REASONING AS PROBLEM SOLVING DEDUCTIVE REASONING: –what, if any, conclusions necessarily follow? INDUCTIVE REASONING: –what is the probability that those conclusions (or hypotheses) are true? given a set of facts (premises), P1:If it rains, the game is cancelled P2:the game is cancelled C:? it rained

SOLVING PROBLEMS OF “LOGICAL FORM” LOGIC is a formal system of rules of inference (algorithms) for evaluating the validity of arguments that draw conclusions from premises REASONING is the human ability to evaluate such arguments TWO TYPES OF LOGIC PROBLEMS: CONDITIONAL CATEGORICAL PREMISE 1 if P, then Q All A are B PREMISE 2 P is true Some B are C CONCLUSION ? Q is true ? Some A are C

THE CARD SELECTION TASK (Wason & Johnson-Laird, 1977) AK47 Which card(s) need to be turned over to decide if the following rule is true: “if a card has a vowel on one side, then it has an even number on the other” ? Less than 5% of college students choose the correct cards. Why?

REASONING ABOUT CONDITIONAL PROBLEMS Rips & Marcus, 1977 Premise 1: if P then Q (e.g., if the chair is green, the light is on) Premise 2OperationConclusion?%Corr P is trueaffirming the Q is true100% antecedent(modus ponens) P is falsedenying the % antecedent Q is trueaffirming the % consequent Q is falsedenying the P is false 57% consequent(modus tolens) A K 4 7

SOURCES OF ERRORS IN CONDITIONAL REASONING ENCODING –misinterpret the rule as “biconditional” Q if and only if P –fail to use appropriate schema “if beer is done, then 21” (Griggs & Cox, 1982) SEARCH –fail to look for disconfirming cases (“confirmation bias”)

IMPROVING PERFORMANCE IN THE CARD SELECTION TASK Platt, 1992 (1) Clarify rule as conditional, not biconditional (2) Require subjects to justify choices (3) define task as a search for violations

CATEGORICAL SYLLOGISMS major premiseSome B’s are not A minor premiseNo C’s are B conclusion? Some A’s are not C CAB argument is invalid! Conclusions must be true for all possible encodings and combinations of premises All men are mortal Socrates is a man ? All men are Socrates (W. Allen, 1975)

POCKET GUIDE FOR SOLVING CATEGORICAL PROBLEMS to rejectshow that premises as invalid:can be combined so: All A are B Some A are not B No A are B Some A are B Some A are B No A are B Some A are not B All A are B and, since most syllogisms are invalid, when in doubt, throw it out

A fail to make a valid inference: some B’s are Asome A’s are B no C’s are Bno B’s are C ? some A’s are not C? some A’s are not C 60% corr80% corr make an invalid inference (illicit conversion): all A’s are B all C’s are Ball B’s are C ? all A’s are C fail to systematically search problem space: no A’s are B all B’s are C ? no A’s are C SOURCES OF ERRORS IN CATEGORICAL REASONING A AA B B B B B B CC C C C

BELIEF BIAS IN DEDUCTIVE REASONING all A’s are B some B’s are c ? some A’s are C All sharks are animals some animals are pets ? some sharks are pets all dogs are animals some animals are mean ? some dogs are mean all women are bad drivers all wealthy people are republicans all professors are absent minded etc