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Meanings as Instructions
for how to Build Concepts
Paul M. Pietroski
University of Maryland
Dept. of Linguistics, Dept. of Philosophy
http://www.terpconnect.umd.edu/~pietro
In our last episode…
Humans acquire words, concepts, and
grammars
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
(After all, kids are really good at acquiring words.)
Two Pictures of
Lexicalization
Further lexical
information
Concept
of
adicity n
Concept
of
adicity n
(initial
concept)
Perceptible
Signal
Word: adicity n
Concept
of
adicity n
further lexical
information
Word:
adicity k
Concept
of
adicity k
Perceptible
Signal
Puzzles for the idea that
Words 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 mortal
A mortal wound is fatal
Lexicalization as Monadic-Concept-Abstraction
KICK(x1, x2)
KICK(event)
Concept
of
adicity n
(before)
Concept
of
adicity n
Word:
adicity -1
Concept
of adicity
-1
Perceptible
Signal
Articulation and
Perception of Signals
Language
Acquisition
Device in its
Initial State
Experience
and
Growth
PHONs
Language Acquisition
Device in
a Mature State
(an I-Language):
GRAMMAR
LEXICON
initial
concepts
SEMs
introduced
concepts
other
acquired------>
concepts
initial
concepts
Language Acquisition
Device in
a Mature State
(an I-Language):
GRAMMAR
LEXICON
what kinds of concepts
do SEMs interface
with?
SEMs
introduced
concepts
other
acquired------>
concepts
initial
concepts
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 horses’
RIDE(_) & FAST(_)
RIDE(_) & [THEME(_, _) & HORSES(_)]
'ride horses fast’
FAST(_)
RIDE(_) & [THEME(_, _) & HORSES(_)] &
‘ride fast horses’
HORSES(_)]
RIDE(_) & [THEME(_, _) & FAST(_) &
Yeah, yeah. But…
• how could infants use (largely innate) nonmonadic
concepts to introduce monadic concepts?
• is there evidence that they do so
• what about polysemy
• what kind of quantifier is that red thing in
RIDE(_) & [THEME(_, _) & HORSES(_)]
• and what kind of conjunction does that blue ampersand
indicate
A Possible Mind
KICK(x1, x2)
KICK(x1, x2)
AGENT(_, x1)
PATIENT(_, x2)
KICK(_, x1, x2)
≡df
a prelexical concept
for some _, KICK(_, x1, x2)
generic “action” concept
≡df AGENT(_, x1) & KICK(_) & PATIENT(_, x2)
CAESAR , PF:‘Caesar’
Called(CAESAR, PF:‘Caesar’)
Called(_, PF:‘Caesar’)
mental labels for a person and a sound
a thought about what the person is called
≡df CAESARED(_)
KICK(_) introduced via: KICK(_, x1, x2) AGENT(_, x1) PATIENT(_, x2)
&
KICK(_, x1, x2) introduced via:
KICK(_, x1, x2)
for some _
A Possible Mind
‘kick’ fetches KICK(_)
‘Caesar’ fetches CAESARED(_)
‘that Caesar’ directs construction of the complex concept
CONTEXTUALLY-INDICATED(_) & CAESARED(_)
‘kick that Caesar’ directs construction of the complex concept
KICK(_) & [PATIENT(_, _) & CONT-INDICATED(_) &
CAESARED(_)]
 binds the variable of each monadic concept in its scope
[PATIENT(_, _) & CONTEXTUALLY-INDICATED(_) &
CAESARED(_)]
|___________________________________________|___________
____|
PATIENT(_, _) links its second variable to the local /monadic concept
[PATIENT(_, _) & CONTEXTUALLY-INDICATED(_) &
A Relevant Empirical Consideration
Not even English provides good evidence for lexical nouns that simply
label singular (saturating) concepts like CAESAR, TYLER, or BURGE
Every Tyler I saw at the party 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
At noon, we saw Tyler Burge
At noon, we saw Professor Burge
At noon, we saw Professor Tyler Burge
A Relevant Empirical Consideration
Not even English provides good evidence for lexical verbs that simply
label polyadic (unsaturated) concepts like KICK(x1, x2) or EAT(x1, x2)
The baby kicked
The ball was kicked
I kicked the dog a bone
I get no kick from Champagne, but I get a kick out of you
I ate very well last night. We dined at a nice restaurant.
The fish was selected, cooked, and then eaten.
Compare: I fueled the car.
I fueled up.
