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Time and Space V
Pavel Caha
March 27 2023
1 / 24
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Paths and locations
2 / 24
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(1) PATH
PATH
from
LOCATION
PLACE
under
GROUND
the bed
3 / 24
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(2) MOTION DESCRIPTION
FIGURE
the cockroach
EVENT
V
emerged
PATH
PATH
from
LOCATION
PLACE
under
GROUND
the bed
4 / 24
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(3) MOTION DESCRIPTION
FIGURE
the cockroach
EVENT
V PATH
PATH LOCATION
PLACE
under
GROUND
the bed
path verb
5 / 24
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Verb‐framed vs. sattelite framed languages
(4) Spanish
a. Juan
Juan
{ ??corrió/
ran/
*anduvó/*
walked/
gateó
crawled
} a
LOC
la
the
tienda.
store
‘John ran/walked/crawled to the store’
6 / 24
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Verb‐framed vs. sattelite framed languages
(4) Spanish
a. Juan
Juan
{ ??corrió/
ran/
*anduvó/*
walked/
gateó
crawled
} a
LOC
la
the
tienda.
store
‘John ran/walked/crawled to the store’
b. La
the
botella
bottle
entró
moved.in
a
LOC
la
the
cueva
cave
(flotando).
floating
‘The bottle floated into the cave’
(Lit. ‘The bottle went into the cave floating’)
6 / 24
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(5) MOTION DESCRIPTION
FIGURE
la botella
EVENT
V PATH
PATH LOCATION
PLACE
a
GROUND
la cueva
entró
7 / 24
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(6) MOTION DESCRIPTION
FIGURE
Juan
EVENT
V
anduvó
PATH
PATH
XXX
LOCATION
PLACE
a
GROUND
la tienda
8 / 24
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(7) Czech
a. Petr
Petr
{ se plazil/
crawled
belhal
limped
} do
into
obchodu
store
‘Petr crawled/limped to the store.’
9 / 24
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(7) Czech
a. Petr
Petr
{ se plazil/
crawled
belhal
limped
} do
into
obchodu
store
‘Petr crawled/limped to the store.’
(8) MOTION DESCRIPTION
FIGURE
Petr
EVENT
V
se belhal
PATH
PATH LOCATION
PLACE GROUND
obchodu
do
9 / 24
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Paths and aspect (Zwarts 2005)
10 / 24
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3 types of paths
(9) a. Alex swam (*in/for an hour)
11 / 24
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3 types of paths
(9) a. Alex swam (*in/for an hour)
b. Alex swam to the beach (in/*for an hour)
11 / 24
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3 types of paths
(9) a. Alex swam (*in/for an hour)
b. Alex swam to the beach (in/*for an hour)
c. Alex swam towards the beach (*in/for an hour)
11 / 24
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3 types of paths
(9) a. Alex swam (*in/for an hour)
b. Alex swam to the beach (in/*for an hour)
c. Alex swam towards the beach (*in/for an hour)
d. Alex ran around the lake / though the grass (in/for an
hour)
11 / 24
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Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
12 / 24
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Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
12 / 24
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Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
12 / 24
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.
Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
b. The children laughed for a minute / *in a minute
12 / 24
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.
Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
b. The children laughed for a minute / *in a minute
(11) Telic verbs (achievements, accomplishments)
12 / 24
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.
Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
b. The children laughed for a minute / *in a minute
(11) Telic verbs (achievements, accomplishments)
a. John broke the stick in a second/*for seconds.
12 / 24
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.
Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
b. The children laughed for a minute / *in a minute
(11) Telic verbs (achievements, accomplishments)
a. John broke the stick in a second/*for seconds.
b. Mary arrived in two minutes/*for two minutes.
12 / 24
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.
Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
b. The children laughed for a minute / *in a minute
(11) Telic verbs (achievements, accomplishments)
a. John broke the stick in a second/*for seconds.
b. Mary arrived in two minutes/*for two minutes.
c. Michael found gold in just ten minutes/*for two
minutes.
12 / 24
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.
Telicity (situation aspect)
▶ Telos: the natural endpoint of an event
(10) Atelic verbs (states, activities)
a. John remained under the bed for an hour / *in an hour
b. The children laughed for a minute / *in a minute
(11) Telic verbs (achievements, accomplishments)
a. John broke the stick in a second/*for seconds.
b. Mary arrived in two minutes/*for two minutes.
c. Michael found gold in just ten minutes/*for two
minutes.
12 / 24
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divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
13 / 24
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divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
13 / 24
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.
divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
(13) divisivity: Take a predicate P (e.g., chocolate vs. five apples).
13 / 24
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.
divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
(13) divisivity: Take a predicate P (e.g., chocolate vs. five apples).
a. The predicate is divisive if it is possible to split it in two
parts, and the predicate applies to each part (apples,
chocolate)
13 / 24
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.
divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
(13) divisivity: Take a predicate P (e.g., chocolate vs. five apples).
a. The predicate is divisive if it is possible to split it in two
parts, and the predicate applies to each part (apples,
chocolate)
b. The predicate is non‐divisive if it is impossible to split it
in this way (the apple, five apples)
13 / 24
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.
divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
(13) divisivity: Take a predicate P (e.g., chocolate vs. five apples).
a. The predicate is divisive if it is possible to split it in two
parts, and the predicate applies to each part (apples,
chocolate)
b. The predicate is non‐divisive if it is impossible to split it
in this way (the apple, five apples)
(14) cumulativity: Take a predicate P (e.g., chocolate vs. five
apples).
