November 16, 2009 REASONING Reasoning usually refers to problems that are amenable to formal logic in the form of deductive reasoning. (Inductive reasoning is also involved, to some extent). Induction: start with a specific case and ask what general rule you can abstract; tells you what is more probably true Deduction: start with general assertions and ask what specifically follows from that assertion; tells you what must be true Deductive Reasoning Are People Logical? Isn?t logic just formalizing the rules of everyday thought? If that?s the case, then errors are just the result of misreading, carelessness, etc. BUT, the errors we make happen all the time, and generally are systematic Wasen?s Card Selection Task Each card has a letter on one side and a digit on the other. Verify this rule: if there is a vowel on one side, there is an even number on the other. Flip a minimum number of cards. Case-based reasoning Theory that we are good at scenarios with which we are familiar. This is due to case-based reasoning, where we remember how we have solved the problem before. Pragmatic reasoning schemas Bundles of ?if-then? rules which are activated for situations like permissions, obligations, or causations. Pragmatic reasoning is more useful and simple than formal logic. Evolutionary view We evolved as a social animal, and we evolved to be able to do social exchange. Part of social exchange is the ability to catch cheaters. ?Cheaters? are destructive to the community, and thus it is vital to acknowledge them. This view seems interesting BUT people are still good at the problem when it doesn?t involve cheating, but instead involves precaution. Bottom Line: People are not logic machines who can plug in information to a logical formula. The familiarity of a problem doesn?t matter too much. We still don?t know the critical features of a problem that lead to successful reasoning. Syllogisms Three statements: two premises and a conclusion There are over 500 forms of syllogisms because you can use the terms ?all,? ?none,? ?some,? etc. Syllogism errors Conversion errors ? incorrect reversing of terms Conversational implicature ? ?some? has conversational implications of ?some, but not all? Atmosphere ? vague feeling that a certain deduction is correct Belief bias ? inability to ignore the content of the premises when it affects your decision Inductive Reasoning Analogical reasoning is an example of this; you can extend knowledge from a situation you do understand to one that is less easily understood. Good analogies share characters AND important relations. Analogies are used in teaching, literature, learning, persuasion, etc. Not all properties and relations follow Again, inductive reasoning does NOT guarantee correctness, but rather gives us an idea of the probable answer. Steps to using analogy Retrieval of source ? ideally have structural similarity Mapping: new situation to source Extension ? use source and mapping to make predictions Deriving the right source is hard, mapping is easy (generally speaking)
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