Two Roles for Words on this View
(1) In lexicalization…
acquiring a (spoken) word is a process of pairing a sound with a
concept—the concept lexicalized—storing that sound/concept pair in
memory, and then using that concept to introduce a concept that can be
combined with others via certain (limited) composition operations
sound-of-‘kick’/KICK(x1, x2)
sound-of-‘kick’/KICK(x1, x2)/KICK(_)
at least for “open class” lexical items (nouns, verbs, adjectives/adverbs)
the introduced concepts are monadic and conjoinable with others
(2) in subsequent comprehension…
a word is an instruction to fetch an introduced concept from the relevant
address in memory
Caveat: Polysemy
1st approximation, ‘book’ fetches BOOK(_)
2nd approximation, ‘book’ fetches one of
-abstractBOOK(_), +abstractBOOK(_)
A Possible Course of Lexicalization
sound-of-‘book’/-abstractBOOK
(adicity of initial concept not obvious)
sound-of-‘book’/-abstractBOOK/-abstractBOOK(_)
sound-of-‘book’/-abstractBOOK/-abstractBOOK(_)
|
+abstractBOOK/+abstractBOOK(_)
Caveat: Polysemy
1st approximation, ‘book’ fetches BOOK(_)
2nd approximation, ‘book’ fetches one of
-abstractBOOK(_), +abstractBOOK(_)
But we also have to think about…
‘coloring book’
‘blank book’ ‘book a cruise’
3rd approximation, ‘book’ fetches one of
‘book a criminal’
…
-abstractBOOK1(_), +abstractBOOK1(_)
-
abstractBOOK1(_), +abstractBOOK1(_)
…
Polysemy via Austin/Chomsky
SEM(‘hexagonal’) = fetch@‘hexagonal’
SEM(‘republic’) = fetch@‘republic’
SEM(‘hexagonal republic’) =
CONJOIN[fetch@‘hexagonal’, fetch@‘republic’]

HEXAGONAL(_) & REPUBLIC(_)
Her country is hexagonal/mountainous/nearby
Her country is a republic/politically stable/wealthy
two or more Introduced-CONCEPTS may reside at the ‘country’ bin
A Slightly More Interesting Example
two or more I(ntroduced)-CONCEPTS may reside at ‘country’
fetch@‘country’  TERRA-COUNTRY(_)
POLIS-COUNTRY(_)
CONJOIN[fetch@‘country’, fetch@‘hexagonal’] 
TERRA-COUNTRY(_) & HEXAGONAL(_)
POLIS-COUNTRY(_) & HEXAGONAL(_)
CONJOIN[fetch@‘country’, fetch@‘republic’] 
TERRA-COUNTRY(_) & REPUBLIC(_)
POLIS-COUNTRY(_) & REPUBLIC(_)
Caveat: Subcategorization
Not saying that a verb meaning is merely an instruction to fetch a (tensefriendly) monadic concept of things that can have participants
Distinguish:
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 (indexable) terms, one term, two terms, …
Caveats
POSSE facts may reflect, among other things (e.g. statistical experience),
the adicities of concepts lexicalized,
the verb ‘put’ may have a (lexically represented) POSSE of three in part
because the concept lexicalized is PUT(x, y, z)
though note: speakers of English still say ‘I put the cup ON THE table’,
not ‘I put the cup the table’.
