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Two Kinds of Concept Introduction Two Kinds of Concept Introduction

Two Kinds of Concept Introduction - PowerPoint Presentation

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Two Kinds of Concept Introduction - PPT Presentation

Paul M Pietroski University of Maryland Dept of Linguistics Dept of Philosophy Human Language System tuned to Spoken English SoundBrutus kicked Caesar ID: 326261

concept number caesar brutus number concept brutus caesar kick concepts kicked amp adicity verb instructions monadic fetch cucumber successor

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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 aboutadicitySlide11
Slide12

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

)}xy{

precedes(x, y) df

ANCESTRAL:predecessor(x, y

)}xy{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

)]}xy{precedes

(x, y) df ANCESTRAL:

predecessor(x, y

)}xy[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)]}

xye{kicked

(e, x, y)

 past(e) & kick(e

, x, y)}xy

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) = 

:xye{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 conceptsx{socratizes(

x) df

(x = Socrates)

λe.kick(

e) =

df

:

xy

e{kick(e

, x, y)

 agent(e,

x) & (e) &

patient(e, y)}_____________________________________________________

Introduce nonmonadic concepts in terms of monadic conceptsSocrates =df

x:socratizes(x)

xye{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 conceptsx{socratizes(

x) df

(x = Socrates)

λe.kick(

e) =

df

:

xy

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 conceptsx{socratizes(

x) df

(x = Socrates)

λe.kick(

e) =

df

:

xy

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!