Cognitive Processes PSY 334 Chapter 10 Reasoning Midterm

Cognitive Processes PSY 334 Chapter 10 – Reasoning

Midterm 2 Results

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

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

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

Syllogisms o Syllogism – a series of premises followed by a logical conclusion. o All poodles are pets Congruent 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?

Content-Free (Abstract) o Subjects did better judging syllogisms that were consistent with reality (congruent). o 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?

Conditionals o If-then statements. n n Antecedent – the “if” part. Consequent – the “then” part. o Rules of inferences using conditionals: n n n 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.

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

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

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

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

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

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

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

Explanations o Three proposed theories: n n n 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. o A cheating context improves the results.

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

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

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

Limitations o Atmosphere hypothesis describes what people do, but doesn’t explain why. o People violate predictions of the atmosphere hypothesis. n n 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.

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

Possible Interpretations Is it this way? Or this?

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