Logic: Mental Models

1. Logic: Mental Models

2. How is logical reasoning done? • Create concrete situations • Mental Models • Johnson-Laird and colleagues • Build models of situations • Find a description that characterizes the models • That description is the conclusion • The more models that must be built, the harder the problem.

3. Some examples • All Academics are Bean-countersAll Bean-counters are Clean • All Archers are ButchersSome Butchers are Camel Riders • All Aardvarks are Boring • No Candles are Boring

4. Illusions from the Paper • Only one of the following premises is true about a hand of cards:There is a king in the hand or there is an ace, or bothThere is a queen in the hand or there is an ace, or bothThere is a jack in the hand or there is a 10, or bothIs it possible there is an ace in the hand?

5. Problem 2 • Suppose you know the following about a particular hand of cardsIf there is a jack in the hand, then there is a king in the hand, or else if there isn’t a jack then there is a king in the hand.There is a jack in the hand.What if anything follows?

6. Natural Language and Logic • The previous problem arises because language does not work like logic • We do not evaluate what people say based only on the rules of logic. • We want to understand what people are trying to communicate with us.

7. Questions? • How does this approach explain content effects? • How does this approach explain truth effects? • Does this tell us anything about reasoning that isn’t in logic situations?

8. Limitations of deduction • Deductive reasoning is truth-preserving • We are never 100% certain of the truth of any fact • Beliefs are based on observation and forms of reasoning that are not truth-preserving • If we are never 100% certain of truth, then there are limits on the value of truth-preserving operations.