So there is no reason to conclude that ‘put’ simply labels PUT(x, y, z)
Two Kinds of Facts to Accommodate
Flexibilities
Brutus kicked Caesar
Caesar was kicked
The baby kicked
I get a kick out of you
Brutus kicked Caesar the ball
Inflexibilities
Brutus put the ball on the table
*Brutus put the ball
*Brutus put on the table
Two Pictures of
Lexicalization
further
“flexibility” facts
(as for ‘kick’)
Concept
of adicity
n
Concept
of
adicity n
(before)
Concept
of adicity
n
Word: adicity
(SCAN) n
further “posse” facts
(as for ‘put’)
Concept
of
adicity -1
Perceptible
Signal
Perceptible
Signal
Word:
adicity -1
“Negative” Facts to Accommodate
Striking absence of certain (open-class) lexical meanings
that would be permitted
if I-Languages permit nonmonadic semantic types
“Negative” Facts to Accommodate
Brutus sald a car Caesar a dollar
sald
 SOLD(x, w, z, y)
[sald [a car]]  SOLD(x, w, z, a car)
[[sald [a car]] Caesar]
x sold y to z
(in exchange) for w
 SOLD(x, w, Caesar, a car)
[[[sald [a car]] Caesar]] a dollar]  SOLD(x, $, Caesar, a car)
_________________________________________________
Brutus tweens Caesar Antony
tweens
 BETWEEN(x, z, y)
[tweens Caesar]  BETWEEN(x, z, Caesar)
[[tweens Caesar] Antony]  BETWEEN(x, Antony, Caesar)
“Negative” Facts to Accommodate
Alexander jimmed the lock a knife
 JIMMIED(x, z, y)
jimmed
[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)
“Negative” Facts to Accommodate
Brutus talls Caesar
 IS-TALLER-THAN(x, y)
talls
[talls Caesar]  IS-TALLER-THAN(x, Caesar)
_________________________________________________
*Julius Caesar
Julius
 JULIUS
Caesar  CAESAR
Emprical Point…
There is little to no evidence of any lexical items
ever fetching supradyadic concepts
Brutus gave Caesar the ball
Brutus kicked Caesar the ball
Brutus gave/kicked the ball to Caesar
Various (e.g., Larson-style) analyses of ditransitive
constructions, without ditransitive verbs
But…
If the basic mode of semantic composition is conjunction of monadic
concepts,
then we can start to explain the absence of lexical meanings like…
SOLD(x, w, z, y)
BETWEEN(x, z, y)
JIMMIED(x, z, y)
COMES-FROM(x, y)
IS-TALLER-THAN(x, y)
TYLER
Language Acquisition
Device in
a Mature State
(an I-Language):
GRAMMAR
LEXICON
what kinds of concepts
do SEMs interface
with?
SEMs
introduced
concepts
other
acquired------>
concepts
initial
concepts
Idea
• 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 horses’
RIDE(_) & FAST(_)
RIDE(_) & [THEME(_, _) & HORSES(_)]
'ride horses fast’
FAST(_)
RIDE(_) & [THEME(_, _) & HORSES(_)] &
‘ride fast horses’
HORSES(_)]
RIDE(_) & [THEME(_, _) & FAST(_) &
Meanings as Instructions for
how to build (Conjunctive) Concepts
The meaning (SEM) of [rideV fastA]V is the following instruction:
CONJOIN[execute:SEM(‘ride’), execute:‘SEM(‘fast’)]
CONJOIN[fetch@‘ride’,
fetch@‘fast’]
Executing this instruction yields a concept like
RIDE(_) & FAST(_)
But the meaning (SEM) of [rideV horsesN]V is NOT the following instruction:
CONJOIN[execute:SEM(‘ride’), execute:SEM(‘horses’)]
CONJOIN[fetch@‘ride’, fetch@‘horses’]
Executing this instruction would yield a concept like
RIDE(_) & HORSES(_)
Meanings as Instructions for
how to build (Conjunctive) Concepts
The meaning (SEM) of [rideV fastA]V is the following instruction:
CONJOIN[fetch@‘ride’, fetch@‘fast’]
Executing this instruction yields a concept like
RIDE(_) & FAST(_)
The meaning (SEM) of [rideV horsesN]V is the following instruction:
CONJOIN[fetch@‘ride’, DirectObject:SEM(‘horses’)]
CONJOIN[fetch@‘ride’, Thematize-execute:‘SEM(‘horses’)]
Executing this instruction would yield a concept like
RIDE(_) & [THEME(_, _) & HORSES(_)]
RIDE(_) & [THEME(_, _) & HORSE(_) & PLURAL(_)]
Meanings as Instructions for
how to build (Conjunctive) Concepts
The meaning of [[rideV horsesN]V fastA]V is the following instruction:
CONJOIN[execute:SEM([rideV horsesN]V), execute:SEM(fastA)]
Executing this instruction yields a concept like
RIDE(_) & [THEME(_, _) & HORSES(_)] & FAST(_)
The meaning of [[rideV [fastA horsesN]N]V is the following instruction:
CONJOIN[fetch@‘ride’, DirectObject:SEM([fastA horsesN]N)]
Executing this instruction yields a concept like
RIDE(_) & [THEME(_, _) & FAST(_) & HORSES(_)]
Meanings as Instructions for
how to build (Conjunctive) Concepts
On this view, meanings are neither extensions nor concepts.
Familiar difficulties for the idea that lexical meanings are concepts
polysemy
1 meaning, 1 cluster of concepts (in 1 mind)
intersubjectivity
1 meaning, 2 concepts (in 2 minds)
jabber(wocky)
1 meaning, 0 concepts (in 1 mind)
But a single instruction to fetch a concept from a certain address
can be associated with more (or less) than one concept
Meaning constancy at least for purposes of meaning composition