Composite Meanings Paul M Pietroski Dept of Linguistics Dept of Philosophy University of Maryland Examples of Lexical Neutrality Mass Count Mary had a little lamb which would ID: 490240
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Slide1
Lexical Neutrality Composite Meanings
Paul M. PietroskiDept. of Linguistics, Dept. of PhilosophyUniversity of MarylandSlide2
Examples of Lexical Neutrality
Mass Count Mary had a little lamb, which would have been a sheep among sheep. Singular Plural Collective/Distributive
Each of the horses that ate all the hay also
ate some grass.
Adicity The baby kicked, I kicked a stone that was kicked,
and Mother Hubbard kicked the dog a bone.Other Polysemies
This book is heavy, but it got a good review in the paper.
Torcello
is where Venice used to be. Deep greens and blues are the colors I choose. We painted brown dogs with brown paint.Slide3
Composite Meanings
“things” that words and phrases “have” compose in certain wayshumans use, in communication and intrapersonallyHuman
Languages pair with pronunciations
--languages that human children can naturally acquire
--procedures that generate boundlessly many meaning-pronunciation pairs in accord with certain
substantive constraintsSlide4
Human Languages: unbounded and constrained
Bingley is ready to please (a) Bingley is ready to please relevant parties
(b) Bingley is ready to be pleased by relevant parties
Bingley is eager to please (a) Bingley is eager to
please relevant parties #(
b) Bingley is eager to be pleased by relevant parties
Bingley is easy to please #(a) Bingley can easily
please relevant parties
(b) Bingley can easily be pleased by relevant parties Slide5
The dragon ate a large pizza yesterdayThe dragon ate a pizza yesterdayThe dragon ate a pizzaThe dragon ate some pizzaThe dragon ate somethingThe dragon
ate Lexical Neutrality amid Systematic ConstraintsSlide6
The dragons ate a large lamb yesterdayThe dragons ate a lamb yesterdayThe dragons ate a lambThe dragons ate some lambThe dragons ate somethingThe dragons ate
Lexical Neutrality amid Systematic ConstraintsSlide7
The sheep ate a large dragon yesterdayThe sheep ate a dragon yesterdayThe sheep ate a dragonThe sheep ate some dragonThe sheep ate somethingThe sheep ate
We eat fish, and this fish is one of the fish we fish for.
Lexical Neutrality amid Systematic Constraints
on either
reading of ‘sheep’Slide8
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
Lexical items can be combined
in ways that suggest
neutrality
with regard to various
conceptual distinctions that
seem to reflect real distinctions.
Maybe the meanings of ‘lamb’
‘eat’, ‘kick’, ‘Venice’, ‘pizza’, ‘fish’,
‘green’, ‘idea’, ‘sleep’, ‘furious’, …
are so
combinable
because acquiring a lexicon
lets
us
efface
many
typological distinctions. Slide9
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
lamb
in acquiring lexical items,
kids may
label
some old concepts
and
introduce
some “neutral” concepts
LAMB-
BEAST
(x
)
LAMB
-STUFF(μ)
LAMB(_)
lamb
+
singular
LAMB(_)^
COUNTABLE(_)^
~PLURAL(_)
LAMB-
BEASTS(xx
)Slide10
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
CONSUME
(x
,
y
)
FUEL-
UP
(x
)
INGEST(x
,
y
)
eat
CONSUME
(e
,
x
,
y
)
CONSUME(
e)^AGENT(e
,
x)^PATIENT(e
,
y
)
lamb
LAMB-
BEAST
(x
)
LAMB
-STUFF(μ)
LAMB(_)
LAMB-
