Paul M Pietroski University of Maryland Dept of Linguistics Dept of Philosophy Human Language System tuned to Spoken English SoundBrutus kicked Caesar ID: 326261
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Slide1
Two Kinds of Concept Introduction
Paul M. PietroskiUniversity of MarylandDept. of Linguistics, Dept. of PhilosophySlide2
Human
Language System,tuned to“Spoken English”Sound(‘Brutus
kicked Caesar’)
Meaning(‘Brutus
kicked Caesar’)
Brutus
kicked(
_
,
_
) Caesar
kicked(Brutus, Caesar)
Human Language System,tuned to“Spoken English”
Sound(‘kicked’)
Meaning(‘kicked’)
kicked(_, Caesar)
kicked(_, _)
y
.
x
.
kicked(x
, y)Slide3
Human
Language System,tuned to“Spoken English”
Sound(‘Brutus kicked Caesar on Monday’)
Meaning(‘Brutus
kicked Caesar on Monday’)
Brutus
kicked(
_
,
_
,
_) Caesar
kicked(_, Brutus, Caesar) & on(_, Monday)
on(_, Monday) kicked(_, _
, Caesar) kicked(_, Brutus, Caesar) Slide4
Human
Language System,tuned to“Spoken English”
Sound(‘kicked’)
Meaning(‘kicked
’)
Brutus
kicked(
_
,
_
,
_) Caesar
on(_, Monday) kicked(
_, Brutus, Caesar) y.
x.e.kicked(e, x, y
)Slide5
Human
Language System,tuned to“Spoken English”
Sound(‘kicked’)
Meaning(‘kicked
’)
Brutus
kicked(
_
,
_
,
_) Caesar
on(_, Monday) kicked(
_, Brutus, Caesar) y.
x.e.kick(e, x, y
) & past(e)Slide6
Human
Language System,tuned to“Spoken English”
Sound(‘kicked’)
Meaning(‘kicked
’)
Brutus
kicked(
_
,
_
,
_) Caesar
on(_, Monday) kicked(
_, Brutus, Caesar) y.x
.e.kick(e, x, y) &
past(e) & agent(e, x) & patient(e
, y)Slide7
Human
Language System,tuned to“Spoken English”
Sound(‘kicked’)
Meaning(‘kicked
’)
Brutus kicked Caesar (today)
Brutus kicked
Brutus kicked Caesar the ball
Caesar was kicked
I get no kick from champagne,
but I get a kick out of you
That kick was a good one
y.x.e.
kicked(e, x, y)Does a child who acquires ‘kicked’ start with
kicked(_, _) y.x.kicked(x
, y) kick(_, _, _)
y.x.
e
.
kick(e
,
x
,
y
)
or some other
concept(s
), perhaps like
e
.
kick(e
)
?Slide8
Human
Language System,tuned to“Spoken English”
Sound(‘gave’)
Meaning(‘gave
’)
Brutus gave the ball (to Caesar)
Brutus gave (at the office)
Brutus gave Caesar the ball (today)
The painting was given/donated
z
.y.
x.e.gave(e, x,
y, z)Does a child who acquires ‘gave’ start withgave(_, _, _)gave(_, _, _, _)
z.y.x.
e.gave(e, x
, y, z)…
e
.
give(e
)
The rope has too much giveSlide9
Big Questions
To what degree is lexical acquisition a “cognitively passive” process in which (antecedently available) representations are simply labeled and paired with phonological forms?
To what degree is lexical acquisition a “cognitively creative” process in which (antecedently available) representations are used to introduce other representations that exhibit a new combinatorial format?
