June 6: General Introduction and “Framing Event Variables”
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Transcript of June 6: General Introduction and “Framing Event Variables”
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June 6: General Introduction and “Framing Event Variables”
June 13: “I-Languages, T-Sentences, and Liars”
June 20: “Words, Concepts, and Conjoinability”
June 27: “Meanings as Concept Assembly Instructions”
SLIDES POSTED BEFORE EACH TALK terpconnect.umd.edu/~pietro
(OR GOOGLE ‘pietroski’ AND FOLLOW THE LINK) [email protected]
Meanings FirstContext and Content Lectures, Institut Jean Nicod
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Reminders of last two weeks...
Human Language: a language that human children can naturally acquire
(D) for each human language, there is a theory of truth that is also the core of an adequate theory of meaning for that language
(C) each human language is an i-language: a biologically implementable procedure that generates expressions that connect meanings with articulations
(B) each human language is an i-language for which there is a theory of truth that is alsothe core of an adequate theory of meaning for that i-language
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(D) for each human language, there is a theory of truth that is also the core of an adequate theory of meaning for that
language
Good Ideas Bad Companion Ideas
“e-positions” allow for “e-positions” are Tarskian variables
conjunction reductions that have mind-independent values
Alvin moved to Venice happily. Alvin moved to Venice.
ee’e’’[AL(e’) & MOVED(e, e’) & T0(e, e’’) & VENICE(e’’) & HAPPILY(e)]ee’e’’[AL(e’) & MOVED(e, e’) & T0(e, e’’) & VENICE(e’’)]
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(D) for each human language, there is a theory of truth that is also the core of an adequate theory of meaning for that language
Good Ideas Bad Companion Ideas
“e-positions” allow for “e-positions” are Tarskian variables
conjunction reductions that have mind-independent values
Alvin moved to Venice happily. Alvin moved Torcello to Venice.
Alvin moved to Venice. Alvin chased Pegasus.
Alvin chased Theodore happily.
Theodore chased Alvin unhappily.
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(D) for each human language, there is a theory of truth that is also the core of an adequate theory of meaning for that language
Good Ideas Bad Companion Ideas
“e-positions” allow for “e-positions” are Tarskian variables
conjunction reductions that have mind-independent values
as Foster’s Problem reveals, the meanings computed are humans compute meanings truth-theoretic properties of via specific operations human i-language expressions Liar Sentences don’t Liar T-sentences are true
preclude meaning theories (‘The first sentence is true.’ iff
for human i-languages the first sentence is true.)
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(D) for each human language, there is a theory of truth that is also the core of an adequate theory of meaning for that language
Good Ideas Bad Companion Ideas
“e-positions” allow for characterizing meaning
conjunction reductions in truth-theoretic terms
yields good analyses as Foster’s Problem reveals, of specific constructions
humans compute meanings via specific operations such
characterization also
helps address foundational Liar Sentences don’t issues concerning how preclude meaning theories human linguistic
expressions for human i-languages could exhibit
meanings at all
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Weeks 3 and 4: Short Form
• In acquiring words, kids use available concepts to introduce new ones
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• Meanings are instructions for how to access and combine i-concepts
--lexicalizing RIDE(_, _) puts RIDE(_) at an accessible address
--introduced concepts can be conjoined via simple operations that require neither Tarskian variables nor a Tarskian ampersand
'ride fast' RIDE( )^FAST( )'fast horse'
FAST( )^HORSE( )'horses'
HORSE( )^PLURAL( )
PLURAL( ) => COUNTABLE(_)
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Weeks 3 and 4: Short Form
• In acquiring words, kids use available concepts to introduce new ones.
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• Meanings are instructions for how to access and combine i-concepts
--lexicalizing RIDE(_, _) puts RIDE(_) at an accessible address
--introduced concepts can be conjoined via simple operations that require neither Tarskian variables nor a Tarskian ampersand
'fast horses' FAST( )^HORSES( )
'ride horses' RIDE( )^[Θ( , _)^HORSES(_)]
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Weeks 3 and 4: Short Form
• In acquiring words, kids use available concepts to introduce new ones.