BEASTS(xx
)
EAT(_)Slide11
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
KICK(x
,
y
)
KICKED(x
)
WAS-
KICKED
(y
)
kick
KICK(e
,
x
,
y
)
KICK(
e)^AGENT(e
,
x)^PATIENT(e
,
y
)
lamb
LAMB-
BEAST
(x
)
LAMB
-STUFF(μ)
LAMB(_)
LAMB-
BEASTS(xx
)
KICK(
_)Slide12
a few uses of lamb Lexical Item
a Pronunciation paired with a Meaning (and maybe some other
information)
Language
Acquisition
Device
prelinguistic
concepts
various cognitive modules
Human Faculty of LanguageSlide13
a few uses of lamb <
PHON: lamb (other info)
SEM:
lamb>
a few uses of eat <PHON:
eat
(other info)
SEM
: eat>
a few uses of kick <
PHON: …
book (other info
)
Venice
SEM
:
…
>
green
…
Language
Acquisition
Device
prelinguistic
concepts
various
cognitive
modules
Human
Faculty of
LanguageSlide14
a few uses of lamb
a few uses of eat
a few uses of kick
book Venice
green …
Language
Acquisition
Device
prelinguistic
concepts
various
cognitive
modules
Human
Faculty of
Language
but these presumably
VARY along many dimensions, including…
lexical items are
remarkably COMBINABLE in meaningful ways
--mass/count
--singular/plural
--collective/distributive
--
adicity
--type/token
--intentional/spatial
--etc.Slide15
What are Human Linguistic Meanings?What are the meanings of
atomic HL-expressions?easy, eager, readylamb, eat, Venicedog, brown, paintWhat are the meanings of
complex HL-expressions?Easy guests eagerly please those who are ready for them.Little lambs eat ivy in Venice, whose residents eat lamb
We painted brown dogs with brown paint.
How can atomic meanings be so neutral
while complex meanings are so constrained
?Slide16
What are Human Linguistic Meanings?Representations of a special sort
Meaning[Fido] = the concept Fido Meaning[dog] = the concept dog(_)
Meaning[brown dog] =
&[brown(_), dog(_)]Representeds
of a special sort Meaning[Fido] = the dog
Fido Meaning[dog] = the Fregean
Begriff is-a-dog(_)
Meaning[
brown dog] = &[is-brown(_), is-a-dog(_)]
concepts as composable mental
symbols:how and why do we get neutral concepts?
Begriffs
as functions
from entities (e.g., dogs)
to truth
values:
how
and why do we
get
attached
to
neutral
functions
?Slide17
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[brown] = fetch
@address:brown
brown(_)
Meaning[brown dog] = Join(Meaning[
brown], Meaning[
dog]) =
Join(fetch@address:
brown
,
fetch
@address:
dog
)
brown(_)^dog
(_)
executing
a lexical
instruction
accesses
a
concept
that can be combined with others via certain (limited) operationsSlide18
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[brown] =
fetch@address:brown
brown(_)
Meaning[brown dog] = Join(Meaning[
brown], Meaning[dog
]) brown(_)^dog
(_)
executing
a phrasal
instruction
builds
a
concept
that is combinable with others via certain (limited) operations
|
MORE RESTRICTED THAN TARSKIAN CONJUNCTIONSlide19
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[book] =
fetch@address:book
spatial-book(_)
content-book(_)Meaning[water] = fetch@address:
water
functional-water(_)
science-water(_)
a
fetchable
concept must be combinable with others, but…
a “lexical address”
need not be the address of
exactly one
concept
an
instruction
may be
executable
in
two or more ways
(perhaps including
ad
hoc
ways)Slide20
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[book] =
