### 2 4 6 task

```2 4 6 task
• You guess the secret rule
• 2 4 6 < yes, fit the secret rule
• 7 9 11 < yes, fits the rule
• Rule is ascending (increasing numbers)
Another attempt
• 2 4 6
• 7
< yes, fits the rule
2 1 < no, do not fit the rule
-2 4.5 400 < no
-1 -3 -5 < no
• 8 10 12 < yes
-5
-3 -1 < no
• 1
0
13 20 < no
3 5 < yes
• 6 10 18 < no
• 33 35 37 < yes
0
7
10 < no
ANSWER: positive numbers, increasing by 2
• Exemplar = set of 3 numbers that you generate
Positive/ negative exemplars
• Your own hypothesis (H)
•
•
•
•
•
E.g. H: numbers add to 12
Proposed exemplar: 7 2 3
Exemplar fits H  “positive” exemplar
E.g., if proposed exemplar: 7 2 1
Exemplar doesn’t fit H  “negative”
exemplar
expectations
• E.g. H: numbers add to 12
• Proposed exemplar : 7 2 1
• Expectation  “no” response, doesn’t fit
the rule
• If the response increases confidence in H,
then it’s said to be “confirming”
Another expectation
• E.g. H: numbers add to 12
• Proposed positive exemplar: 7 2 3
• E.g., he expected a “no” response
because he had low confidence in H 
then the hypothesis is “disconfirmed”
Heuristics for induction and
hypothesis testing
• Rule-of-thumb: Not guaranteed to work,
but more likely to get the answer
– 1) form general hypotheses (not specific
ones)
• E.g. H: numbers increasing by 2 (specific)
• More general version  numbers increasing
– 2) form counterfactual hypotheses (i.e.,
opposing hypotheses)
More heuristics
– 2) form counterfactual hypotheses
• E.g. H: numbers increasing
• Counterfactual (opposing) H: numbers decreasing
– 3) use extreme examples (exemplars)
• E.g., exemplar : 7 9 1
• Extreme exemplar: -7 9,000 1 million
– 4) use multiple hypotheses
• Have at least 2 hypotheses in mind always
• Pick an exemplar that tells which hypothesis is
right (discriminating between hypotheses)
More heuristics
– 5) seek disconfirming evidence  find
exemplars that show your hypothesis is wrong
• Peoples’ natural inclination is to seek confirming
evidence (confirmation bias)
Science as hypothesis testing
• We had H in 2 4 6 task; in science, it’s
called a “theory”
• We had exemplars in 2 4 6 task; in
science, they are “experimental results”
• In 2 4 6 task, we compared the response
(yes or no) with our hypothesis; in science,
the scientist compares the results to the
theory
```