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• Meanings are instructions for how to access and combine i-concepts
--lexicalizing RIDE(_, _) puts RIDE(_) at an accessible address
--introduced concepts can be conjoined via simple operations that require neither Tarskian variables nor a Tarskian ampersand
'fast horses' FAST( )^HORSES( )
'ride horses' RIDE( )^[Θ( , _)^HORSES(_)]
Meaning('fast horses') = JOIN{Meaning('fast'), Meaning('horses')} Meaning('ride horses') = JOIN{Meaning('ride'), Θ[Meaning('horses')]}
= JOIN{fetch@'ride'), Θ[Meaning('horses')]}
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Weeks 3 and 4: Short Form
• In acquiring words, kids use available concepts to introduce new ones
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• Meanings are instructions for how to access and combine i-concepts
--lexicalizing RIDE(_, _) puts RIDE(_) at an accessible address
--introduced concepts can be conjoined via simple operations that require neither Tarskian variables nor a Tarskian ampersand
'ride horses' RIDE( )^[Θ( , _)^HORSES(_)]
'ride fast horses' RIDE( )^[Θ( , _)^FAST(_)^HORSES(_)]
'ride horses fast' RIDE( )^[Θ( , _)^HORSES(_)]^FAST( )
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Weeks 3 and 4: Very Short Form
• In acquiring words, kids use available concepts to introduce i-concepts, which can be “joined” to form conjunctive monadic concepts,
which may or may not have Tarskian satisfiers.
'fast horses' FAST( )^HORSES( ) 'ride horses' RIDE( )^[Θ( , _)^HORSES(_)]
'ride fast horses' RIDE( )^[Θ( , _)^FAST(_)^HORSES(_)] 'ride fast horses fast' RIDE( )^[Θ( , _)^FAST(_)^HORSES(_)]^FAST( )
• Some Implications
Verbs do not fetch genuinely relational concepts
Verbs are not saturated by grammatical arguments
The number of arguments that a verb can/must combine with
is not determined by the concept that the verb fetches
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Words, Concepts, and Conjoinability
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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
FACT: human children are the world’s best lexicalizers
SUGGESTION: focus on lexicalization is independently plausible
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Constrained Homophony Again
• A doctor rode a horse from Texas
• A doctor rode a horse, and
(i) the horse was from Texas
(ii) the ride was from Texas
why not…
(iii) the doctor was from Texas
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Leading Idea (to be explained and defended)
• In acquiring words, we use available concepts to introduce new ones
Sound(’ride’) + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + ’chase’
• The new concepts can be systematically conjoined in limited ways
'rode a horse from Texas'
RODE(_) & [Θ(_, _) & HORSE(_) & FROM(_, TEXAS)]
RIDE(_) & PAST(_) & [Θ(_, _) & HORSE(_) & [FROM(_, _) & TEXAS(_)]]
RODE(_) & [Θ(_, _) & HORSE(_)] & FROM(_, TEXAS)
y[RODE(x, y) & HORSE(y)] & FROM(x, TEXAS)
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A doctor rode a horse from Texas
A doctor rode a horse that was from Texas
x{Doctor(x) & y[Rode(x, y) & Horse(y) & From(y, Texas)]}
&
A doctor rode a horse from Texas
&A doctor rode a horse and the ride was from Texas
ex{Doctor(x) & y[Rode(e, x, y) & Horse(y) & From(e,
Texas)]}
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A doctor rode a horse from Texas
A doctor rode a horse that was from Texas ex{Doctor(x) & y[Rode(e, x, y) & Horse(y) & From(y, Texas)]}
&
A doctor rode a horse from Texas
&A doctor rode a horse and the ride was from Texas
ex{Doctor(x) & y[Rode(e, x, y) & Horse(y) & From(e,
Texas)]}
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A doctor rode a horse from Texas
&A doctor rode a horse and the ride was from Texas
ex{Doctor(x) & y[Rode(e, x, y) & Horse(y) & From(e,
Texas)]}
But why doesn’t the structure below support a different meaning:A doctor both rode a horse and was from Texas
ex{Doctor(x) & y[Rode(e, x, y) & Horse(y) & From(x, Texas)]}
Why can’t we hear the verb phrase as a predicate that is satisfied by x iff x rode a horse & x is from Texas?