Are the concepts that kids lexicalize already as systematically combinable as words? Or do kids use these “L-concepts,” perhaps shared with other animals, to introduce related
concepts that exhibit a more distinctively human format?Slide10
Outline
Describe a “Fregean” mind that can use its cognitive resources to introduce mental symbols of two sorts (1)
polyadic concepts that are “logically fruitful”
(2) monadic concepts that are “logically boring,” but more useful than “mere abbreviations” like
x
[mare(x)
≡
df
horse(
x
) & female(x
) & mature(x)
]Suggest that the process of acquiring a lexicon involves concept introduction of the second sort. For example, a child might use give(_,
_, _) or give(_,
_, _, _) to introduce
give(_).Offer some evidence that this suggestion is correctsay something aboutadicitySlide11Slide12
Quick Reminder about Conceptual Adicity
Two Common MetaphorsJigsaw Puzzles
7th
Grade Chemistry
-
2
+1
H
–
O
–
H
+1Slide13
Jigsaw Metaphor
a Thought:
Brutus
sangSlide14
Jigsaw Metaphor
Unsaturated
Saturater
Doubly
Un
-
saturated
1st
saturater
2nd
saturater
one
Monadic Concept
(
adicity
: -1)
“filled by” one
Saturater
(
adicity
+1)
yields a complete Thought
one
Dyadic Concept
(
adicity
: -2)
“filled by” two
Saturaters
(
adicity
+1)
yields a complete Thought
Brutus
Sang( )
Brutus
Caesar
KICK(_, _)
Slide15
7th Grade Chemistry Metaphor
a molecule
of water
-
2
+1
H
(
O
H
+1
)
-1
a single atom with
valence -2
can combine with
two atoms of
valence +1
to form a stable moleculeSlide16
7th Grade Chemistry Metaphor
-
2
+1
Brutus
(
Kick
Caesar
+1
)
-1Slide17
7th Grade Chemistry Metaphor
+1
Na
Cl
-1
an atom with
valence -1
can combine with
an atom of
valence +1
to form a stable molecule
+1
Brutus
Sang
-1Slide18
Extending the Metaphor
Aggie
b
rown
( )
Aggie
cow( )
Aggie
brown-cow( )
Aggie is
(a)
cow
Aggie is brown
Aggie is
(a) brown
cow
-1
-1
+1
+1
-1Slide19
Extending the Metaphor
Aggie
Conjoining two
monadic (
-1
)
concepts can
yield a complex
monadic (
-1
)
concept
brown
( )
&
cow
( )
Aggie
cow( )
-1
+1
Aggie
b
rown
( )
-1
+1
-1Slide20
Outline
Describe a “Fregean” mind that can use its cognitive resources to introduce mental symbols of two sorts (1)
polyadic concepts that are “logically fruitful”
(2) monadic concepts that are “logically boring,” but more useful than “mere abbreviations” like
x
[mare(x)
≡
df
horse(
x
) & female(x
) & mature(x)
]Suggest that for humans, the process of “acquiring a lexicon” involves concept introduction of the second sort. For example, a child might use give(_,
_, _)
to introduce give(_).Offer some evidence that this suggestion is correctSlide21
Zero is a number
every number has a successorZero is not a successor of any
numberno two numbers have the same
successorfor every property of
Zero: if every number
that has it is such that its successor has it,
then
every
number
has it
Frege’s Hunch:these thoughts are not as
independent as axioms should beSlide22
Nero is a cucumber
every cucumber has a doubterNero is not a doubter of any
cucumberno two cucumber
s have the same doubterfor every property of
Nero: if
every cucumber that has it is such that its doubter
has it,
then
every
cucumber has it
Related Point:these thoughts are not as
compelling as axioms should beSlide23
Zero is a number
() Nero is a
cucumberevery
number has a successor
x{(x
)
y[
(
y
,x)]}
every cucumber has a doubter
Zero is not a successor of any number
~x{(, x) &
(x)}Nero is not a
doubter of any cucumberIf we want to represent what the arithmetic thougts imply— and what they follow from—then the formalizations
on the right are better than ‘P’, ‘Q’, and ‘R’. Slide24
Zero is a number
() Nero is a
cucumberevery
number has a successor
x{(x
)
y[
(
y
,x)]}
every cucumber has a doubter
Zero is not a successor of any number
~x{(, x) &
(x)}Nero is not a
doubter of any cucumberBut we miss something if we represent the property of being a number with an atomic monadic concept, as if number( )
