Cognitive Processes PSY 334 Chapter 10 – Reasoning

Midterm 2 Results

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.

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

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.

Syllogisms  Syllogism – a series of premises followed by a logical conclusion.  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)  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?

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.

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.

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”

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!

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!

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

Sample Wason Task E K 4 7 E87% K16% 462%Affirming the consequent 725%Failure to apply modus tollens

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?

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.

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.

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.

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).

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.

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.

Possible Interpretations Is it this way? Or this?

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