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• In acquiring words, we use available concepts to introduce new ones
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• The new concepts can be systematically conjoined in limited ways
'rode a horse from Texas'
RODE(_) & [Θ(_, _) & HORSE(_) & FROM(_, TEXAS)]RODE(_) & [Θ(_, _) & HORSE(_)] & FROM(_, TEXAS)y[RODE(e, x, y) & HORSE(y)] & FROM(x, TEXAS)
if 'rode' has a rider-variable, why can’t it be targeted by 'from Texas’?
Verbs don’t fetch genuinely relational concepts.A phrasal meaning leaves no choice
about which variable to target.
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• In acquiring words, we use available concepts to introduce new ones
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• The new concepts can be systematically conjoined in limited ways
'rode a horse from Texas'
RODE(_)^[Θ(_, _)^HORSE(_)^FROM(_, TEXAS)]RODE(_)^[Θ(_, _)^HORSE(_)]^FROM(_, TEXAS)y[RODE(e, x, y) & HORSE(y)] & FROM(x, TEXAS)
Composition is simple and constrained, but unbounded.
Phrasal meanings are generable, but always monadic.Lexicalization introduces concepts that can be
systematically combined in simple ways.
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• In acquiring words, we use available concepts to introduce new ones
Sound('ride') + RIDE(_, _) ==> RIDE(_) + RIDE(_, _) + 'ride'
• DISTINGUISH
Lexicalized concepts, L-concepts
RIDE(_, _) GIVE(_, _, _) ALVIN HORSE(_)RIDE(_, _, ...) MORTAL(_, _)
Introduced concepts, I-concepts
RIDE(_) GIVE(_) CALLED(_, Sound('Alvin'))MORTAL(_) HORSE(_)
hypothesis: I-concepts exhibit less typology than L-conceptsspecial case: I-concepts exhibit fewer adicities than L-concepts
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Conceptual Adicity
Two Common Metaphors
• Jigsaw Puzzles
• 7th Grade Chemistry -2+1H–O–H+1
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Jigsaw Metaphor
A
THOUGHT
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Jigsaw Metaphor
UnsaturatedSaturater
Doubly Un-
saturated
1stsaturater
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
BrutusSang( )
Brutus CaesarKICK(_, _)
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7th Grade Chemistry Metaphor
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
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7th Grade Chemistry Metaphor
-2+1Brutus(KickCaesar+1)-1
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7th Grade Chemistry Metaphor
+1NaCl-1
an atom with valence -1 can combine with
an atom of valence +1 to form a stable molecule
+1BrutusSang-1
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Extending the Metaphor
AggieBrown( )
AggieCow( )
AggieBrownCow( )
Brown( ) &
Cow( )
Aggie is (a) cow
Aggie is brown
Aggie is (a) brown cow
-1 -1+1 +1
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Extending the Metaphor
AggieBrown( )
AggieCow( )
Aggie
-1 -1+1 +1
Conjoining twomonadic (-1)concepts can
yield a complexmonadic (-1)
concept
Brown( ) &
Cow( )
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Conceptual Adicity
TWO COMMON METAPHORS--Jigsaw Puzzles--7th Grade Chemistry
DISTINGUISHLexicalized concepts, L-concepts
RIDE(_, _) GIVE(_, _, _) ALVIN Introduced concepts, I-concepts
RIDE(_) GIVE(_)CALLED(_, Sound(’Alvin’))
hypothesis: I-concepts exhibit less typology than L-conceptsspecial case: I-concepts exhibit fewer adicities than L-concepts
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A Different (and older) Hypothesis
(1) concepts predate words
(2) words label concepts
• Acquiring words is basically a process of pairing pre-existing concepts with perceptible signals
• Lexicalization is a conceptually passive operation
• Word combination mirrors concept combination
• Sentence structure mirrors thought structure
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Bloom: How Children Learn the Meanings of Words
• word meanings are, at least primarily, concepts that kids have prior to lexicalization
• learning word meanings is, at least primarily, a process of figuring out which
existing concepts are paired with which word-sized signals
• in this process, kids draw on many capacities—e.g., recognition of syntactic cues and speaker intentions—but no capacities specific to acquiring word meanings
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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…”
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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…”
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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 Caesar
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Concept of
adicity n
Concept of
adicity n
PerceptibleSignal
Quirky information for lexical items like ‘kick’
Concept of
adicity -1
PerceptibleSignal
Quirky information for lexical items like ‘put’
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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.
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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.
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Quirks and Provisos, or Normal Cases?