differs from cucumber( ) and carrot( ) only in terms of its specific content.Slide25
Zero is a number
() Nero is a
cucumberevery
number has a successor
x{(x
)
y[
(
y
,x)]}
every cucumber has a doubter
Zero is not a successor of any number
~x{(, x) &
(x)}Nero is not a
doubter of any cucumberWe miss something if we represent the number zero with an atomic singular concept, as if the concept Zero
differs from concepts like Nero and Venus only in terms of its specific content.Slide26
Zero is a number
() Nero is a
cucumberevery
number has a successor
x{(x
)
y[
(
y
,x)]}
every cucumber has a doubter
Zero is not a successor of any number
~x{(, x) &
(x)}Nero is not a
doubter of any cucumberWe miss something if we represent the successor relation with an atomic relational concept, as if successor-of( , )
differs from doubter-of( , ) and planet-of( , ) only in terms of its specific content.Slide27
Fregean Moral
The contents of number( ), Zero
, and successor-of( , ) seem to be
logically related in ways that the contents of cucumber( ),
Nero, and doubter-of( , ) are not
So perhaps we should try to re-present
the contents of the arithmetic concepts, and
reduce (re-presentations of) the arithmetic axioms
to “sparer” axioms that reflect (all and only)
the “
nonlogical” content of arithmeticSlide28
Frege’s Success (
with help from Wright/Boolos/Heck
)
(Defs) Definitions of
number(x),
Zero, and successor-of(
y
,
x
)
in terms of
number-of(x,
) and logical notions
(HP) {[x:number-of(x,
) = number-of(x
, )] one-to-one
(, )} __________________________________________(DP) Dedekind-
Peano AxiomsA mind that starts with (HP) could generate “Frege Arithmetic,” given a consistent fragment of Frege’s (2nd-order) Logic.Slide29
Some Truths
number-of[Zero, z.~(z =
z)]number-
of[One
, z.(z =
Zero)]
number-
of
[
Two
,
z.(z = Zero) v (
z = One)]
...Zero = x:number-of[x
, z.~(z = z)]
One = x:number-of[x,
z.(z = Zero)]Two = x:number-of[x,
z.(z = Zero) v (z = One)]
…x{number-of
(x, )
number
(
x
)
&
one-to-
one
(
,
λy.
precedes
(
y
,
x
)
]}
x{
number
(
x
)
(
x
=
Zero
)
v
precedes
(
Zero
,
x
)
}
x{
number(
x
)
[
number-of
(
x
,
)
]}
some initial clues to let us cotton on and “get” the concept
number-
of
[
x
,
]
We can call these definitions in the OED sense without saying that the truths are analytic. Slide30
Frege’s Direction of Definition
Zero =df x:number-of[x
, z.~(z = z
)]
x{number(x
)
df
(
x
=
Zero) v precedes
(Zero, x
)}xy{
precedes(x, y) df
ANCESTRAL:predecessor(x, y
)}xy{predecessor(x, y
) df ∃∃
{number-of(x, ) & number-of(
y, ) & ∃z[~
z & w{w [
w
v
(
w
=
z
)]}]}
The idea is not that
our
concepts
Zero
,
number
( )
, and
predecessor
(
x
,
y
)
had decompositions all along. But once we have the concept
number-
of
(
x
,
)
, perhaps with help from
Frege
, we can imagine an ideal thinker who
starts
with this concept and
introduces
the others
—either to interpret us, or to suppress many aspects of logical structure until they become relevant.Slide31
A Different Direction of Analysis
x{number-of(x
, )
df
number(x
) & one-to-
one
(
,
λy.precedes
(y, x
)]}xy{precedes
(x, y) df ANCESTRAL:
predecessor(x, y
)}xy[predecessor(x,
y) df successor(y,
x)]as if primitive thinkers—who start with number(x),
one-to-one(,
) and successor(x
,
y
)
—were trying to interpret (or become) thinkers who use the sophisticated concept
number-
of
(
x
,
)
and thereby come to see how the Dedekind-
Peano
axioms can be re-presented
such thinkers don’t use
number-
of
(
x
,
)
to introduce
number
(
x
)
but they
might
use
kick
(
x
,
y
)
/
give
(
x
,
y
,
x
)
to introduce
kick
(
e
)/
give
(
e
)Slide32
Some Potential Equivalences
x{socratizes(x) (
x = Socrates)}
Socrates = x:
socratizes(x)
x
y
{
kicked
(x,
y)
∃e[kicked(e
, x, y)]}
xye{kicked
(e, x, y)
past(e) & kick(e
, x, y)}xy
e{kick(e, x,
y) agent(
e
,
x
)
&
kick
(
e
)
&
patient
(
e
,
y
)
}
λe.