fetch@address:book
spatial-book(_)
content-book(_)Meaning[mimsy] = fetch@address:
mimsy
a “lexical address”
need not be the address of exactly one concept
and some
instructions
may
not
be executable
(there might be nothing to fetch)Slide21
Meanings as Instructions for How to Build Concepts
in some cases, executing
a Meaning will yield a
CONCEPT that has an
extension relative to a “situation” in which the
Meaning was executed in
other cases, not so much Slide22
Meanings as Instructions for How to Build Concepts
Meaning[lamb] =
fetch@address:
lamb
lamb(_
)
Meaning[
eat
] =
fetch@address:eat
consume(_)
eat(_
)
ROOM FOR TWO (related) KINDS OF NEUTRALITY
--two or more
fetchable
concepts at
one
lexical address
-
-
fetchable
concepts may be
introduced
as neutral
more “natural”
more permissive
more permissive than
lamb-
beast(x
)Slide23
restrict EAT(_) to get
CONSUME(_)relax CONSUME(_) to get EAT(_)build both concepts from more basic conceptstake both concepts as basic
CONSUME
(_)
EAT(
_)Slide24
compare
: &[CONSUME(…
, x); LAMB-
BEAST(x)] &[SHARE
(
…
, x); LAMB-BEAST(x)]
EAT
(_)^PAST(_)^[THEME(_ , _)^LAMB(_)]
|_______|
EAT(_)^PAST(_)^
[THEME(_, _)^[ONE(_)^LAMB(_)]]
|_______________|
compare
:
&[CONSUME
(
…
,
μ
)
; LAMB
-
STUFF
(μ)
]
&
[INGEST
(
…
,
μ
)
; LAMB
-STUFF
(μ)
]
[
eat+
past
lamb
]
[
eat+
past
a
lamb
] Slide25
CONSUME(
_)^PAST(_)^[THEME(_ , _)^LAMB(_)]
|_______|
CONSUME
(_)^PAST(_)^[THEME(_, _)^[ONE(_)^LAMB(_)]]
|_______________|
[
eat+
past
lamb
]
[
eat+
past
a
lamb
]
executing
eat
this way
yields a more restricted
conceptSlide26
EAT(_)^PAST(_)^
[THEME(_ , _)^LAMB(_)]
|_______|
EAT(_)^PAST(_)^
[THEME(_, _)^[ONE(_)^LAMB(_)]] |_______________|
[
eat+
past
lamb
]
[
eat+
past
a
lamb
]
[
eat+
past
]
CONSUME(_)^PAST(_)
Slide27
EAT(_)^PAST(_)^
[THEME(_ , _)^LAMB(_)] |_______|
EAT(_)^PAST(_)^
[THEME(_, _)^[ONE(_)^LAMB(_)]] |_______________|
[
eat+
past
lamb
]
[
eat+
past
a
lamb
]
CRUCIAL:
the
“neutral” concepts
need not be
primitive
even if
they are fetched via lexical
roots
.
Don’t
analyze beast-
concept
s
in terms of
neutra
l
-
concepts
just because
lamb
is a component of
a
lamb
and
LAMB
(_
)
is
a component of
ONE(_)^LAMB(_)Slide28
Meaning[dog] = fetch@address:
dog dog-beast(_)
Meaning[brown] =
fetch@address:brown
brown(_)
Meaning[paint] =
fetch@address:paint
paint-stuff(_)
dog(_)
applies to an entity
iff that entity is a dog
paint(_)
applies to
some stuff
iff
that stuff
is paint
brown(_)
applies to
???
iff
that
??
is …
?
Another Route to the Same ConclusionSlide29
Believe, if you like, thatany “stuff” is a portion/quantity of stuff
paint/paint(_) applies to things of a special sort: paint-portionsthere are some “minimal” paint-portions that are the basic elements of a lattice whose supremum is the totality of paint
P12
3 P
12 P1
3 P23
P1 P2 P
3
Metaphysics is
not
the
solutionSlide30
Without Neutral Nouns, Adjectives are Puzzling
If the meaning of brown is…a concept, does it
apply to certain dogs and paint (portions)? Meaning[brown
] = brown(_)
Meaning[brown dog] = brown(_) & dog(_)Meaning[
brown paint] = brown(_) & paint(_)
a function, what does
it
map to (truth) values?
Meaning[brown] = λ? . T Brown(?)
Meaning[brown dog] = λe
. T
Brown(e) & Dog(e
)
Meaning[
brown
paint
] =
λπ
. T
Brown(π
) &
Paint(π
)
Slide31
Double Bookkeeping for Adjectives?