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
why not: I between him her
BIGGER(x1, x2) This is bigger than that why not: This bigs that
MORTAL(…?...) Socrates is mortal
A mortal wound is fatal
FATHER(…?...) Fathers father
Fathers father future fathersEAT/DINE/GRAZE(…?...)
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Lexicalization as Concept-Introduction (not mere labeling)
Concept of
type TConcep
t of
type TConcept
of type T*
PerceptibleSignal
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Lexicalization as Concept-Introduction (not mere labeling)
PerceptibleSignal
Number(_)
type:<e, t> Number(_
)type:
<e, t>NumberOf[_,
Φ(_)]type:
<<e, t>, <n, t>>
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Lexicalization as Concept-Introduction (not mere labeling)
Concept of
type TConcep
t of
type TConcept
of type T*
PerceptibleSignal
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Concept of
adicity -1 Concept
of adicity -
1 Concept of
adicity -2
PerceptibleSignal
ARRIVE(x) ARRIVE(e, x)
One Possible (Davidsonian) Application: Increase Adicity
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Concept of
adicity -2 Concept
of adicity -
2 Concept of
adicity -3
PerceptibleSignal
KICK(x1, x2) KICK(e, x1, x2)
One Possible (Davidsonian) Application: Increase Adicity
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Concept of
adicity n Concept
of adicity
nConcept
of adicity -1
PerceptibleSignal
KICK(x1, x2) KICK(e)
KICK(e, x1, x2)
Lexicalization as Concept-Introduction: Make Monads
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Concept of
adicity n
Concept of
adicity n(or n−1)
PerceptibleSignal
Concept of
adicity nConcept of
adicity −1
PerceptibleSignal
Further lexical
information(regarding flexibilities)
further lexical information
(regarding inflexibilities)
Two Pictures of Lexicalization
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Experienceand
Growth
LanguageAcquisition
Device in itsInitial State
Language AcquisitionDevice in
a Mature State(an I-Language):
GRAMMAR LEXICON
PhonologicalInstructions
Semantic InstructionsLexicalizable
concepts
Introduced concepts
Articulation and Perception
of Signals
Lexicalized concepts
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Concept of
adicity n
Concept of
adicity n(or n−1)
PerceptibleSignal
Concept of
adicity nConcept of
adicity −1
PerceptibleSignal
Further lexical
information(regarding flexibilities)
further lexical information
(regarding inflexibilities)
Two Pictures of Lexicalization
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Subcategorization
A 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, …
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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 cup
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On any view: 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
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On any view: Two Kinds of Facts to Accommodate
• Flexibilities– The coin melted– The jeweler melted the coin– The fire melted the coin– The coin vanished– The magician vanished the coin
• Inflexibilities– Brutus arrived– *Brutus arrived Caesar
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Concept of
adicity n Concept
of adicity n
Concept of adicity
−1
PerceptibleSignal
further POSSE information,
as for ‘put
Two Pictures of Lexicalization
Word: SCAN -1
Last Task for Today(which will carry over to next time):
offer some reminders of the reasons for adopting the second picture
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Absent Word Meanings
Striking absence of certain (open-class) lexical meanings that would be permitted if Human I-Languages permitted 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 concepts
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Proper Nouns
• even English tells against the idea that lexical proper nouns label singular concepts (of type <e>)
• Every Tyler I saw was a philosopherEvery philosopher I saw was a Tyler There were three Tylers at the partyThat Tyler stayed late, and so did this onePhilosophers have wheels, and Tylers have stripesThe Tylers are coming to dinnerI 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 concepts
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Concept of
adicity n Concept
of adicity
nConcept
of adicity -1
PerceptibleSignal
TYLER TYLER(x)
CALLED[x, SOUND(‘Tyler’)]
Lexicalization as Concept-Introduction: Make Monads
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Concept of
adicity n Concept
of adicity
nConcept
of adicity -1
PerceptibleSignal
KICK(x1, x2) KICK(e)
KICK(e, x1, x2)
Lexicalization as Concept-Introduction: Make Monads
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Concept of
adicity n Concept
of adicity
nConcept
of adicity -1
PerceptibleSignal
TYLER TYLER(x)
CALLED[x, SOUND(‘Tyler’)]
Lexicalization as Concept-Introduction: Make Monads
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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 concepts
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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 $
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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 car
Brutus 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 anonymously
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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)
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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
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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 concepts
I’ll come back to this next week
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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
FACT: human children are the world’s best lexicalizers
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One of Aristotle’s Observations
Some animals are born early, and take time to grow into their “second nature”
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One of Aristotle’s Observations
Some animals are born early, and take time to grow into their “second nature”
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Experienceand
Growth
LanguageAcquisition
Device in itsInitial State
Language AcquisitionDevice in
a Mature State(an I-Language):
GRAMMAR LEXICON
PhonologicalInstructions
Semantic InstructionsLexicalizable
concepts
Introduced concepts
Articulation and Perception
of Signals
Lexicalized concepts
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Weeks 3 and 4: Very Short Form
• In acquiring words, kids use available concepts to introduce i-concepts, which can be “joined” to form conjunctive monadic concepts,
which may or may not have Tarskian satisifiers.
