1. sports
2. climbing

Almost as a ‘variable-force’ modal∗
Andrew McKenzie
University of Kansas
[email protected]
Lydia Newkirk
University of Kansas
[email protected]
WCCFL 33 ◦ Mar. 27, 2015
1i Summary
◦ almost is a necessity counterfactual, weakened by domain restriction
◦ meaning depends on conversational backgrounds: circumstantial modal
base and expectation ordering source
◦ understand almost when closeness isn’t a factor
◦ apply insight from understudied languages : almost is like the ‘variableforce’ modals in PNW languages
◦ sketch out the role of context in JalmostK
◦ explore differences with ordinary counterfactuals
1
Observations and puzzle pieces
2i The basics of almost
∗
Many thanks we offer to Aynat Rubinstein, any audience at KU, Marianne McKenzie,
Eric Wenski, Eliza Wilcox, Samuel and Carol Newkirk, the KU College of Liberal Arts
and Sciences, the KU Undergraduate Research Center, and almost all our anonymous
reviewers.
1
(1)
I almost climbed Mount Everest.
(Horn, 2002) : two basic components of meaning
1. polar condition : I didn’t climb ME = ¬p(w) = 1
2. proximal condition : I got close to climbing ME :
◦ scalar alternatives I made it to a stage close to completion
∃q ≈ p & q(w) = 1
Horn (2002), Penka (2006), Amaral and Del Prete (2010)
◦ modal closeness In some close accessible world, I climbed ME
∃w0 ≈ w & p(w0 ) = 1
Sadock (1981), Rapp and von Stechow (1999), Morzycki (2001)
We will follow a modal account, but not one of closeness
3i Closeness isn’t a requirement
You can do practically nothing and still almost do it
(2)
(3)
John almost killed Harry (McCawley, 1972)
´
Emile
almost kissed Ad`ele.1 (Martin, 2005)
This applies to climbing Mount Everest: impediments at any stage can
stop you, but almost remains felicitous
(4)
I almost climbed Mount Everest, but. . .
◦
◦
◦
◦
◦
◦
◦
◦
1
I ran out of oxygen near the summit
The weather got bad
I broke my leg halfway up
I got sick at base camp
The Sherpas went on strike
Nepal wouldn’t grant me a visa
I couldn’t raise the money
I decided to stay home and eat Cheetos
´
Or in the original French, Emile
a failli embrasser Ad`ele.
2
4i Polar intuitions
Polar condition : not just ¬p ; there is some particular impediment.
but-clause follow-ups can highlight these, as we saw
The impediment causes the failure of some of the necessary conditions
for p
5i Refining the polar condition
(5)
NEC(p)(w) :=
the smallest Q ∈ P(W) such that w ∈ p ↔ w ∈ ∩Q
The polar condition states that w doesn’t hold for any member of some
subset of NEC(p)(w)
(6)
JalmostK ≈ ∃Z[ Z ⊆ NEC(p)(w) & w ∈ ∪Z . . .
◦ entails ¬p(w)
◦ provides an anaphor for the proximal condition (we’ll see)
◦ explains why:
– almost is upward entailing
– the polar condition can be negated
– evaluative adverbs ignore polar condition
(they ignore any restrictor)
Nouwen (2006)
6i Proximal intuition
On the modal accounts2 , the modal force is one of possibility, since
removing the impediment does not guarantee success.
(7)
2
I almost climbed Mt Everest, but the weather turned bad halfway up.
→ in some close world(s) where the weather stays good, I climb
Mt Everest
Sadock (1981); Rapp and von Stechow (1999); Morzycki (2001)
3
However, our intuition is clear that (7) is more confident: I would have
succeeded.
Is almost a necessity modal after all?
7i Variable force?
Switching examples makes this question even starker
Context: You lost a basketball game 72-71, after missing a last-second shot
(8)
We almost won the game. → strong would reading
Context: You lost a basketball game 72-67. It was tied with five minutes to
go, but then your star player got hurt.
(9)
We almost won the game. → could reading
(8) is clear necessity / (9) is clear possibility
Almost thus seems to have a variable modal force. What is the motivation for the change?