Meaning[dog] = fetch@address:dog
dog(e
)
Meaning[brown] =
fetch@address:brown
brown-
thing
(e
) brown-stuff(
π) Meaning[
paint] = fetch@address:paint
paint
(
π
)
dog
(e
)
applies to
an entity
iff
that entity
is a dog
paint
(
π
)
applies to
some (portion of) stuff
iff
that stuff
is paint
Slide32
One Response: Double Bookkeeping for Adjectives
Meaning[dog] = fetch@address:dog
dog(e)
Meaning[brown] = fetch
@address:brown
brown-surfaced-thing
(e
)
brown-stuff(π
) Meaning[paint
] = fetch@address:paint
paint
(
π
)
dog
(e
)
applies to
an entity
iff
that entity
is a dog
paint
(
π
)
applies to
some (portion of) stuff
iff
that stuff
is paint
Slide33
The brown dog is expensive. The brown
dogSing is expensive. The brown dog(–Count) is expensive.
The brown dogs are expensive. Every one of the brown dogs
is expensive. The
brown paint is expensive.The brown paint
Sing is expensive. The brown paint
(–Count) is expensive. The brown paints are expensive
.
Every one of the brown
paints is expensive.The rabbit
Sing is brown.
The rabbit(–Count) is brown
.Most
of the
rabbit
Sing
is brown.
But
it has a white tail.
Most
of the rabbit
(–Count)
is brown.
It
has been overcooked.
The
banana
Sing
is brown
The banana
(–Count)
is brown.
Singular
Noun Neutrality:
Mass/Count
PluralSlide34
Meaning[brown] = fetch@address:
brown brown-thing(e
)
brown-stuff
(π)
Meaning[brown dog] =
Join(Meaning[brown
],
Meaning[
dog]) &[brown-thing
(e), dog
(e)]
&[
brown-
stuff
(
π
)
,
dog
(
π
)
]
Meaning[
brown
paint
] =
Join
(Meaning[
brown
],
Meaning[
paint
])
&[
brown-
thing
(e
)
,
paint
(e
)
] &[brown-
stuff(π), paint
(
π
)
]Slide35
But Less Redundancy Would be Nice
dog+s
dog+
dog[+PL (+CT)] [–PL (+CT)] [–CT]
Meaning[brown
√dog+s] =
Join(Meaning[brown],
Meaning[
dog], Meaning[+PL])
brown(_)^[
dog(_)^plural(_)]
Meaning[brown √paint] =
Join
(Meaning[
brown
],
Meaning[
paint
])
brown(_)^
paint
(_)Slide36
Meaning[√dog] =
fetch@address:√dog Meaning[√
dog+count] =
Join(fetch@address:√
dog, fetch@address:+count
)Meaning[[√
dog+plural] =
Join(
Meaning[
√dog], fetch@address:+plural)
One is free to add… Meaning[dog] = Meaning[
√dog+count] = fetch
@address:dog Meaning[dogs
] =
Meaning[
dog
+
plural
]
=
Join(
Meaning[
dog
],
Meaning[
+plural
]
)Slide37
Meaning[√paint] =
fetch@address:√paint Meaning[√paint
+count] =
Join(fetch@address:√
paint, fetch@address:+count
)Meaning[√
paint+plural] =
Join(
Meaning[
√paint], fetch@address:+plural)
One is free to add… Meaning[paint] = Meaning[
√paint]
Lexicon as stock of atomic elements vs.
Lexicon
as memorized listSlide38
Examples of Lexical Neutrality
Mass Count Mary had a little lamb, which would have been a sheep among sheep. Singular Plural Collective/Distributive
Each of the horses that ate all the hay also
ate some grass.
Adicity The baby kicked, I kicked a stone that was kicked,
and Mother Hubbard kicked the dog a bone.Other Polysemies
This book is heavy, but it got a good review in the paper.