'fast horses' FAST( )^HORSES( ) 'ride horses' RIDE( )^[Θ( , _)^HORSES(_)]
'ride fast horses' RIDE( )^[Θ( , _)^FAST(_)^HORSES(_)] 'ride fast horses fast' RIDE( )^[Θ( , _)^FAST(_)^HORSES(_)]^FAST( )
• Some Implications
Verbs do not fetch genuinely relational concepts
Verbs are not saturated by grammatical arguments
The number of arguments that a verb can/must combine with is not determined by the concept that the verb fetches
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Words, Concepts, and Conjoinability
THANKS!
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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
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Lots of Conjoiners
• P & Q purely propositional
• Fx &M Gx purely monadic
• ??? ???
• Rx1x2 &DF Sx1x2 purely dyadic, with fixed orderRx1x2 &DA Sx2x1 purely dyadic, any order
• Rx1x2 &PF Tx1x2x3x4 polyadic, with fixed order
Rx1x2 &PA Tx3x4x1x5 polyadic, any order
Rx1x2 &PA Tx3x4x5x6 the number of variables in the
conjunction can exceed
the number in either conjunct
NOT EXTENSIONALLY EQUIVALENT
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Lots of Conjoiners, Semantics
• If π and π* are propositions, then TRUE(π & π*) iff TRUE(π) and TRUE(π*)
• If π and π* are monadic predicates, then for each entity x: APPLIES[(π &M π*), x] iff APPLIES[π, x] and APPLIES[π*, x]
• If π and π* are dyadic predicates, then for each ordered pair o: APPLIES[(π &DA π*), o] iff APPLIES[π, o] and APPLIES[π*, o]
• If π and π* are predicates, then for each sequence σ: SATISFIES[σ, (π &PA π*)] iff SATISFIES[σ, π] and
SATISFIES[σ, π*] APPLIES[σ, (π &PA π*)] iff APPLIES[π, σ] and
APPLIES[π*, σ]
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Lots of Conjoiners
• P & Q purely propositional
• Fx &M Gx purely monadic
Fx^Gx ; Rex^Gx a monad can “join” with a monad
or a dyad (with order fixed)
• Rx1x2 &DF Sx1x2 purely dyadic, with fixed orderRx1x2 &DA Sx2x1 purely dyadic, any order
• Rx1x2 &PF Tx1x2x3x4 polyadic, with fixed order
Rx1x2 &PA Tx3x4x1x5 polyadic, any order
Rx1x2 &PA Tx3x4x5x6 the number of variables in the
conjunction can exceed
the number in either conjunct
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A Restricted Conjoiner and Closer, allowing for a smidgeon of dyadicity
• If M is a monadic predicate and D is a dyadic predicate,
then for each ordered pair <x, y>:
the junction D^M applies to <x, y> iff
D applies to <x, y> and M applies to y
• [D^M] applies to x iff
for some y, D^M applies to <x, y>
D applies to <x, y> and M applies to y
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A Restricted Conjoiner and Closer, allowing for a smidgeon of dyadicity
• If M is a monadic predicate and D is a dyadic predicate,
then for each ordered pair <x, y>:
the junction D^M applies to <x, y> iff
D applies to <x, y> and M applies to y
• [Into(_, _)^Barn(_)] applies to x iff
for some y, Into(_, _)^Barn(_) applies to <x, y>
Into(_, _) applies to <x, y> and Barn(_) applies to y