kick
(
e
)
=
:
x
y
e{
kick
(
e
,
x
,
y
)
agent
(
e
,
x
)
&
(
e
)
&
patient
(
e
,
y
)
}
Slide33
Some Potential Equivalences
x{socratizes(x) (
x = Socrates)}
fixes the (one-element) extension of socratizes(_
)
x
y
e{
kick(e, x
, y)
agent(e, x
) & kick(e
) & patient(e, y
)}λe.kick(e) =
:xye{kick(e,
x, y)
agent(e,
x
)
&
(
e
)
&
patient
(
e
,
y
)
}
constrains (but does not fix) the extension of
kick
(
_
)
,
which is neither fully defined nor an unconstrained atom
Slide34
Two Kinds of Introduction
Introduce monadic concepts in terms of nonmonadic conceptsx{socratizes(
x) df
(x = Socrates)
λe.kick(
e) =
df
:
xy
e{kick(e
, x, y)
agent(e,
x) & (e) &
patient(e, y)}_____________________________________________________
Introduce nonmonadic concepts in terms of monadic conceptsSocrates =df
x:socratizes(x)
xye{kick
(
e
,
x
,
y
)
df
agent
(
e
,
x
)
&
kick
(
e
)
&
patient
(
e
,
y
)
}Slide35
Two Kinds of Introduction
Introduce monadic concepts in terms of nonmonadic conceptsx{socratizes(
x) df
(x = Socrates)
λe.kick(
e) =
df
:
xy
e{kick(e
, x, y)
agent(e,
x) & (e) &
patient(e, y)}_____________________________________________________
My suggestion is not that our concepts Socrates and kick(e, x,
y) have decompositions. But a child who starts with these concepts might
introduce kick(e)
and
socratizes
(
x
)
. Slide36
Two Kinds of Introduction
Introduce monadic concepts in terms of nonmonadic conceptsx{socratizes(
x) df
(x = Socrates)
λe.kick(
e) =
df
:
xy
e{kick(e
, x, y)
agent(e,
x) & (e) &
patient(e, y)}_____________________________________________________
The monadic concepts—unlike number-of(x, )—won’t help much if your goal is to show how logic is related to arithmetic. But they might help if you want to specify word meanings in a way that allows for “logical forms” that involve using conjunction to
build complex monadic predicates as in… ∃e{∃x[agent
(e, x) &
socratizes
(
x
)
]
&
kick
(
e
)
&
past
(
e
)
}Slide37
Two Conceptions of Lexicalization(1)
LabellingAcquiring words is basically a process of pairing pre-existing concepts with perceptible signalsLexicalization is a conceptually passive operation
Word combination mirrors concept combination(2) Reformatting
Acquiring words is also a process of introducing concepts that exhibit a certain composition formatIn this sense, lexicalization is cognitively creative
Word combination does not mirror combination of the pre-existing concepts that get lexicalized Slide38
Bloom: How Children
Learn the Meanings of Words
word
meanings are, at least primarily,
concepts that kids have prior
to lexicalizationlearning word meanings is, at least
primarily, a
process of figuring out
which
existing concepts
are
paired with which
word-sized signalsin this process, kids draw on many
capacities—e.g., recognition of syntactic cues and speaker intentions
—but no capacities specific to acquiring
word meaningsSlide39
Lidz,
Gleitman, and Gleitman
“Clearly, the number of noun phrases required for the grammaticality of a verb in a sentence is a function of the number of participants logically implied by the verb meaning
. It takes only one to sneeze, and therefore
sneeze is intransitive, but it takes two for a kicking act (kicker and
kickee), and hence kick
is transitive
.
