Exam 2 Flashcards
Subset
A collection of objects that is contained within another set
Infinite sets
They contain an infinite number of items
Ex set of real numbers
Can a subset be infinite?
Yes example within the set of real numbers, the subset of integers is infinite
Can there be a finite subset of an infinite set?
Yes, the numbers 22, 23, 24 of natural number subset are a finite subset
The learning problem
Learning infinite sets from finite subsets is impossible without help. And only a certain type of help is actually helpful
Positive evidence
Is evidence about which items are present in the infinite set
Problem with positive evidence
There is no guarantee that we will get the relevant evidence. It might happen, it might not
Negative evidence
Evidence about which items are absent from the infinite set
Benefit of negative evidence
You can eliminate potential infinite set from consideration. You can test hypotheses and over time you find the right one
Learning language is…
The generalisation from a finite subset to an infinite set
Fact 1 of learning language
All human languages can be characterised as an infinite set of sentences
Fact 2 of learning language
The input children receive when learning language is finite. This has to be true because humans learn language in a finite amount of time
Language
Is an infinite set of sentences
Language input
Is a finite set of sentences that is a subset of the infinite set of the language
Fact 3 of learning languages
All children succeed at language acquisition, except for atypical circumstances (diseases, disorders, imprisonment etc)
Positive evidence for language acquisition
Just another name for input and people to speak to (and around) children
Negative evidence for language acquisition
Some sort of response by the parent after a child produces an ungrammatical sentence but crucially not after a grammatical sentence. Forms of explicit disapproval, non sequiturs, repetitions, recasts, questions
Explicit disapproval
Parent says no or shakes head
Non sequiturs
Parent fails to understand child
Repetitions
Parent repeats the child utterance
Recasts
Parent corrects the child utterance
Questions
Parent asks for more info
What do children do with negative evidence?
They ignore or misinterpret it
Fact 4 of learning language
Negative evidence would guarantee that the infinite set can be learned