Meanings as Instructions for how to Build Concepts Paul M. Pietroski University of Maryland Dept. of Linguistics, Dept. of Philosophy pietro

Meanings as Instructions

for how to Build Concepts

Paul M. PietroskiUniversity of Maryland

Dept. of Linguistics, Dept. of Philosophyhttp://www.terpconnect.umd.edu/~pietro

TimHunte

r

DarkoOdic

JeffLidzJustin

Halberda

not pictured: Norbert Hornstein

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Some basic questions about words, word meanings, and how they combine

A general proposal about what word meanings are, how they combine, and how they relate to psychology

A detailed case study of how to bring experimental methods to bear on rather abstract theoretical questions

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Some basic questions about words, word meanings, and how they combine

A general proposal about what word meanings are, how they combine, and how they relate to psychology

A detailed case study of how to bring experimental methods to bear on rather abstract theoretical questions

General Perspective: the questions are better than my answers

I study linguistic meaning because of what it reveals about human nature…not because I’m really interested in communication, languages, metaphysics, reference, truth, …

One of Aristotle’s Observations

Some animals are born early, and take time to grow into their “second nature”

One of Aristotle’s Observations

Some animals are born early, and take time to grow into their “second nature”

Infant Child

Modules: Vision Audition

…

Experienceand

Growth

LanguageAcquisition

Device in itsInitial State


…

Language AcquisitionDevice in a

Mature State:

GRAMMAR LEXICON

Catterpillars become Butterflies,Humans acquire Languages

Humans acquire Words and Grammars

• Dramatic change in a critical period, early in the life cycle

• Large components of this change might well be viewed as “evicted embryology” (or a kind of pupal stage) that allows for environmental influence

• Of course, infants also acquire concepts in the critical period

Hard to see how one could acquire words, as opposed to meaningless sounds (or signs), without acquiring concepts

Indeed, one might think that words pair sounds with concepts

Infant Child


…

initial concepts

Experienceand

Growth

LanguageAcquisition



…

Language AcquisitionDevice in a

Mature State:

GRAMMAR LEXICON

acquired concepts

initial concepts

Humans acquire words, concepts, and grammars

What are words?

What are concepts?

What are grammars?


What are words?

What are concepts?

What are grammars?

How are words related to concepts and grammars?

How are words, concepts, and grammars related

to whatever makes humans distinctive,

linguistically and cognitively?

What makes humans linguistically special?

(i) Lexicalization: capacity to acquire words

(ii) Combination: capacity to combine words

(iii) Lexicalization and Combination

(iv) Distinctive concepts that get paired with signals

(v) Something else entirely




(iii) Lexicalization and Combination










FACT: kids are the best lexicalizers on the planet



FACT: kids are the best lexicalizers on the planet

Idea (to be explained and defended)

• In acquiring words, we use available concepts to introduce new ones

'ride' + RIDE(x1, x2) ==> RIDE(_) + 'ride' + RIDE(x1, x2)

• Words are then used to fetch the introduced concepts

when you hear the word ‘ride’…..fetch the concept RIDE(_)

• The new concepts can be systematically conjoined

'ride fast' RIDE(_) & FAST(_)

'ride horses’ RIDE(_) & [THEME(_, _) & HORSES(_)]

'ride horses fast’ RIDE(_) & [THEME(_, _) & HORSES(_)] & FAST(_)

‘ride fast horses’ RIDE(_) & [THEME(_, _) & FAST(_) & HORSES(_)]

What are words, concepts, and grammars? How are they related?

How are they related to whatever makes humans distinctive?

Did a relatively small change in our ancestors lead to both the

"linguistic metamorphosis” that human infants undergo, and

significant cognitive differences between us and other primates?


What are words, concepts, and grammars? How are they related?

How are they related to whatever makes humans distinctive?

Did a relatively small change in our ancestors lead to both the

"linguistic metamorphosis” that human infants undergo, and

significant cognitive differences between us and other primates?

Maybe…

we’re cognitively special because we’re linguistically special, and

we’re linguistically special because we acquire words, and

acquiring words is a cognitively creative process, but

grammars are simple (or “Minimal” in Chomsky’s sense)


Humans Acquire...

Words

• can combine grammatically to form phrases and sentences

'horse', 'brown', 'brown horse',

'horses', 'ride', 'ride horses',

'every’, ‘every horse’, ‘ride every horse’,

‘We saw them ride every brown horse’, …

• can be understood and used (externally and internally)

• seem to be distinctively human, although there are many animal

communication systems

Humans Acquire...

Concepts

• can combine to form complex concepts and thoughts

HORSE, BROWN, BROWN_HORSE,

HORSES, RIDE, RIDE_HORSES,

EVERY, EVERY_HORSE, RIDE_EVERY_HORSE,

WE_SAW_THEM_RIDE_EVERY_BROWN_HORSE, …

• can be used to think about things

• seem not to be distinctively human, although there are many distinctively human

concepts

Humans Acquire...

Grammars

• can be used to combine words into phrases and sentences

• can be used to understand phrases and sentences, in terms of the component words

• human grammars seem to be distinctively human

• but other animals surely use various procedures to combine concepts into thoughts (see Fodor, Gallistel)


What are words?

What are concepts?

What are grammars?


How are words, concepts, and grammars related to whatever makes humans distinctive,


How are human grammars related to older animal procedures for combining concepts?


What are words?

What are concepts?

What are grammars?