Of
course there are quirks and provisos to these systematic form-to-meaning-correspondences…”
Brutus kicked Caesar the ball
That kick was a good one
Brutus kicked
Caesar was kickedSlide40
Lidz,
Gleitman, and Gleitman
“
Clearly, the number of noun phrases required for the grammaticality of a verb in a sentence is a function of the number of participants logically implied by the verb meaning
. It takes only one to sneeze, and
therefore sneeze
is intransitive, but
it takes two for a kicking act (kicker and
kickee
)
, and
hence
kick is transitive
. Of course there are quirks and provisos to these systematic form-to-meaning-correspondences…”Slide41
Why Not...
Clearly
, the number of noun phrases required for the grammaticality of a verb in a sentence is
not a function of the number of participants logically implied by the verb meaning
. A paradigmatic act of kicking has exactly two participants
(kicker and kickee
)
, and
yet
kick
need not be transitive
. Brutus kicked Caesar the ball Caesar was kicked Brutus kicked Brutus gave Caesar a swift kick
Of course there are quirks and
provisos. Some verbs do require a certain number of noun phrases in active voice sentences. *Brutus put the ball*Brutus put*Brutus sneezed CaesarSlide42
Concept
of
adicity
n
Concept
of
adicity
n
Perceptible
Signal
Quirky information for lexical items like ‘kick’
Concept
of
adicity
-1
Perceptible
Signal
Quirky information for lexical items like ‘put’Slide43
Clearly, the number of noun phrases required for the
grammaticality of a verb in a sentence is
a function of
the number of participants logically implied by the verb meaning.
It takes only one to sneeze, and
therefore
sneeze
is intransitive, but
it
takes two for a kicking act
(kicker and
kickee),
and hence
kick is transitive. Of course there are quirks and provisos to these systematic form-to-meaning-correspondences.
Clearly, the number of noun phrases required for the grammaticality of a verb in a sentence isn’t
a function of the number of participants logically implied by the verb meaning. It takes only one to sneeze, and usually
sneeze is intransitive. But it usually takes two to have a kicking; and yet kick
can be untransitive.
Of course there are quirks and provisos. Some verbs do require a certain number of noun phrases in active voice sentences. Slide44
Clearly, the number of noun phrases required for the
grammaticality of a verb in a sentence is
a function of
the number of participants logically implied by the verb meaning.
It takes only one to sneeze, and
therefore
sneeze
is intransitive, but
it
takes two for a kicking act
(kicker and
kickee),
and hence
kick is transitive.
Of course there are quirks and provisos to these systematic form-to-meaning-correspondences.Clearly, the number of noun phrases required for the grammaticality of a verb in a sentence isn’t
a function of the number of participants logically implied by the verb meaning. It takes only one to sneeze, and sneeze is
typically used intransitively; but a paradigmatic kicking has exactly two participants, and
yet kick can be used intransitively
or ditransitively.