Torcello
is where Venice used to be. Deep greens and blues are the colors I choose. We painted brown dogs with brown paint.Slide39
Very Little Evidence for Semantic “Supradyadicity”
fetch@address:give
give(
e, a, r
, p) She
gave the museum a painting give(e
, a, p
)
She gave (to) the museum a painting She gave a painting to the museum
fetch
@address:kick
give(e, a,
r
,
p
)
She
kicked the dog a bone
kick(e
,
a,
p
)
She
kicked (to) the dog a bone
She kicked a bone to the dogSlide40
Very Little Evidence for Semantic “Supradyadicity”
fetch@address:sell sell(e
, a, r
, p)
She sold the museum a painting.
sell(e,
a, r,
p
,
??) She sold the museum a painting for $1 sell(e,
a, p,
ben) She sold the painting for Bob
sell(e,
a,
p
)
She sold the
painting
sell(e
,
p
)
The painting was sold to BobSlide41
(
x
) (
y
) (
z)
a thief jimmied a lock with a knife
for some lock
y
,
e
was a jimmying by x of y
&
for some knife
z
,
e
was (done) with
z
‘jimmy’
λ
y
.
λ
x
.
λ
e
. T
e
is a jimmying by
x
of
ySlide42
(
x
) (
y
) (
z)
a thief jimmied a lock a knife
Why not
…
‘jimmy’
λz
.
λ
y
.
λ
x
.
λ
e
. T
e
is a jimmying by
x
of
y
with
z
And
why
is
passivizing
OK
?
The lock was jimmied.Slide43
(
x
) (
y
) (
z)
a thief jimmied a lock with a knife
v
‘jimmy’
λ
y
.
λ
e.
JimmyOf
(e
,
y
)
for some thief
x
,
e
was (done) by
x
&
for some lock
y
,
e
was a jimmying
of
y
&
for some knife
z
,
e
was (done) with
z
#
λ
y
.
λ
x
.
λ
e.
JimmyByOf
(e
,
x
,
y
)
#
λ
y
.
λ
z
.
λ
e.
JimmyWithOf
(e, z,
y)
# λy.λ
z.λ
x
.
λ
e.
JimmyByWithOf
(e
,
x
,
y
,
z
)Slide44
(
x
) (
y
) (
z)
a thief jimmied a lock with a knife
v
‘jimmy’
λ
y
.
λ
e.
JimmyOf(e
,
y
)
for some thief
x
,
e
was (done) by
x
&
e
was a jimmying
&
for some lock
y
,
Patient(e
,
y
)
&
for some knife
z
,
e
was (done) with
z
JimmyOf(e,
y
)
Jimmy(e
) &
Patient(e
,
y
)
Jimmy(e
) &
Past(e
)Slide45
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
KICK(x
,
y
)
KICKED(x
)
WAS-
KICKED
(y
)
kick
KICK(e
,
x
,
y
)
KICK(
e)^AGENT(e
,
x)^PATIENT(e
,
y
)
lamb
LAMB-
BEAST
(x
)
LAMB
-STUFF(μ)
LAMB(_)
LAMB-
BEASTS(xx
)
KICK(
_)Slide46
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
CONSUME
(x
,
y
)
FUEL-
UP
(x
)
INGEST(x
,
y
)
eat
CONSUME
(e
,
x
,
y
)
CONSUME(
e)^AGENT(e
,
x)^PATIENT(e
,
y
)
lamb
LAMB-
BEAST
(x
)
LAMB
-STUFF(μ)
LAMB(_)
LAMB-
BEASTS(xx
)
EAT(_)Slide47
The linguists ate the pizzas
Xy[Xy
Pizza(y)]
x
y[(y
x)
Pizza(y
)]
Xy[OneOf(y, X)
Pizza(y)]
there is a set, x, such that
there are sm things, the Xs, such that
each thing,
y
, is such that
each thing,
y
, is such that
it
y
is an element of
it
x
it
y
is one of
them
X
iff
it
y
is a (relevant) pizza
iff
it
y
is a (relevant) pizza
does the
English sentence imply
,
in addition to the pizzas,
(1) a further set/collection of the pizzas
(2) a thing eaten that that has the pizzas as “elements”Slide48
The linguists counted the sets