8i St’´at’imcets modals
ka deontic/circumstantial modal
(10)
´
´
´
zuqwsas
ka ta sk’ukwmi7ta
ti7 ku swuw’a,
lh-cw7´aoz-as
it kill
IRR DET child
DEIC DET cougar, COMP - NEG -3
kw s-quscit´ıtas
DET NOM -they shoot it
‘That cougar would/could have killed a child if they hadn’t shot
it’3
Ctxt 1 : The cougar had been on a rampage and had a child cornered.
(→ would / X almost )
Ctxt 2 : Cougars sometimes kill children when they venture into builtup areas (→ could / # almost )
3
The gloss has been simplified a bit for presentation
4
9i ‘Variable-force’
◦ ‘Variable-force modals’ are found in several American languages
◦ Their modal force isn’t actually variable
◦ Almost’s probably isn’t, either
◦ Variety of mechanisms for resolving these
St’´at’imcets
Gitksan
Nez Perce
Rullmann et al. (2008)
∀, weakened by
domain restriction4
Peterson (2010)
∃, strengthened by
domain restriction
Deal (2011)
∃, varies with
entailment environment
Almost behaves most like the St’´at’imcets kind
10i Ordering source
Rullmann et al. employ a choice function, but Peterson and others:
Ordering source instead
An ordering semantics restricts the domain to ideal accessible worlds
Based on Kratzer (1981/2012) Portner (2009).
We assume the Limit Assumption.
4
Kratzer (2012) suggests we can replace this kind with upper-end degree modals.
5
11i Weakening necessity
An ordering source doesn’t reliably weaken necessity on its own
A second ordering source does weaken it.
◦ von Fintel and Iatridou (2008) : One OS remains a priority
(11) You ought to take Route 2
OS 1 : Get to Boston in under 3 hours
OS 2: Take the scenic route (but still get to Boston)
◦ Sequential ordering: The results of the first ordering are run through
the second5
Best for OS 1 = The worlds where you get to Boston in under
three hours
Best for OS 2 = the worlds where you take the scenic route
and get to Boston in under three hours
5
Katz et al. (2012) offer an ordered merging of premise sets to get the same result
without a sequence: g*(w) = g1 (w) ∗ g2 (w)
6
12i Weakening necessity
13i Relative strength
The ratio of scenic Boston worlds / Bestg0 (w) (Bestg(w) (∩f(w))) to Boston
worlds / Bestg(w) (∩f(w)) will give the strength of necessity:
7

1 · strong




→ 0 weak
|Bestg’(w) (Bestg(w) (∩f(w)))|
(12)
=
|Bestg(w) (∩f(w))|




0 · infelicitous (empty domain)
14i Contextual effects
If OS is important, context should affect modal strength. For almost, it
does.
(1)
I almost climbed Mt Everest
◦ Turning point : where the impediment takes place
◦ Circumstances : what had happened up to the turning point
◦ Expectations : of what would ensue
As circumstances and expectations lower, modal strength weakens.
15i Adjusting circumstances
8
16i Adjusting expectations
17i Summary of the hypothesis
◦ almost is a ‘variable-force’ modal of the St’´at’imcets type.
◦ necessity modal affected by context
◦ actual closeness isn’t always required
◦ circumstances have an effect on strength
◦ so do expectations
◦ these can be linked to conversational backgrounds (Kratzer 2012)
– circumstances : modal base
– expectations : ordering source
2
Analysis
18i Denotation for almost
Given that restricted modal base, we can build a denotation for (verbal)
almost (mixing sets and functions, we know)
9
(13)
JalmostK = λghs, hst, tii λg0 hs, hst, tii λfhs, hst, tii λpst λws .
∃Z[ Z ⊆ P(NEC(p)(w)) & w 6∈ ∪Z &
∀w0 [ w0 ∈ Bestg’(w) (Bestg(w) (Cw (Z))) → w0 ∈ p ] ]
Given conversational backgrounds g, g0 , f; proposition p, and
world w:
There’s a set of propositions Z such that Z is a subset of conditions necessary for w ∈ p that don’t hold of w, and such that in all worlds w0 that
are most ideal with respect to g0 out of those most ideal with respect to g,
where Z holds and Z is compatible with the circumstances of w0 , w0 ∈ p
READ :
semi-formally: There’s a set missing necessary conditions that, when
assumed, and when compatible with the circumstances, entails p in the
most ideal accessible worlds.