Concepts:Composable Mental Representations

Two Common Metaphors

• Jigsaw Puzzles

• 7th Grade Chemistry -2

+1H–O–H+1

Jigsaw Metaphor

A

THOUGHT

A

THOUGHTUnsaturatedSaturater

Doubly Un-

saturated

firstsaturater

secondsaturater 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

BrutusSang( )

BrutusCaesar

KICK(1, 2)

7th Grade Chemistry Metaphor

a molecule

of water

a molecule

of water

-2 +1H(OH+1)-1

a single atom with valence -2 can combine with

two atoms of valence +1 to form a stable molecule


-2+1Brutus(KickCaesar+1)-1


+1NaCl-1

an atom with valence -1 can combine with

an atom of valence +1 to form a stable molecule

+1BrutusSang-

1

Extending the Metaphor

AggieBrown(

)

AggieCow( )

AggieBrownCow( )

Brown( ) & Cow( )

Aggie is (a) cow

Aggie is brown

Aggie is (a) brown cow

-1 -1+1 +1

Extending the Metaphor

AggieBrown(

)

AggieCow( )

AggieBrown( ) &

Cow( )

-1 -1+1 +1

Conjoining twomonadic (-1)concepts can

yield a complexmonadic (-1)

concept


What are words?

What are concepts?

What are grammars?





Grammars:Procedures for Combining Words

• Church: function-in-intension vs. function-in-extension

--a procedure that pairs inputs with outputs in a certain way

--a set of input-output pairs

• Frege: each Function determines a "Course of Values”

• Chomsky: I-language vs. E-language

--a biologically implementable procedure that pairs phonological structures (PHONs) with

semantic structures (SEMs)

--a set of <PHON, SEM> pairs

I-Language/E-Language

function in Intension implementable procedure that pairs inputs with

outputs

function in Extension set of input-output pairs

|x – 1| +√(x2 – 2x + 1)

{…(-2, 3), (-1, -2), (0, 1), (1, 0), (2, 1), …}

λx . |x – 1| = λx . +√(x2 – 2x + 1)

λx . |x – 1| ≠ λx . +√(x2 – 2x + 1)

Extension[λx . |x – 1|] = Extension[λx . +√(x2 – 2x + 1)]

Experienceand

Growth

LanguageAcquisition


Language AcquisitionDevice in

a Mature State(an I-Language):

GRAMMAR LEXICON

PHONs

SEMs

Experienceand

Growth

LanguageAcquisition




GRAMMAR LEXICON

PHONs

SEMs

initial concepts

acquired concepts

initial concepts

Articulation andPerception of Signals


What are words?

What are concepts?

What are grammars?





• It seems that concepts must predate words

Old idea: words label concepts

• Acquiring words is basically a process of pairing concepts with perceptible signals

• Word combination should mirror concept combination

• Sentence structure should mirror thought structure

Concept

ofadicity

n

Concept

ofadicity

n

Concept

ofadicity

n

Concept

ofadicity

n Word: adicity n

PerceptibleSignal

Further lexicalinformation

KICKED(1, 2) ‘Brutus kicked Caesar’

‘Brutus kicked Caesar the ball’‘Caesar was kicked’

‘Brutus kicked’ ‘Caesar got a kick’

But what about…

Puzzles for the idea thatWords simply Label Concepts

• Apparent mismatches between how words combine (grammatical form) and how concepts combine (logical form)

KICK(x1, x2) The baby kicked

RIDE(x1, x2) Can you give me a ride?

BEWTEEN(x1, x2, x3) I am between him and her

BIGGER(x1, x2) That is bigger than that

FATHER(…?...) Fathers father

MORTAL(…?...) Socrates is mortalA mortal wound is fatal



BEWTEEN(x1, x2, x3) I am between him and her

why not: Between I him her

BIGGER(x1, x2) This is bigger than that

why not: This bigs that



x2:HORSE(x2)[RODE(Peter, x2)] Peter rode every horse

why not: Every horse rode Peter

or: Every horse Peter rode

That dog is a poodle That dog is a fatherThat dog is brown That dog is yoursThat dog is a brown poodle That dog is (a) your father

Puzzles for the simple idea thatWords simply Label Concepts


• Humans are special linguistically AND cognitively

• Why bother with human syntax (nouns, verbs, prepositions, classifiers, ...)? Why not just pair concepts with signals, and pronounce logical forms "straight"?

• If the labeled concepts can combine without the words, why create the problem of mapping covert expressions into formally distinct overt expressions?

• It seems that concepts must predate words

A less old idea: words help thinkers use available concepts to introduce new ones

• Acquiring words is a formally creative process

• Grammatical structure may not reflect initial conceptual structure

Lexicalization as Concept-Abstraction

Concept of

adicity n

Concept of

adicity n

(initial concept)

Concept of

adicity n

Concept of

adicity n Concept

of adicity k

Concept of

adicity k

PerceptibleSignal

Concept of

adicity n

Concept of

adicity n

Concept

ofadicity

n

Concept

ofadicity

n Word: adicity n

PerceptibleSignal

(initialconcept)

Concept

of adicity

n

Concept

of adicity

n Concept of

adicity k

Concept of

adicity k

PerceptibleSignalWord:

adicity k

Further lexicalinformation

further lexical information

Two Pictures of Lexicalization

Lexicalization as Monadic-Concept-Abstraction

Concept of

adicity n

Concept of

adicity n

(before)

Concept of

adicity n

Concept of

adicity n Concept

of adicity -1

Concept of

adicity -1

PerceptibleSignal

Word: adicity -1

KICK(x1, x2) KICK(event)

Experienceand

Growth

LanguageAcquisition




GRAMMAR LEXICON

PHONs

SEMs

initial concepts

acquired concepts

initial concepts


Experienceand

Growth

LanguageAcquisition




GRAMMAR LEXICON

PHONs

SEMs

initial concepts

other acquired------>

conceptsinitial

concepts


introduced concepts

Documents

Meanings as Instructions for how to Build Concepts Paul M. Pietroski University of Maryland Dept. of Linguistics, Dept. of Philosophy pietro