· A little history, a little philosophy
What
is the problem of induction? From
(H)ume to (K)ant.
How can we predict?
How do we know if past instances will “project” to future ones?
Deductive Problem: The conclusion is given in the premises
All cats are animals.
All Siamese cats are cats.
Therefore, all Siamese cats are animal
Hume and Kant were interested in induction.
If I see 3 cats which miaow, how can I predict for sure that the next cat I see will miaow?
Hume (1711-1776): 1st to seriously address this
No real basis for induction, but there are certain “rules” of generalization which make us act as if we can predict
“The supposition that the future resembles the past is NOT founded (in logic) but is derived entirely from habit.”
Kant (1724-1804): No real basis for induction, but the human mind will impose on experience certain kinds of regularity (e.g., cause) – the MIND imposes the regularity
How much inductive regularity can we acquire from EXPERIENCE vs. how much is given in human MINDS?
QUESTIONS:
· Is the human mind innately endowed to make generalizations about CAUSALITY and/or PROPERTIES OF OBJECTS?
· To what degree are INFANTS willing to make the same inductive inferences that humans are?
Which prediction do you prefer?
The next crow I see will be black.
The next crow I see will be black before 2010 or yellow after 2010.
Haven’t seen any crows AFTER 2010, so why do we reject the 2nd one?
Do we rely on past instances?
We’ve never seen crows which change color over time in some arbitrary way.
We rely on related background knowledge: nothing in experience which tells us that animals will change color on New Year’s Day 2010.
Babies/young children don’t have the same kind of background knowledge/experience that adults have
Developmentalists
want to know
What we know at Day 0?
How do we get off the ground to make inductive generalizations about
things?
We’re constantly making predictions based on limited evidence.
How many times do you have to experience things in order to make inductive conclusions?
· Where to go to dinner?
· Why did the car stall?
· What does “spore” mean?
· How many samples does the Center for Disease Control take before telling Daschle it’s safe to go back to work?
First signs:
Social regularities: recognition of caregiver’s voice, learning interactive routines
There aren’t any incredible salient characteristics which differentiate one voice from another, yet adults do this all the time.
How do infants learn to do it? Prenatally, infants get some auditory input and at birth, they distinguish/prefer mother’s voice over all others
Mothers, when breastfeeding a young infant, unconsciously jiggle infant to stimulate sucking: suck-stop-jiggle-suck-stop-jiggle.
After a week or so, this routine develops; infants come to expect to be jiggled and start to suck immediately upon jiggling
Visual expectancies:
Infant views a display consisting of lights which go on and off in a certain pattern; after a few repetitions, the baby’s eyes move to where they expect the next light to be: the infant is PREDICTING
Later infancy:
Learning common sequences in speech: statistical regularity
Higher probability pairings are more likely to occur within a word
Learning correlated features of objects:
Show babies sets of nonsense objects, one at a time; infants can figure out what features are correlated
What cues to causality do infants use?
Billiard ball experiments:
One ball moves and makes contact with another stationary ball; upon contact, the stationary ball starts moving
Vs.
One ball moves toward a second stationary ball, and the stationary ball starts moving before the first one hits it.
6 month olds don’t perceive these 2 events as different, but 10 month olds display surprise when they see the 2nd one (since the moving ball hasn’t yet hit the stationary ball, they don’t expect the stationary ball to start moving).
By first grade, child understands more than 5,000-6,000 words; average that out over the child’s lifetime and the child has to learn 5-6 words a day, on average (at least learn something about the word’s meaning).
· What does “cup” refer to?
Kids learn based on a few examples.
What does “strike” refer to? This is more difficult: bowling/baseball/union
· What kinds of inferences do toddlers make?
Toddlers assume that new words referring to novel objects refer to CATEGORIES of objects
Although they can make some mistakes: “doggie” = medium-sized fury animals
But they don’t make off-the-wall inferences.
· How do preschoolers learn new words?
Are kids born with specific constraints on hypotheses about words
OR
Are there general perceptual/cognitive tendencies which influence word learning?
OR
Do they rely on social feedback (how adults use the words)
OR
Are there linguistic and paralinguistic cues?
When I say “Oh look at that GEX”
Hmmm what’s a gex? It’s preceded by “that” – tells me something about what I’m looking for; probably not an action; probably an object. And I’m supposed to “look” therefore it’s visual.
Paralinguistic cues: social cues around utterances:
“Looks like a” tulla. – draws attention to SHAPE
“Has a” fram. – draws attention to some smaller detail of the object.
“Is made of” snork. – material
These phrases help constrain children’s inferences about what words mean.
e.g., adults rely on similarity to make inferences about what might have caused the car to stall.
Here’s what Piaget thought:
Piaget’s theory: physical similarity plays an overwhelming role in preschool children’s inferences
Preoperational or “prelogical” thought entails perceptual boundedness
But eventually, we have to be able to go beyond perceptual similarities to make certain inferences: e.g., what’s more like a dolphin: a shark vs. cat
Piaget’s theory is wrong in it’s extreme form.
Evidence against: Preschoolers quite readily make inferences which transcend the senses/transcend the salient.
Can classify objects either by SHAPE or FUNCTION.
Laser pointer: is it more like a FLASHLIGHT or a PEN
By age 3-4, children can easily classify by FUNCTION, even if shapes are the same, even though function isn’t as salient as shape
By age 4, go beyond “perceptual salience” to classify objects and infer unseen properties
By age 4, separate appearance from reality. E.g. candle shaped like an apple.
Ask child: What is this really? Child: Apple.
Then light wick. Now what is it? Child? Candle.
What is it really? Candle
What does it look like? Apple
Shows that kids can differentiate FUNCTION from SHAPE
3 year olds: have problems with this
by 4-5, kids can do this
Piaget predicted that 4-5 year olds, when asked “What is it really” should say “Apple”, even though you’ve lit the wick. But kids actually say “It acts like a candle and it’s really a candle”; they’re not as caught by the shape as Piaget predicted
Analogy works with older kids: “An atom is kind of like the solar system”
Older kids understand the relationships between the parts is what is important, not the minor details.
Is Madagascar more similar to Zaire or Australia?
Depends on whether you mean geographical location or geographical status (both large islands).
The real question is:
Can children select the right kind of similarity to make a specific inference?
Kids make use phrases such as “has a”, “made of” to help direct their attention.
DEVELOPMENTAL PROBLEM
OF INDUCTION:
Starting with very little knowledge or experience, how do infants, toddlers, and preschoolers make so many generalizations about their world, given such a capricious and unpredictable (sorry folks, I missed the rest)
1. Look for sources of regularity in the child’s array of experience.
Can the child learn to expect this regularity?
And realize that
Different colors on cats don’t matter, but 2 pointy ears DO matter
2. Instead of asking how the child learns to “go beyond” similarity, investigate:
What kinds of similarity do children notice?
How does this depend on the problem at hand?
How do they learn to associate different kinds of problems with dimensions of similarity?
3. Look for grounding in a history of physical and perceptual-motor experience