19i For example
Context: I climbed halfway up Mt Everest, when the weather turned bad and
I had to quit
(1)
I almost climbed Mount Everest (in w0 )
1. Turning point : when the weather turned bad
2. Necessary conditions: NEC(p)(w0 ) / Z
I decide to climb Mt Everest
I raise the funds
I fly to Nepal
I arrive at base camp (+ weather/health)
I climb up halfway (+ w/h)
¡2-¿I climb to the last camp (+ w/h)
I take the last step (+ w/h)
3. Modal base : the circumstances that led to/permit the turning point
fc (w0 )
10
Mt Everest is in Nepal, etc.
I decide to climb Mt Everest
I raise the funds
I fly to Nepal
I arrive at base camp
I climb up halfway
20i Counterfactual supposition
The meaning of almost adopts the propositions in Z as true premises.
This set is combined with the modal base: fc (w0 ) ∪ Z
(14)
Cw (Z) := ∩H, where H is the maximal consistent subset in fc (w) ∪
Z such that fc (w) ⊆ H
Let us suppose that Cw0 (Z) = { w1 , w2 , w3 , w4 , w5 , w6 }.
21i Realistic worlds
The first ordering source is realistic, gR (w).
Since it involves reality, it includes the circumstances (fc (w0 )). This already removes most oddball worlds.
It also includes the negation of the supposition
As such, it might not order the worlds in Cw0 (Z), if they’re all equally
good or bad with respect to reality. But let’s suppose for this case that one
world is removed to select the most realistic ones:
(15)
BestgR (w) (Cw0 (Z)) = { w1 , w2 , w3 , w4 , w5 }
22i Expected worlds
The second ordering source is expectational, gE (w). This leaves only
the worlds best satisfying some set of expectations.6
6
We have not really investigated whose expectations it has to be. This ought to be
some source of further variation or speaker disagreement.
11
gE (w0 ) = expectations
w1
If I decide to CME, I will raise the funds X
If I raise the funds, I will fly to Nepal
X
If I fly to Nepal, I will climb to base X
camp
If I climb to base camp, I will reach
halfway
If I reach halfway, I will reach the last
camp
If I reach the last camp, I will reach the
summit
BestgR (w0 ) (Cw0 (Z))
w2 w3 w4
w5
X X X
X
X X X
X
X X X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
BestgE (w0 ) (BestgR (w0 ) (Cw0 (Z)))
The Best of the best worlds are { w1 , w2 , w3 , w4 } : the most expected
among the most realistic
23i Calculating strength
The ratio of the number of expected worlds to the number of realistic
worlds gives us the strength
|most expected worlds among the most realistic|
|most realistic worlds|
|Bestg (w ) (Bestg (w ) (Cw0 (Z)))|
E
R
0
0
|Bestg (w ) (Cw0 (Z))|
R
0
=
= strength
|{w1 ,w2 ,w3 ,w4 }|
|{w1 ,w2 ,w3 ,w4 ,w5 }|
=
4
5
=
relatively
strong
24i Circumstance effect
We saw that changing circumstances affects the necessity of almost.
This emerges from these ratios: The closer you get to actual success, the
higher the ratio.
|BestgR (w) | |BestgE (w) | Strength
I decide to climb ME
12
3
0.25
I raise the funds
9
3
0.33
I fly to Nepal
8
3
0.38
I arrive at base camp
7
3
0.43
I climb up halfway
6
3
0.50
I make the last camp
5
3
0.60
I take the last step
3
3
1.00
12
25i Expectation effect
Expectation effects will affect the size of BestgE (w0 ) . The worse the expectation, the fewer Best of the best worlds you’ll have. This also weakens
almost, by lowering the ratio.
