grammatical number to look at! Negatives are weird-- McCawley, to give an old example, wanted to always handle them at the S level. We don't need to look above the NP if we don't look at negatives, but extrapolating from that to a hypothetical negative grammatical number is unwarranted.

You're right that in principle we could give a hypothetical zero number a drastically different semantics than singular or plural or dual. But if zero number was drastically different from singular or plural or dual etc., then it would be highly unlikely that a linguist describing a language would end up describing that "zero number" as a grammatical number (rather than, e.g. an affixed negative quantifier).

Now now, an adjective is not an argument. What's "drastically different" about generalizing from what we know about grammatical number, and what we know about negation? Negation leads to a lot of complications, so it's not saying much to say that the analysis would be different.

I think I've been clear on my view that, if a linguist were to stumble upon a language with a marker that does what you've been describing (e.g. something with the semantics of a negative quantifier), they would likely describe it as an affixed negative quantifier, rather than as a zero number. (Maybe as a concrete comparison, you could imagine a hypothetical linguist looking at things like thing - things - nothing (maybe imagine a language where this is more robust), and imagine if they would describe that as a singular, plural, and zero number, or as singular, plural, and an affix that creates a negative quantifier.) But I suspect we won't get far debating which hypothetical is the most likely hypothetical, so I'll drop this thread here.

But really, I made that comment because you were talking about cat-ZERO as Ø, which you recognized leads to problems, and I was trying to present an alternative. It's my intuition, but I don't think the hypothetical "Cat-ZERO slept here" is a statement about the set of no cats. It's a statement about the set of cats-that-slept-here. And when you think of it that way, there's no problems with the cardinality of the set being any number.

I...don't understand how you're having intuitions about the semantic properties of nonexistent abstract objects like "zero number". What I did in my post was stipulate a semantics for zero number, one that was a natural extension of the semantics of grammatical number, and explore some of the properties of that semantics. I don't know how you could do anything else besides that, when talking about hypothetical formal objects.

I don't see a difference here; we are both speculating, hopefully by extrapolating from concepts that do exist. If speculation is wrong, I would point out that you are the one who claims to have proven something by speculating about nonexistent objects.

Fair enough. (Again, it still seems to me unlikely that, if faced with some kind of affixal marking on nouns that has the semantic properties of a negative quantifier, a linguist would describe that as a zero number, rather than a negative quantifier. But again, I don't think we'll get anywhere discussing this.)

BTW, this goes for other numbers too. If I say "One cat slept here and one cat slept there", I'm still not talking about a set of one cat, and in fact pragmatically the two sets must be different. The relevant sets are still "the cats who slept (here/there)".

Again, not sure why you're assuming that the semantics of numerals necessarily tells us anything about the semantics of grammatical number.

I think we're running into problems here because (in this discussion at least) you're a splitter and I'm a lumper. You're focused on how grammatical number, numerals, and quantifiers differ; I'm focused on how they're the same. And this is mostly a matter of focus, not ultimate truth. Of course I recognize that these things differ... but languages are full of weird little differences, and that doesn't prevent us from abstracting upwards. To me it's obvious that these things are related, and I find it bizarre that you expect that each category tells us nothing about the others.

Of course it's true that certain aspects of the meaning of numerals and grammatical number are the same, at least on an intuitive level. But I don't think this intuitive similarity necessarily means that, once you explicitly spell out a semantics for numerals and grammatical number, that they should be the same. I think this is similar to how zero and the empty set are intuitively quite similar, but they aren't formally the same kind of object. Numerals and grammatical number are intuitively quite similar, but that doesn't mean that they are formally the same kind of object.

I think the difference between us isn't (fundamentally) about lumping vs. splitting, but rather a different kind of focus: I'm coming at this from the point of view of formal semantics, whereas (I assume) you're coming at this more intuitively. So I care about formalizing the meaning of different expressions in a precise way, hopefully to accurately capture their range of entailment patterns, interactions with other kinds of operators, etc. Since grammatical number and numerals have different semantic behaviors, if you look at them closely, you'll be forced to give them different kinds of denotations. So for me, the "weird little differences" are important clues that tell you things about the formal properties of numerals vs. grammatical number.