13 / 24
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.
divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
(13) divisivity: Take a predicate P (e.g., chocolate vs. five apples).
a. The predicate is divisive if it is possible to split it in two
parts, and the predicate applies to each part (apples,
chocolate)
b. The predicate is non‐divisive if it is impossible to split it
in this way (the apple, five apples)
(14) cumulativity: Take a predicate P (e.g., chocolate vs. five
apples).
a. The predicate is cumulative if it applies to the sum of
two objects in its denotation (chocolate + chocolate =
chocolate)
13 / 24
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divisivity, cumulativity
(12) a. Michael ate apples/chocolate for an hour/??in an hour.
b. Michael ate the apple/five apples in an hour.
(13) divisivity: Take a predicate P (e.g., chocolate vs. five apples).
a. The predicate is divisive if it is possible to split it in two
parts, and the predicate applies to each part (apples,
chocolate)
b. The predicate is non‐divisive if it is impossible to split it
in this way (the apple, five apples)
(14) cumulativity: Take a predicate P (e.g., chocolate vs. five
apples).
a. The predicate is cumulative if it applies to the sum of
two objects in its denotation (chocolate + chocolate =
chocolate)
b. The predicate is non‐cumulative if it does not apply to
the sum of two objects in its denotation (five apples +
five apples ̸= five apples)
13 / 24
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.
divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
14 / 24
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
14 / 24
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
(16) divisivity: Take a predicate P (e.g., laugh vs. arrive).
14 / 24
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
(16) divisivity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is divisive if it is possible to split it in two
parts (sub‐intervals), and the predicate applies to each
part (laugh)
14 / 24
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
(16) divisivity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is divisive if it is possible to split it in two
parts (sub‐intervals), and the predicate applies to each
part (laugh)
b. The predicate is non‐divisive if it is impossible to split it
in this way (arrive)
14 / 24
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
(16) divisivity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is divisive if it is possible to split it in two
parts (sub‐intervals), and the predicate applies to each
part (laugh)
b. The predicate is non‐divisive if it is impossible to split it
in this way (arrive)
(17) cumulativity: Take a predicate P (e.g., laugh vs. arrive).
14 / 24
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
(16) divisivity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is divisive if it is possible to split it in two
parts (sub‐intervals), and the predicate applies to each
part (laugh)
b. The predicate is non‐divisive if it is impossible to split it
in this way (arrive)
(17) cumulativity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is cumulative if it applies to the sum of
two objects in its denotation (laugh + laugh = laugh)
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divisivity, cumulativity
(15) a. The children laughed for a minute / *in a minute.
b. Marry arrived in two minutes/*for two minutes.
(16) divisivity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is divisive if it is possible to split it in two
parts (sub‐intervals), and the predicate applies to each
part (laugh)
b. The predicate is non‐divisive if it is impossible to split it
in this way (arrive)
(17) cumulativity: Take a predicate P (e.g., laugh vs. arrive).
a. The predicate is cumulative if it applies to the sum of
two objects in its denotation (laugh + laugh = laugh)
b. The predicate is non‐cumulative if it does not apply to
the sum of two objects in its denotation (arrive + arrive
̸= arrive)
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Back to space
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Back to space
(18) He walked through the tunnel for hours.
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Back to space
(18) He walked through the tunnel for hours.
a. divisivity: every sub‐path counts as a path through the
tunnel
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Back to space
(18) He walked through the tunnel for hours.
a. divisivity: every sub‐path counts as a path through the
tunnel
b. cumulativity: yes
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Problems with sub‐paths I
▶ We get atelic events that unfold along non‐divisive paths
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Problems with sub‐paths I
▶ We get atelic events that unfold along non‐divisive paths
(19) He walked along the river for hours / *in an hour.
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Problems with sub‐paths I
▶ We get atelic events that unfold along non‐divisive paths
(19) He walked along the river for hours / *in an hour.
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Problems with sub‐paths II
▶ We get telic events that unfold along divisive paths
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Problems with sub‐paths II
▶ We get telic events that unfold along divisive paths
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Cumulativity works fine I
A path is cumulative if you can connect two paths in the denotation
of the preposition, and the resulting path is still in the denotation.
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Cumulativity works fine I
A path is cumulative if you can connect two paths in the denotation
of the preposition, and the resulting path is still in the denotation.
(20) He walked along the river for hours / *in an hour.
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Cumulativity works fine I
A path is cumulative if you can connect two paths in the denotation
of the preposition, and the resulting path is still in the denotation.
(20) He walked along the river for hours / *in an hour.
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Cumulativity works fine II
A path is cumulative if you can connect two paths in the denotation
of the preposition, and the resulting path is still in the denotation.
NB: such concatenation must be possible for at least some paths.
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Cumulativity works fine II
A path is cumulative if you can connect two paths in the denotation
of the preposition, and the resulting path is still in the denotation.
NB: such concatenation must be possible for at least some paths.
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Summary
▶ cumulative: along the river, towards the house,
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Summary
▶ cumulative: along the river, towards the house,
▶ non‐cumulative: into the drawer, out of the drawer
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Summary
▶ cumulative: along the river, towards the house,
▶ non‐cumulative: into the drawer, out of the drawer
▶ ambiguous: through the tunnel, around the house
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Path typology (Jackendoff 1983)
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Path typology (Pantcheva 2011)
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References
Jackendoff, Ray. 1983. Semantics and cognition. Cambridge, Ma.:
MIT Press.
Pantcheva, Marina. 2011. Decomposing Path. The nanosyntax of
directional expressions: CASTL, Tromsødissertation.
Zwarts, Joost. 2005. Prepositional aspect and the algebra of paths.
Linguistics and Philosophy 28. 739 – 779.
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