Of course there are quirks and provisos. Some verbs do require a certain number of noun phrases in active voice sentences. Slide45
Lexicalization as Concept-Introduction (not mere labeling)
Concept
of
type T
Concept
of
type T
Concept of
type T*
Perceptible
SignalSlide46
Lexicalization as Concept-Introduction (not mere labeling)
Perceptible
Signal
Number(_)
type:
<
e
,
t
>
Number(_)
type:
<
e
,
t
>
NumberOf
[_,
Φ
(
_)]
type:
<<
e
,
t
>, <
n
,
t
>>Slide47
Lexicalization as Concept-Introduction (not mere labeling)
Concept
of
type T
Concept
of
type T
Concept of
type T*
Perceptible
SignalSlide48
Concept
of
adicity
-1
Concept
of
adicity
-1
Concept of
adicity
-2
Perceptible
Signal
ARRIVE(x
)
ARRIVE(e
,
x
)
One Possible
(
Davidsonian
) Application
:
Increase
AdicitySlide49
Concept
of
adicity
-2
Concept
of
adicity
-2
Concept of
adicity
-3
Perceptible
Signal
KICK(x
1
, x
2
)
KICK(e
, x
1
, x
2
)
One Possible (
Davidsonian
) Application: Increase
AdicitySlide50
Concept
of
adicity
n
Concept
of
adicity
n
Concept
of
adicity
-1
Perceptible
Signal
KICK
(x
1
, x
2
)
KICK
(
e
)
KICK
(e
, x
1
, x
2
)
Lexicalization as
Concept-Introduction: Make
Mona
dsSlide51
Concept
of
adicity
n
Concept of
adicity
n
(or
n−1
)
Perceptible
Signal
Concept of
adicity
n
Concept of
adicity
−1
Perceptible
Signal
Further lexical
information
(regarding flexibilities)
further lexical
information
(regarding inflexibilities)
Two Pictures of
Lexicalization Slide52
Concept
of
adicity
n
Concept of
adicity
n
Concept of
adicity
−1
Perceptible
Signal
further
POSSE
information,
as for ‘put
Two Pictures of
Lexicalization
Word:
SCAN
-1
offer some reminders of some reasons
(in addition to passives/nominalizations)
for adopting the second pictureSlide53
Absent Word Meanings
Striking absence of certain (open-class) lexical meanings that
would be permitted
if Human
I-Languages
permitted non
monadic
semantic types
<
e
,<
e,<e
,<e, t>>>> (instructions to fetch)
tetradic concepts <
e,<e,<e, t
>>> (instructions to fetch) triadic concepts <e
,<e, t>> (instructions to fetch) dyadic concepts
<e
> (instructions to fetch) singular conceptsSlide54
Absent Word Meanings
Striking absence
of certain (open-class) lexical meanings that
would be permitted
if I-Languages permit nonmonadic
semantic types
<
e
,<
e
,<
e
,<e
, t>>>> (instructions to fetch) tetradic
concepts
<e,<e,<e
, t>>> (instructions to fetch) triadic concepts
<e,<e
, t>> (instructions to fetch)
dyadic concepts
<
e
>
(instructions to fetch)
singular
conceptsSlide55
Absent Word Meanings
Brutus sald
a car Caesar a dollar
sald
SOLD(x
,
$,
z
,
y)
[sald [a car]]
SOLD(x, $, z, a car)
[[sald [a car]] Caesar]
SOLD(x, $, Caesar, a car)
[[[sald [a car]] Caesar]] a dollar]
SOLD(x
,
a dollar,
Caesar, a car)
_________________________________________________
Caesar bought a car
bought a car from Brutus for a dollar
bought Antony a car from Brutus for a dollar
x
sold
y
to
z
(in exchange)
for
$
Slide56
Absent Word Meanings
Brutus tweens
Caesar Antony
tweens
BETWEEN(x
,
z
,
y
)
[
tweens
Caesar] BETWEEN(x
, z
, Caesar) [[tweens Caesar] Antony]
BETWEEN(x, Antony, Caesar)_______________________________________________________
Brutus sold Caesar a carBrutus gave Caesar a car *Brutus donated a charity a car
Brutus gave a car away Brutus donated a car
Brutus gave at the office Brutus donated anonymouslySlide57
Absent Word Meanings
Alexander jimmed
the lock a knife
jimmed
JIMMIED(x
,
z
,
y
)
[
jimmed [the lock]
JIMMIED(x, z
, the lock) [[jimmed [the lock]
[a knife]] JIMMIED(x, a knife, the lock)
_________________________________________________Brutus froms Rome
froms
