core knowledge system of mental representations, conceptual content acquisition supported...
TRANSCRIPT
![Page 1: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/1.jpg)
Core Knowledge
• System of mental representations, conceptual content
• Acquisition supported (partially) by innate, domain specific, learning mechanisms
• Entity identification supported by innate, domain specific input analyzers
• Evolutionarily ancient (often)
• Continuous throughout development
![Page 2: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/2.jpg)
Case Study for Today
• Number. Two core systems described inFeigenson, Spelke and Dehaene--1) Analog magnitude representations of
number. Dehaene’s “number sense.”--2) Parallel representation of small sets of
individuals. When individuals are objects, object indexing and short term memory system of mid-level vision (Pylyshyn FINSTs, Triesman’s object-files.)
![Page 3: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/3.jpg)
Core System 1: Analog Magnitude Representations
• Representations of approximate cardinal values of large sets of individuals (at least to the 100s)
![Page 4: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/4.jpg)
![Page 5: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/5.jpg)
![Page 6: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/6.jpg)
![Page 7: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/7.jpg)
![Page 8: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/8.jpg)
Analog Magnitude Models
• Number represented by a quantity linearly related to the cardinal value of the set.
• One: __
• Two: ____
• Three: ______
• Seven: ______________
• Eight: ________________
![Page 9: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/9.jpg)
Weber’s law
• Neural quantity a linear function of real world quantity, variance proportional to the mean
• Neural quantity a logarithmic function of real world quantity, constant variance
![Page 10: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/10.jpg)
8 vs. 16
![Page 11: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/11.jpg)
Weber Fraction Signature
• Seven month-old infants succeed at:• 8 vs. 16 (dots and streams of sounds)• 16 vs. 32• Seven month-old infants fail at:• 8 vs. 12 (both modalities)• 16 vs. 24• By nine months of age, the ratio of
success is 2:3. In both modalities.
![Page 12: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/12.jpg)
Characteristics
• Amodal (input from different modalities transformed into abstract analog magnitude representation of number)
• Computations carried out over these representations:
--addition, subtraction, numerical comparison, multiplication and division. Including in pre-arithmetic infants and preschoolers.
![Page 13: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/13.jpg)
Core System 2
• Parallel individuation, attention/short term memory—signature, limited to 3 or 4 items attended to in parallel (Pylyshyn multiple object tracking, subitizing, limits on short-term working memory)
• Not a dedicated number representational system.
• Implicitly represents the number of individuals in small sets
![Page 14: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/14.jpg)
Converging measures of small-number representations:The locomotor choice task (Feigenson, Carey & Hauser, 2002)
![Page 15: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/15.jpg)
Infant Ordinal Choice
0%10%20%30%40%50%60%70%80%90%
10mos1vs2
12mos1vs2
10mos2vs3
12mos2vs3
10mos3vs4
12mos3vs4
3vs6 2vs4 1vs4
Percent Correct
![Page 16: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/16.jpg)
![Page 17: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/17.jpg)
Box reach task
+ 2 in, 1 out, compared to 1 in, 1 out
+ 3 in, 1 out, compared to 1 in, 1 out
+ 3 in, 2 out, compared to 2 in, 2 out
X 4 in, 2 out, compared to 2 in, 2 out
X 4 in, 1 out, compared to 1 in, 1 out
![Page 18: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/18.jpg)
Parallel Individuation Models
• 1 cracker ■
• 2 crackers ■ ■
• 3 crackers ■ ■ ■
• --one symbol for each individual
• --no symbols for integers
![Page 19: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/19.jpg)
Underlies
• Habituation with small numbers
• Wynn’s addition and subtraction paradigms with small numbers
• Cracker choice
• Reach into box task
• In adults—parallel individuation in attention, short-term memory (Pylyshyn’s Multiple object tracking, subitizing)
![Page 20: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/20.jpg)
Not a dedicated number representation system
• Computations defined over these representations include:
--sum total spatial extent, comparisons of total volume/surface area/contour (simple habituation when individuals have same properties, cracker choice)
--1-1 correspondence, establish numerical equality/inequality; numerical more/less (simple habituation when individuals have distinct properties, box reach choice)
--chunking/set binding (can do two sets, each subject to limit of 3—e.g., cracker choice)
![Page 21: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/21.jpg)
Numerical content
• Criteria of individuation and numerical identity. (spatio-temporal criteria for numerical identity).
• Successor function implicit.
• Operations defined over object files; compose sets, addition, subtraction, 1-1 correspondence to establish numerical equivalence, more less.
![Page 22: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/22.jpg)
DISTINCT CORE SYSTEMS
• Analog Magnitude—
Dedicated number representation, symbol for number
Limited by Weber fraction
Not concerned with properties of individuals, including size, nor with spatial properties of sets, including overall envelope, density of individuals within etc.
Not spontaneously deployed for sets under 4.
![Page 23: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/23.jpg)
Parallel individuation
• Limited by absolute set size. Cannot represent sets of 4 or greater.
• No summary symbol for number.• Binds properties of individuals in
representations, including size• Some number relevant computations
defined over object files, but also very sensitive to continuous quantities like total front surface area.