Xy[Xy
Set(y)]
x
y[(y
x)
Set(y)]
Xy[OneOf(y, X)
Set(y)]there is a set,
x, such that there are sm
things, the Xs, such that each thing, y
, is such that
each thing,
y
, is such that
it
y
is an element of
it
x
it
y
is one of
them
X
iff
it
y
is a (relevant) set
iff
it
y
is a (relevant) set
does the
English sentence imply
,
in addition to the sets,
(1) a further set/collection of the sets
(2) a
thing
eaten that that has the sets as “elements”Slide49
TWO CONCEPTIONS OF PLURAL VARIABLES
Five entities: a, b,
c, d
, e
Link: dba
= d
⊕
b
⊕a a mereological
sum with 3 atoms (d, b, a);
it can be the value of a singular variable
Boolos
:
dba
=
e
, no;
d
, yes;
c
, no;
b
, yes; a, yes
five
answers
to a
yes/no question:
is
…
a
value of
an
unsingular
variable?Slide50
a = 1,
b = 10, c = 100,
d = 1000,
e = 10000
Link:
01011 = 1000⊕10
⊕
1
a mereological sum with 3 atoms (d, b
, a); it can be the value of a singular variable
Boolos: 01011 = 1000+10
+1
five
answers
to a
yes/no question:
is
…
a
value of
an
unsingular
variable?
TWO CONCEPTIONS OF PLURAL VARIABLESSlide51
Xy[OneOf(y, X)
Sheep(x)] there are one or more things, the Xs, such that each thing, y
, is such that ity
is one of them
X iff
ity is a sheep
XY:~Plural(Y)
[SomeOf(Y
, X)
Sheep(Y)] there are one or more things, the Xs, such that any one or more things that are not plural, the Ys, are such that
theyy
are some of themX
iff theyy
are sheep
Slide52
X:Countish(X){Y:Countish(Y)[SomeOf(Y, X)
Sheep(Y)]} there be one or more things, the Xs, such that any one or more things, the Ys, be such that theyy
be some of themX iff
theyy be sheep
X:
~Countish(X){Y:~Countish(Y)[SomeOf(Y, X)
Sheep(Y)]} there be some stuff, the X, such that any stuff, the Y, be such that
it
y be some of itX iff ity be sheep (stuff)
we can allow for assignments
of value (e.g.,
sm
mutton or
sm
mud)
to variables, and not insist that
each assignment assign one or more
values to each variableSlide53
X:Countish(X){Y:Countish(Y)[SomeOf(Y, X)
Sheep(Y)]} there be some (one or more things) that be countish, the X, such that any (one or more things) that be countish, the Y, be such that it-or-
theyy be some of it-or-themX
iff it-or-they
y be sheepX:
~Countish(X){Y:~Countish(Y)[SomeOf(Y, X)
Sheep(Y)]} there be some (stuff) that be not countish, the X, such that
any (stuff) that be not
countish
, the Y, be such that it-or-theyy be some of themX iff it-or-they
y be sheepX
Y[SomeOf(Y, X) Sheep(Y
)]} there be some (stuff-or-thing-or-things), the X, such that any (stuff-or-thing-or-things), the Y, be such that
it-or-
they
y
be some of
them
X
iff
it-or-
they
y
be sheep
Slide54
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
Lexical items can be combined
in ways that suggest
neutrality
with regard to various
conceptual distinctions that
seem to reflect real distinctions.
