I will propose an 'intensional' theory of
Main empirical argument comes from DP-external subatomic quantifiers
Absolute atoms are often used in analyses of
If we give up on
Analysis with absolute atoms
a.
b.
Counting modififers/quantifiers count absolute atoms, and never complex entities
Counting and non-counting quantifiers
"Most of the suitcases are yellow."
"I drank most of the coffee"
The cover distributivity operator Δ quantifies over absolute atoms
Certain expressions access parts of absolute atoms (Link 1983, Krifka 1990, Wągiel 2018, 2019)
To account for sub-atomic phenomena, we need another order,
Whenever
But
Alternatively, Cheirchia 1998a,b, 2010 maintains that all such cases are also built on atomic entities
If
We can then postulate
Part in part of the NP is probably a mass noun, with existential force coming from something else
Some of the NP might be underlyingly Some NP of the NP
This suggests:
This should be true in both scenarios, but is only true in the second case
This suggests:
If
Partly needs to know if the number property of the head noun of its 'associate'
This is unlikely to be syntactic agreement, given that none of the sentences are unacceptable
How does partly access the necessary information compositionally?
To save
But I think that'll have unwelcome consequences, at least conceptually
Δ: Homogeneous distributivity operator (details omitted here)
Atomic | Sub-atomic | |
---|---|---|
partly | ❌ | ✅ |
all | ✅ | ✅ |
mostly | ✅ | ✅ |
half | ✅ | ✅ |
mostly | ✅ | ❌ |
Δ | ✅ | ✅ |
If there are no absolute atoms, how do DP-external quantifiers know what to quantify over?
My answer: Count nouns have the intensional effect of making
Partly presupposes that the current domain doesn't have relative atoms, so cannot be in the direct scope of a plural count noun
Operators like Δ reset the current domain
Intensional effects
∴ partly can directly operate on the extensions of singular count and mass nouns
A mass and a plural may be co-extensional, but differ intensionally
Caveat: I will be formally sloppy in certain compositional details. See the Appendix of the handout version of this talk for more formally precise details
Extensions of number morphology don't require reference to absolute atoms
Key assumption: number morphology, including mass/count, has intensional effects
New aspect of intensionality: restricted domains
Notation:
The VP is interpreted relative to this new restricted domain,
Assumption: Nouns take scope at the DP edge and intensionally affect both NP and VP. Extensionally they simply reconstruct (cf. Charlow 2014, 2020)
Counting modifiers/quantifiers like numerals require relative atoms
This accounts for why it's bad to say "three furniture", "six logo"
Complication: 'How many triangles are there?', von Neumann universe
Without absolute atoms, we reanalysed
Empirical motivation: Semantic restrictions on DP-external quantifiers like partly
Key idea: Plural count nouns introduce relative atoms; some expressions need them
Consequence: One domain and one partial order
(Skipped: Comparisons with other similar theories: Rothstein 2010, Landman 2011, 2016, Sutton & Filip 2016, Rothstein 2017, Sutton & Filip 2017)
pan
bread
san-ko
three-
/
/
san-hon
three-
/
/
san-mai
three-
/
/
san-kin
three-
/
/
san-hukuro
three-
Cf. Schwarzschild 1995
Relatedly, how to account for relative atoms of conjunction and disjunction
In the present system, all nouns can be seen as group nouns
Co-extensional nouns may differ in intensional aspects (this logo, these letters)
A cat is more than the collection of its parts; so is a committee
Plural to group shift might be reponsible for the not so clear judgments in some cases
Cf. Erbach & Sudo 2023 on potatoes
'How then did you come, on foot, or in a chariot?'
'I did not come, Sir, on foot. I came in a carriage.'
'Then if you came, Sire, in a carriage, explain to me what that is. Is it the pole that is the chariot?'
'I did not say that.'
'Is it the axle that is the chariot?'
'Certainly not.'
'Is it the wheels, or the framework, or the ropes, or the yoke, or the spokes of the wheels, or the goad, that are the chariot?'
And to all these he still answered no.
'Then is it all these parts of it that are the chariot?'
'No, Sir.'
'But is there anything outside them that is the chariot?'
And still he answered no.
'Then thus, ask as I may, I can discover no chariot. [...]'
And Milinda the king replied to Nâgasena, and said: 'I have spoken no untruth, reverend Sir. It is on account of its having all these things—the pole, and the axle, the wheels, and the framework, the ropes, the yoke, the spokes, and the goad—that it comes under the generally understood term, the designation in common use, of "chariot."'
'Very good! Your Majesty has rightly grasped the meaning of "chariot."'