I decide to climb ME
I raise the funds
I fly to Nepal
I arrive at base camp
I climb up halfway
I make the last camp
I take the last step
|BgR (w) |
12
9
8
7
6
5
3
high expectation
|BgE (w) |
Str.
3
0.250
3
0.333
3
0.375
3
0.425
3
0.500
3
0.600
3
1.000
low expectation
|BgE (w) |
Str.
1
0.083
1
0.111
1
0.125
1
0.143
1
0.167
1
0.200
1
0.333
26i Summary of the analysis
◦ Almost is a necessity counterfactual
◦ A circumstantial modal base preserved despite the supposition
◦ A realistic ordering source
◦ An ordering source delivering expectations
◦ The nature of these CB’s determines the most ideal worlds
◦ The ratio of expected worlds to realistic worlds = strength
. . . but what happens when it fails?
3
Failure
27i Means to fail
◦ Unlike PNW modals, negation can scope above almost
(16) We didn’t almost win.
◦ And of course, almost statements can be false or infelicitous
13
◦ Jalmost pK ' There is a Z that missing that, when assumed and compatible with circumstance, entails p.
◦ Jnot almost pK ' Either there is no Z missing, or there’s no Z compatible
with circumstance that when assumed, entails p.
28i Working out a failure
◦ (polar) No Z missing : p holds, so almost p is infelicitous.
(17) We didn’t almost win, we did win.
◦ (proximal) No Z compatible with circumstance that when assumed,
entails p.
Z isn’t compatible with circumstance, or it is but doesn’t entail p.
(18) We didn’t almost win, we got blown out.
29i Low expectation
If we lower expectation so the strength is 0.000, the set of ideal worlds
is empty → vacuous quantification
Context: We lost the basketball game 125-57. It was 70-9 at halftime.
(19)
#We almost won the game
Skill difference → expectation of winning is nil
|BestgR (w) | |BestgE (w) | Strength
circumstances
12
0
0.000
(Question : Does failure only occur at 0.000? Or could there be a limit slightly
above 0.000?)
14
30i Interfering circumstance
If the supposition is inconsistent with the circumstances, almost fails.
Context: I was in Vancouver yesterday, arriving for the conference
(20)
#I almost climbed Mount Everest yesterday (in w0 )
NEC(p)(w0 ) here includes the proposition n, that I was in Nepal.However,
in fc (w0 ) is v, that I was in Vancouver yesterday. Supposition adds n to the
modal base.
(21)
fc (w0 ) ∪ {n} ⊇ { v, n }
Propositions v and n are incompatible— Cw0 (Z) removes the supposition n.
So the modal worlds are those where I’m in Vancouver. Those can’t be worlds
where I’m climbing Mount Everest the same day, so the use of almost fails.
31i Interfering circumstance
By eliminating the supposition, it is no longer a counterfactual modal
base. But the polar condition of almost specifies that it is a counterfactual.
We end up with a contradiction.
This explains the inability of certain types of impediments to be the
focus of almost
Presuppositions:
(22)
#I almost kissed the King of France yesterday, because there is no King of
France
Non-transient properties:
Context:
Bill is blind. He went to Paris last
week, and walked right past the Eiffel Tower.
(25)
#Bill almost saw the Eiffel Tower, but he’s blind.
Context: Sam sees well. He went to Paris last week, and right before he got
to the Eiffel Tower, a mime blinded him with a strobe light, and scurried away.
Unable to see for a bit, he walked right past the Eiffel Tower.
(26) Sam almost saw the Eiffel Tower, but he was blinded.
15
32i Summary of failure
almost p is infelicitous when
◦ p is true
◦ there is no Z that when assumed, entails p
– no compatibility of Z w/ circumstance: contradictory counterfactual
– expectations set strength to 0: no most ideal worlds
This account of failure also lets us explain several other facts about
almost
4
Further explanations
4.1
Differences from counterfactuals
34i No idle supposition
Sometimes, a true would-CF corresponds to a false almost-clause
(23)
a. The Aztecs would’ve beaten the Romans
b. #The Aztecs almost beat the Romans
Ordinary counterfactuals (OCf) allow pretty much any supposition,
overt or not. Almost does not, because it only allows suppositions compatible with the circumstances.