(I guess this is just a roundabout way to say that I'm a "splitter" and you're a "lumper", but it's me tying that to a different kind of theoretical/conceptual/philosophical/whatever background.)

I'm not sure why you're making that assumption. Is it supposed to hold for all grammatical numbers? i.e. is singular supposed to be semantically equivalent to the numeral one? Or is it a special assumption you're making just for our hypothetical zero number?

Try to keep our different orientations in mind here. Do I think singular is the same as "one"? No, I expect there to be quirky differences, like everything else in language. Do I think they are completely unrelated? No, I think their prototypical meanings both involve 1*. I think we've disagreed before about prototypes and your natural classes, so if the disagreement is there we're going to have to just let it rest.

Yeah, I think we've disagreed before about the formal structure of the meanings of functional items (I think the notion of "prototypical meanings" is not a good way of formalizing the meaning of functional items), and I don't think this thread is the right place to rehash this. Happy to let it rest.

* Or maybe "not plural", in a singular/plural system. Maybe singular is unmarked. I'm curious what you'd think of the earlier discussion Brad, Richard W, and I were having about alignments and null marking, starting here: viewtopic.php?p=41619#p41619

I think that "alignment", at least as it's used in the typological literature (e.g. to discuss morphosyntactic alignment in agreement, case-marking, syntax, etc.), should be thought of as a purely descriptive term, rather than any kind of fundamental primitive of the language faculty. I think that there are various kind of different properties, processes, constructions, etc. that epiphenomenally give rise to patterns that can be described as nom-acc, erg-abs, etc. I'm coming at this from the point of view of a generative linguist who believes that certain properties of natural language are innate to humans (i.e. I believe in UG), whether built-in to some language-specific part of human cognition, or whether they arise epiphemenally from the interaction of independent properties of human cognition, but similar points have been made by linguists of a very different theoretical/philosophical background, e.g. Scott DeLancey in "The Blue Bird of Ergativity".

So, to a certain extent, I think that much of the debate in that discussion is a debate about the "right way" to describe something, which isn't actually very interesting to me personally, and I don't really have much of a stake in it. If your description framed in terms of morphosyntactic alignment accurately characterizes the data, then it's just as good (at being a description of the data) as any other description framed in terms of morphosyntactic alignment. I don't think any theory framed in terms of morphosyntactic alignment is the "right" theory of what's actually going on in the human language faculty. To me, much of the discussion there kind of feels like the debate whether we should use π or τ as our circle constant: both options work, and it doesn't really have an impact on what's going on "under the hood".

Re: the points about null marking: I do think there is a formal difference between a morpheme that's realized as null, versus something that's just not there. And there are, in principle, ways to tell the difference, even if it might be very difficult. I think a good example of an argument for the presence of a morpheme that's realized as null is Matthewson (2006), who looks at temporal reference in St’at’imcets, a language which doesn't have any overt markers of tense. She ends up arguing that it does actually have tense markers that really are there (at least in the syntactic representation that compositional semantics makes reference to). In particular, she argues that St’at’imcets has a single nonfuture tense, which is realized as null.

In contrast, for instance, Pancheva and Zubizarreta (2020) argue that, in Paraguayan Guaraní, another language without overt tense markers, you really just don't have semantic tense on any level. And they provide a semantics for temporal interpretation that makes do without the semantic category of tense. NB: "tense" here (and also in Matthewson 2006) is a technical term: it refers to operators that introduce a temporal variable (the "reference time", or "topic time"), and tell you something about how it relates to the time of utterance/time of evaluation—whether it precedes/coincides/follows the time of evaluation. Pancheva and Zubizarreta (2020) propose that, in Paraguayan Guaraní, you're always manipulating the time of evaluation, rather than a reference time introduced by a tense operator. They sort of end up saying that you're basically always using the historical present in Paraguayan Guaraní.

