Cognitive Processes PSY 334

1. Cognitive ProcessesPSY 334 Chapter 10 – Reasoning

2. Midterm 2 Results

3. Logic vs Human Reasoning • Logic – a subdiscipline of philosophy and mathematics that formally specifies what it means for an argument to be correct. • Human deviations from logic were thought to be malfunctions of the mind. • AI systems guided by logic are also deficient, lacking common sense. • Prescriptive or normative models do not predict human behavior very well.

4. Demos of Human Irrationality • Four main areas of research have studied how humans deviate from prescriptive models: • Reasoning about conditionals • Reasoning about quantifiers • Reasoning about probabilities • Decision making

5. Two Kinds of Reasoning • Reasoning – the process of inferring new knowledge from what we already know. • Deductive reasoning – conclusions follow with certainty from their premises. • Reasoning from the general to the specific. • Inductive reasoning – conclusions are probable (likely) rather than certain. • Reasoning from the specific to the general. • Probabilistic – based on likelihoods.

6. Syllogisms • Syllogism – a series of premises followed by a logical conclusion. • All poodles are petsCongruent 84% All pets have names .: All poodles have names – T or F? All pets are poodles Incongruent 74%All poodles are vicious.: All pets are vicious -- T or F?

7. Content-Free (Abstract) • Subjects did better judging syllogisms that were consistent with reality (congruent). • Content-free syllogisms use symbols instead of meaningful sentences: All P are B Abstract 77% All B are C .: All P are C – T or F?

8. Conditionals • If-then statements. • Antecedent – the “if” part. • Consequent – the “then” part. • Rules of inferences using conditionals: • Modus ponens -- If A then B, observe A, conclude B • Modus tollens – If A then B, observe not-B, conclude not-A • Notation: negation, implication, therefore.

9. Modus Ponens and Tollens • If Joan understood this book, then she would get a good grade. If P then Q • Joan understood .: she got a good grade. • This uses modus ponens. P .: Q • If Joan understood this book, then she would get a good grade. If P then Q • She did not get a good grade .: she did not understand this book. ~Q .: ~P • This uses modus tollens.

10. Logical Fallacies • Denial of the antecedent: • If P then Q, not-P, conclude not-Q • If P then Q, not-P, conclude Q • Affirmation of the consequent: • If P then Q, Q, conclude P • If P then Q, Q, conclude not-P • Subjects seem to interpret the conditional as a biconditional – “if” means “if and only if”

11. Denial of the Antecedent • If Joan understood this book, then she would get a good grade. If P then Q • Joan did not understand .: she got a bad grade. – This is not necessarily true. • This is a fallacy. ~P .: ~Q • If it rains, then I will carry an umbrella. • It is not raining .: I will not carry an umbrella. • But I may carry an umbrella for shade!

12. Affirmation of the Consequent • If Joan understood this book, then she would get a good grade. If P then Q • Joan got a good grade .: she understood the book. This is not necessarily true. • This is a fallacy. Q .: P • If someone is abused as a child, then they will show certain symptoms. • They show symptoms .: They were abused as a child. Symptoms may not be of abuse!

13. How People Reason • People may be reasoning in terms of conditional probabilities. • Conditional probabilities can be found that correspond to acceptance rates for fallacies. • Wason selection task – if there is a vowel on one side, then there must be an even number on the other side. • Can be explained in terms of probabilities. • Also explained by a permission schema

14. Sample Wason Task E K 4 7 E 87% K 16% 4 62% Affirming the consequent 7 25% Failure to apply modus tollens

15. A Contextualized Version • In order to drink beer, someone must be 21 years of age: DRINKING A BEER DRINKING A COKE 22 YEARS OF AGE 16 YEARS OF AGE Which ones would you check?

16. Explanations • Three proposed theories: • Logic – people routinely fail to apply modus tollens. • Probabilistic – this tasks produces failures only with certain underlying probabilities. • Permission schema – the logical connective is interpreted in terms of social contract. • A cheating context improves the results.

17. Quantifiers • Categorical syllogism – analyzes propositions with quantifiers “all,” “no,” and “some.” • Fallacies: Some A’s are B’s Some B’s are C’s Conclude: Some A’s are C’s • Some women are lawyers, some lawyers are men, conclude some women are men.

18. Atmosphere Hypothesis • People commit fallacies because they tend to accept conclusions with the same quantifiers as the premises. • No A’s are B’s • All B’s are C’s • Conclude No A’s are C’s. • Universal premises go with universal conclusions, particular with particular. • Does not fully explain behavior.

19. Two Forms of Atmosphere • People tend to accept a positive conclusion to positive premises, negative conclusion to negative premises. • Mixed premises lead to negative conclusions. • People tend to accept universal conclusions from universal premises (all, no), particular conclusions from particular premises (some, some not).

20. Limitations • Atmosphere hypothesis describes what people do, but doesn’t explain why. • People violate predictions of the atmosphere hypothesis. • More likely to accept a syllogism if it contains a chain leading from A to C. • People should accept a syllogism with two negative premises, but correctly reject it.

21. Process Explanations • People construct a mental model to think concretely about the situation. • Correct conclusions depend upon choosing the correct mental model. • Errors occur because people overlook possible explanations of the premises: • All the squares are shaded • Some shaded objects have bold borders. • .: Some of the squares have bold borders.

22. Possible Interpretations Is it this way? Or this?

23. Possible Meanings AB AB All A are B B A A B B A A A A B B A A B B B Some A are B Some A are B No A are B