(24)
a. (assuming a lot), Noam Chomsky would’ve won the 1976 Presidential
Election
b. #Noam Chomsky almost won the 1976 Presidential Election
(25)
a. Marie would’ve killed Josie, if she hadn’t died before Josie was born
b. #Marie almost killed Josie (if she hadn’t died before Josie was born)
35i No overt modification
OCf allow modification by if -clauses. Almost does not, even if the supposition expressed is fine.
16
(26)
a. I would’ve climbed Mt Everest if I had the money
b. * I almost climbed Mt Everest if I had the money
(27)
a. If she’d aimed higher, Josie would’ve killed Marie.
b. *If she’d aimed higher, Josie almost killed Marie.
The reason doesn’t seem purely semantic, since you can refer to these
clauses later:
(28)
4.2
a. I would’ve climbed Mt Everest. . . but I didn’t have the money
b. I almost climbed Mt Everest. . . but I didn’t have the money
A myriad of readings
37i Additional result
Various readings of almost have been derived by scope with a decomposed predicate
(29) Josie almost killed Marie
(`a la McCawley (1972))
(non-incipient / counterfactual)
almost [ ACT(Josie) CAUSE BECOME (dead(Marie)) ]
(non-descriptive / scalar)
ACT(Josie) almost [ CAUSE BECOME (dead(Marie)) ]
(non-culminating / resultative)
[ ACT(Josie) CAUSE BECOME almost [ (dead(Marie)) ]
Dowty (1979) already pointed out problems with decomposition of English verbs.
Rapp and von Stechow (1999) reduce these readings to two, and rely
on scope within the extended verbal projection
38i Single meaning for almost
◦ With an ordering account we can reduce it to one meaning
◦ Different turning points → different circumstances → different readings
17
◦ Linguists can group these together
(29) Josie almost killed Marie
a Josie considered
b Josie decided yes
non-incipient
c Josie aimed
d Josie fired
non-something
f The shot hit Marie
g It hit a vital organ
h Marie bled out
non-culminating
i Marie died
[ does not hold ]
That said, placement of almost affects its complement, which affects
NEC(p)(w), etc.
4.3
Scalar effects
40i Need for closeness
Classically, almost requires closeness. Especially if quantifiers are involved.
(30) Sarah almost met 10 heads of state
(31) We almost watched every Tarantino movie last weekend
But it’s easy to find contexts where closeness doesn’t matter.
Context: Sarah was invited to a party where everyone would meet indefinite
10 heads of state. She opted not to go at the last minute.
(32) Sarah almost met 10 heads of state is true
18
41i Finally some proximity
What about cases where proximity does seem to matter?
Context: Sarah ate 27 chili peppers
(33) Sarah almost ate 30 chili peppers
(34)
#Sarah almost ate 50 chili peppers
Again, it depends on the circumstance and the expectation.
The circumstances get us very close to 30, and little expectation is required.
For the 50-pepper target, the circumstances don’t get us very close, and
there’s even less expectation of success.
42i Non-proximal reading
But we can think of a context where we do expect to finish.
Context: I was in a pepper-eating contest, to 50. I was on a good pace to eat
50, and had eaten 27, when some idiot pulled the fire alarm and we all had to flee.
(35) I almost ate 50 peppers
The circumstance doesn’t get close, but the expectations are strong for
finishing, and almost is licensed.
5
Wrap up
43i Sum up
JalmostK ' There is a set Z of missing necessary conditions for p in w,
such that when Z is compatible with the circumstances of w and hold of
the most expected realistic worlds accessible to w, Z entails p.
◦ Almost behaves like a variable-force modal
◦ i.e. its force doesn’t vary
◦ its force is shaped by conversational backgrounds
◦ it differs in key ways from other counterfactuals
◦ it delivers a myriad of readings, which don’t require closeness
19
44i Possible areas of variation
◦ Different ordering sources
◦ Different modal bases (practically, virtually (Morzycki, 2001))
◦ Gitksan style almost’s (∃w + DR strengthening)
◦ Location in the sentence (scope, focus, quantifier almost)
45i The end
Thank you!
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