HPSLEC62010 - Lecture#6 Inductive Reasoning AGENDA I...

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Lecture #6 Inductive Reasoning AGENDA I. Inductive Reasoning Vs Deductive Reasoning II. Pure Induction III. Theories of Concept Learning A. The Continuity Theory of Concept Learning B. The Non-continuity Theory of Concept Learning C. Comparison of the Two Theories D. More on Rule-Based Induction IV. The Confirmation Bias
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I. Inductive Reasoning Vs Deductive Reasoning Inductive reasoning is to seek a rule or concept From evidence (experience), e.g. every time I see a ruby it has been red. Therefore I come to believe inductively the rule ‘all rubies are red’. Deductive reasoning involves discovering the consequences of assumptions, e.g. I have the rule ‘all rubies are red’, I have a ruby, therefore I deduce that ruby must be red. Example uses ‘Modus Ponens’ A implies B A Therefore B
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What About Rules ? Conceptual Natural Tight c 2 =a 2 +b 2 Product odd numbers is even Opposite charges Attract E=MC 2 Loose Castle early in chess Gaps between prime Numbers increase Tall parents tall kids a c b Exercise promotes health
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Rules (Continued) Rules are supposed to capture regularities: Temporal regularities- future= f(past), weather pattern prediction, stock market projections Spatial regularities- sample food in area, if OK then go back and eat there again. Procedural regularities- Rules of a game, rules of conversation. Attribution regularities- Rubies are red, birds have feathers.
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II. Pure Induction The goal is to keep a ‘completely open mind’ and let the regularities in nature lead to a rule. The alternative is ‘rule based induction.’ One has a tentative rule. Seeks evidence by trying the rule. If it works increase belief in it, if it fails reject it and try another rule. Pure induction is certainly a noble goal, but there are problems with this idea. For one, there are just too many possibilities for an open, unbiased mind to zero in on. One good example of the limitations of pure induction is language learning.
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B.F. Skinner’s Pure Inductive Discovery A. Burrhus Frederic Skinner (1904- 1990). Probably the most anti-theoretical of the behaviorists. Skinner debated Chomsky on language, debated theologians on religion, wrote utopian novels. His main apparatus was the a ‘Skinner box.’ 1904-1990
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The Skinner Box Skinner believed we should learn by induction. No speculative theories.
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