Maybe the meanings of ‘lamb’
‘eat’, ‘kick’, ‘Venice’, ‘pizza’, ‘fish’,
‘green’, ‘idea’, ‘sleep’, ‘furious’, …
are so
combinable
because acquiring a lexicon
lets
us
efface
many
typological distinctions. Slide55
Lexical Neutrality Composite Meanings
Paul M. PietroskiDept. of Linguistics, Dept. of PhilosophyUniversity of MarylandSlide56
Compare: Double Bookkeeping for Place Names
Meaning[hexagonal] = fetch@address:hexagonal
hexagonal(_)
Meaning[France] =
fetch@address:France
France-land
France-institution
Meaning[
France is hexagonal] Saturate(Meaning[hexagonal
], Meaning[France])
hexagonal
(France-land)
hexagonal
(France
-institution)Slide57
Compare: Double Bookkeeping for Place Names
Meaning[republic] = fetch@address:republic
republic(_)
Meaning[France] =
fetch@address:France
France-land
France-institution
Meaning[
France is hexagonal] Saturate(Meaning[republic
], Meaning[France])
republic
(France-land)
republic
(France
-institution)Slide58
Mass Count Singular Plural
Collective/Distributive Adicity
Other Polysemies
lamb
in acquiring lexical items,
kids may
label
some old concepts
and
introduce
some “neutral” concepts
LAMB-BEAST(_)
LAMB-MEAT(_)
LAMB(_)
a lexicon may also include
lamb
=
lamb+
count
LAMB(_)^COUNTABLE(_)Slide59
EATING/CONSUMING
EATING/INGESTING
some cases of eating/consuming
< …,
Y:THEME(E, Y)
{
X:AGENT(E, X)[MEAL-FOR(Y, X)]}>
CONCEPT
PROJECTER
MONADICIZER
CONCEPT
RELAXER
EAT/CONSUME(A, P)
EAT/CONSUME(_)
EAT/INGEST(_)Slide60
Typically, a lexical address will be an address of…a concept lexicalized
but perhaps not fetchable (for purposes of combining with other fetchables)a root concept that is fetchable but not lexicalizeda default
concept, perhaps not the root concept, that is fetched absent contrary indicationsperhaps concepts that can be fetched under “coercion”
EAT/CONSUME(_)
EAT/INGEST(_)
Crucially, the root concept need not be conceptually basic…
might abstract…
dog
(_)
from
dog-thing(_)paint(_)
from paint-stuff(_)kick(_) from
kick(_, _, _)
eat
(_)
from
eat-consume(_, _, _)Slide61
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[Fido] =
fetch@address:Fido
Fido
Meaning[Fido [(izza) dog]] =
Saturate(Meaning[Fido],
Meaning[dog])
dog(Fido)]Slide62
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[Fido] =
fetch@address:Fido
Fido
fido(_) Meaning[Fido [(izza
) dog]] = Join
(Meaning[Fido], Meaning[
dog])
fido(_)^dog
(_)Slide63
Meanings as Instructions for How to Build Concepts
Meaning[dog] = fetch@address:
dog
dog(_)
Meaning[Fido] =
fetch@address:Fido
Fido
fido(_) Meaning[+polarity [Fido [(
izza) dog]]] = CLOSE-
UP:Join(Meaning[Fido
], Meaning[dog])
[
fido(_)^dog
(_)]
|
MORE
RESTRICTED THAN
TARSKIAN
EXISTENTIAL CLOSURESlide64
Does the plural marker imply an extra thing? If each dog is brown, then each one of the dogs is brown.
If each set is grounded, then each one of the sets is grounded.Are “mass nouns” true of quantities? Given some paint
, it is some paint of a certain quantity. Given some paint,
it is a certain quantity of paint. A gallon of paint is
a certain quantity of paint. A gallon is
a certain quantity.What determines what “singularized mass nouns” are true of? at Bar Vampire:
I’ll have a blood, neat. Gimme the good stuff. He’ll have the cheap blood on the rocks. Slide65
Chris ate some tacksChris ateChris ate some grits/hominyChris ate some grit/lye-soaked cornThe dragon ate some glorpHe thought he was eating
fraggis.But in fact, he was eating glorp.The dragon ate.Slide66
Believe, if you like, thatany “stuff” is a portion/quantity of stuff
paint/paint(_) applies to things of a special sort: paint-portionsthere are some “minimal” paint-portions that are the basic elements of a lattice whose supremum is the totality of paint
P12…
n–1
n … P1
2…P1n–1…P
1n…P2
n–1
…P2n…Pn–1n
P1 P2 … Pn
–1 Pn
waive concerns about recycling