![Page 24: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/24.jpg)
Core Knowledge
• System of mental representations, conceptual content
• Acquisition supported (partially) by innate, domain specific, learning mechanisms
• Entity identification supported by innate, domain specific input analyzers
• Evolutionarily ancient (often)
• Continuous throughout development
![Page 25: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/25.jpg)
A third system
• Failure at 4 vs 1--cracker choice--box reach 12, 14, 18, 20 months. When tracking individuals, no representation
of number of individuals beyond 3.No singular/plural distinction defined over
object file representation or analog magnitude
![Page 26: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/26.jpg)
Analog Magnitude Models
• Number represented by a quantity linearly related to the cardinal value of the set.
• One: _________________no principled break• Two: ____• Three: ______• Seven: ______________• Eight: ________________
![Page 27: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/27.jpg)
Parallel Individuation Models
1 cracker ■
________________no principled break
2 crackers ■ ■
3 crackers ■ ■ ■
• --one symbol for each individual
• --no symbols for integers
![Page 28: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/28.jpg)
Third (Core ?) System: Chierchia/Link
Atoms, Semi-lattice of sets constructed out of those atoms. Unified treatment of singular/plural, quantifiers (“no, some, all, each”), count/mass distinction, definite determiner, collective nouns, classifier languages. Cross-linguistically universal
![Page 29: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/29.jpg)
{a,b,c,d,…}
{a,b,c} {a,b,d} {b,c,d} {a,c,d} ...
{a,b} {a,c}
a b
{a,d} {b,c} {b,d} {c,d}
c d ... = At
...
![Page 30: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/30.jpg)
Relation to language acquisition?
• No core knowledge of singular/plural, quantifiers?
• Becomes available to conceptual system only upon learning language?
1) Quinian bootstrapping?
2) Becomes conceptually salient/available only upon mastery in language?
![Page 31: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/31.jpg)
Question 1—When plural marking mastered in English?
• Koudier et al. (on website)
• Wood et al. (will describe)
![Page 32: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/32.jpg)
Koudier et al.
![Page 33: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/33.jpg)
![Page 34: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/34.jpg)
![Page 35: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/35.jpg)
![Page 36: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/36.jpg)
Overall pattern of results
Failure at 20 months with multiple cues,
Failure at 24 months when plurality marked only on noun morphology
Success at 24 months with multiple cues
Success at 36 months (not tested earlier) when plurality marked only on noun morphology
![Page 37: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/37.jpg)
Conclusions
• English learning infants master singular/plural marking between 20 and 24 months.
• “Is a” vs “Are some” before “N” vs “Ns”
• Seems to have adult semantic force from the beginning. (No Quinian scrambling up a bootstrapping ladder to master the semantic force of “a”.
![Page 38: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/38.jpg)
Parallel results—box search task
• Look into box. “Look, this is a ball in the box. I see a ball.”
• Hand to child• “You get the ball.”• vs• Look into box. “Look, there are some balls in the
box. I see some balls.”• Hand box to child.• “You get the balls.”
![Page 39: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/39.jpg)
Dependent Measure
• There is always only 1 ball in the box.• The child reaches in and retrieves it.• Dependent measure—search time for
additional ball(s).Results—at 24 months, children succeed.At 20 fail. At 24 months, fail if marked by
noun morphology alone.“I see my balls in the box.” vs “I see my ball
in the box.” Etc.
![Page 40: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/40.jpg)
Two convergent measures
• Exactly the same age trends.
![Page 41: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/41.jpg)
Relation between verbal/non-verbalsingular/plural marking
• Non-verbal 1-4 task—infants fail even at 20-months.
• Infants come to mark singular-plural by 24 months, fail to do so at 24-months.
• Question—are these developments related?
• If so, direction of causality?
![Page 42: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/42.jpg)
Barner et al.
![Page 43: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/43.jpg)
![Page 44: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/44.jpg)
![Page 45: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/45.jpg)
![Page 46: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/46.jpg)
Conclusions
• English plural marking mastered between 20 and 22 months.
• Success on box-reach task emerges between 20 and 22 months.
• Success on two tasks correlated within this age range. I.e., success on box reach task among 22 and 24 month olds carried by those whose parents say are producing plural morphology.
![Page 47: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/47.jpg)
Direction of causation?
• Conceptual development allows learning of singular/plural distinction?
• Mastery of singular/plural distinction makes conceptual distinction between individual/set of multiple individuals available or more salient?
![Page 48: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/48.jpg)
French and Chinese
• French learning children master singular plural between 16 and 18 months.
• Succeed at 4-1 box search task by 18 months at least (Kouider data).
• Chinese (stay tuned). No singular/plural to master. Fail at 4-1 box search task at 24 months. Age of success not yet known
![Page 49: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/49.jpg)
EFFECT OF LANGUAGE ON THOUGHT
• But—MORE SALIENT? Or QUINEAN BOOTSTRAPPING?
Non-human primates have singular/plural distinction. Succeed at 1vs. 2, 1 vs. 5 under conditions fail at 2 vs. 4 and 2 vs. 5.
Set based quantification part of primate heritage. Not likely to require Quinean bootstrapping.
![Page 50: Core Knowledge System of mental representations, conceptual content Acquisition supported (partially) by innate, domain specific, learning mechanisms Entity](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56649f185503460f94c2ee13/html5/thumbnails/50.jpg)
Next time
• Sarnecka et al replaced with a short paper, Carey in Daedalus. Read that.
An argument that none of the core systems of number representation have the power to represent the positive integers. Quinean bootstrapping needed. A proposal for how it really works.