There are other differences. If you imagine that chip-s is semantically identical to more than one chip, then you'd predict that the following questions should be identical:

(1) Did you eat chips?
(2) Did you eat more than one chip?

Now imagine a scenario where you've only eaten one chip, and someone asks you either (1) or (2). For (1), you could answer "yes", but for (2), you couldn't. This seems to suggest that there's a semantic difference between plural marking and the complex numeral expression more than one. (Facts like these are also the reason why some people want to include atoms/singularities in the denotation of plural nouns, which I briefly alluded to in my original reply.)

Neat example! I would point out, though, that "chips" in (1) can be taken as either a plural, or as a sort of mass noun, and thus (1) can be answered either yes or no. The example doesn't work so well with things firmly on the count-noun side. "Did you explore planets?" is much harder to construe as a mass noun, so it'd be hard to answer "yes" if you only explored Earth today.

I'm not sure what "‘chips’...can be taken...as a sort of mass noun" means, formally, so it's hard for me to evaluate that proposal. (But I suspect that this thread will lead us too far astray, so I'll drop this as well.)

I think the question did you explore planets? is already quite odd by itself, so I can't really have any judgments about possible answers to it. But you could add an any or some in there (did you explore any/some planets?, and it's still possible to answer "yes" if you've only explored one planet. If you want to stick to a theory where plural marking means "strictly more than one", then you'd have to say something special about some or any such that they allow you to reintroduce singletons into the denotation of planet-s.

If you still aren't convinced by this example that plural NPs include singletons in their extension, I'd refer you to Sauerland, Andersson, and Yatsushiro (2005) for other kinds of arguments.

(3) No men can lift the piano.
(4) Zero men can lift the piano.

(3) only has a quantificational reading: there doesn't exist any men that can lift the piano. In other words, the piano is too heavy for anyone to lift. (4) has both a quantificational reading, which seems identical to (3), in which the piano is really heavy, but it also has a (somewhat fantastical) generic reading, something like "generally, groups that contain zero men have the capability to lift the piano", and in that reading the piano is so light that it literally lifts itself, or it can levitate, or something like that. Another (semantic!) difference between no and zero!

Also neat, but I'm not sure I agree. Consider a dialog:

A: That piano is heavy. It'd take three men to lift it.
B: No, no, it lifts itself. You don't need three men, or any men. No men can lift the piano.

There may be a difference in that "zero" is more likely to be used to contradict another number. ("Chomsky hasn't written one readable book, it's zero.")

That's interesting. I think I can replicate that judgment in your example, but it does read as somewhat strained to me. Of course, I'm already theoretically biased against that judgment, so my judgment perhaps is to be taken with a grain of salt.

[zompist]

Just to clarify a few points where I think you misunderstand me or I was unclear...

I think the difference between us isn't (fundamentally) about lumping vs. splitting, but rather a different kind of focus: I'm coming at this from the point of view of formal semantics, whereas (I assume) you're coming at this more intuitively.

I use plenty of intuition, sure, but that's how I was taught-- my prof was in the generative semantics camp, and that was during the period when every class discussion, or every paper, might discover something new. And when no one had unquestionable authority in syntax. And my approach to semantics is highly influenced by Lakoff, McCawley, and Ross.

If you want to stick to a theory where plural marking means "strictly more than one",

I don't; I already said I expect quirks. As it happens prototype theory is good at this: we could say the prototypical meaning of the plural is "more than one", but an easy and systematic extension of this is to collectives. (If we say "I like dogs", it's not strictly speaking a claim to like more than one dog. We could express the same sentiment using the singular: "For pets, there's nothing better than a dog.")

[KathTheDragon]

If you want to stick to a theory where plural marking means "strictly more than one",

I don't; I already said I expect quirks. As it happens prototype theory is good at this: we could say the prototypical meaning of the plural is "more than one", but an easy and systematic extension of this is to collectives. (If we say "I like dogs", it's not strictly speaking a claim to like more than one dog. We could express the same sentiment using the singular: "For pets, there's nothing better than a dog.")

Then there's the old joke: "What's better than a dog? Two dogs."