COMES-
FROM(x
,
y
)
[
froms
Rome]
COMES-
FROM(x
,
Rome)Slide58
Absent Word Meanings
Brutus talls
Caesar
talls
IS-TALLER-
THAN(x
,
y
)
[talls Caesar]
IS-TALLER-THAN(x
, Caesar)_________________________________________*Julius Caesar
Julius JULIUS
Caesar CAESAR
Slide59
Absent Word Meanings
Striking absence of certain (open-class) lexical meanings that
would be permitted
if I-Languages permit nonmonadic
semantic types
<
e
,<
e
,<
e
,<e
, t
>>>> (instructions to fetch) tetradic concepts
<e,<
e,<e, t
>>> (instructions to fetch) triadic concepts
<e,<e, t>>
(instructions to fetch) dyadic concepts
<e
>
(instructions to fetch)
singular
conceptsSlide60
Proper Nouns
even English tells against the idea that lexical proper nouns label singular concepts (of type <e
>)
Every Tyler I saw was a philosopher
Every philosopher I saw was a Tyler
There were three Tylers
at the party
That Tyler stayed late, and so did this one
Philosophers have wheels, and
Tylers
have stripes
The
Tylers
are coming to dinner I spotted Tyler Burge I spotted that nice Professor Burge who we met before
proper nouns seem to fetch monadic concepts, even if they lexicalize singular conceptsSlide61
Concept
of
adicity
n
Concept
of
adicity
n
Concept
of
adicity
-1
Perceptible
Signal
TYLER
TYLER(x
)
CALLED[x
, SOUND(
‘Tyler’
)]
Lexicalization as
Concept-Introduction: Make
Mona
dsSlide62
Concept
of
adicity
n
Concept
of
adicity
n
Concept
of
adicity
-1
Perceptible
Signal
KICK
(x
1
, x
2
)
KICK
(
e
)
KICK
(e
, x
1
, x
2
)
Lexicalization as
Concept-Introduction: Make
Mona
dsSlide63
Concept
of
adicity
n
Concept
of
adicity
n
Concept
of
adicity
-1
Perceptible
Signal
TYLER
TYLER(x
)
CALLED[x
, SOUND(
‘Tyler’
)]
Lexicalization as
Concept-Introduction: Make
Mona
dsSlide64
Lexical Idiosyncracy
can be Lexically EncodedA verb can access a monadic concept
and
impose further (idiosyncratic) restrictions on complex expressions
Semantic
Composition Adicity Number (SCAN
)
(instructions to fetch) singular concepts
+1 singular
<
e
> (instructions to fetch) monadic concepts
-1 monadic <e,
t> (instructions to fetch) dyadic concepts -2 dyadic <e,<
e, t>>
Property of Smallest Sentential Entourage (POSSE)zero NPs,
one NP, two NPs, …
the SCAN of every verb can be -1, while POSSEs vary: zero,
one, two, …Slide65
POSSE facts may
reflect ...the adicities of the original
concepts lexicalized ...
statistics about how verbs are
used (e.g., in active voice)
...prototypicality effects
...other
agrammatical
factors
‘put’ may
have a (lexically represented) POSSE of
three
in part
because --the concept lexicalized was PUT(_, _, _)
--the frequency of locatives (as in ‘put the cup on the table’) is salient and note: * I put the cup the table
? I placed the cupSlide66
On any view: Two Kinds of Facts to Accommodate
FlexibilitiesBrutus kicked Caesar
Caesar was kickedThe baby kicked
I get a kick out of youBrutus kicked Caesar the ball
Inflexibilities
Brutus put the ball on the table
*Brutus put the ball
*Brutus put on the tableSlide67
On any view: Two Kinds of Facts to Accommodate
Flexibilities
The coin meltedThe jeweler melted the coin
The fire melted the coinThe coin vanished
The magician vanished the coin
Inflexibilities
Brutus arrived
*Brutus
arrived CaesarSlide68
Experience
andGrowth
LanguageAcquisitionDevice in itsInitial State
Language Acquisition
Device in
a Mature State(an I-Language):
GRAMMAR
LEXICON
Phonological
Instructions
Semantic Instructions
Lexicalizable
concepts
Introduced concepts
Articulation and Perception of Signals
Lexicalized conceptsSlide69
Two Kinds of Concept Introduction
THANKS!