Lecture_08_Reasoning & Problem Solving Flashcards
Formal Rules of Logic
- Deductive reasoning
- Inductive reasoning
- Conditional reasoning
Reasoning
Drawing conclusions by putting statements (premises) together using logic
1) to make sense of our present experiences and ideas, and to plan for the future
2) to establish and verify facts
Premise
Statement of fact that is assumed to be true
Deductive Reasoning
- Top-down reasoning”
- If the premises are true, the conclusion must also be true.
- Premise 1: All cognitive processes involve brain activities.
- Premise 2: Memory is a cognitive process.
- Conclusion: Memory involves brain activities.
The Problem of Deductive Reasoning
- What’s important is the form of the argument
- The truth of the premise in the real world & your prior knowledge are irrelevant!
- Premise 1: All birds have wings.
- Premise 2: Unicorns are birds. (?)
- Conclusion: Unicorns have wings.
Inductive Reasoning
Bottom-up reasoning
- If the premises are true, the conclusion is also LIKELY to be true.
- Premise 1: Restaurant A has many delicious dishes.
- Premise 2: You order an omelet.
- Conclusion: The omelet is delicious.
The Problem of Inductive Reasoning
The conclusion is likely, but it’s NOT guaranteed to be true.
- Based on probability.
- 80% of brain surgeons are men.
- Lee is a brain surgeon.
- Lee is a man.
Conditional Reasoning
If P-then Q
- Deductive reasoning that involves conditional statements
- Premise 1: If P, then Q
- Premise 2: A statement about whether P or Q is true or not true
- Conclusion: A statement about whether P or Q is true or not true
2 Valid Forms of Conditional Reasoning
- Affirming the antecedent (modus ponens)
- Denying the consequence (modus tollens)
Premise 1: If P, then Q
Premise 2: P
Conclusion: Q
- Valid
- Affirming the antecedent
- Modus ponens
Premise 1: If P, then Q
Premise 2: Q
Conclusion: P
- Invalid
- Affirming the consequence
Premise 1: If P, then Q
Premise 2: ~P
Conclusion: ~Q
- Invalid
- Denying the antecedent
Premise 1: If P, then Q
Premise 2: ~Q
Conclusion: ~P
- Valid
- Denying the consequence
- Modus tollens
Wason’s Card Selection Task
- 4 cards
- Each card has two sides: a letter and a digit.
- Rule: If a vowel is on one side, there is an even number on the other side
- Try to confirm this rule by turning over the fewest number of cards
Why do participants make mistake in Wason’s Card Selection task?
People make mistakes by seeking verification rather than falsification
Logical Fallacies
- Begging the question
- After this, therefore because of this
- Ad hominem
- Slippery slope
Begging the question
Assuming the truth of the conclusion, rather than supporting it
- E.g. Humans help each other because of their kindness
After this, therefore because of this
Correlation isn’t causation
- X occurred, then Y occurred
- Therefore, X caused Y
- E.g. Nearly all heroin addicts used marijuana before they tried heroin. Clearly, marijuana use leads to heroin addiction
Ad Hominem
Criticizing an individual who makes an argument
- E.g. Freud used cocaine. Therefore, we should not bother reading his books
Slippery Slope
Because after stating A and B condition, there aren’t condition of C, D, E, or more
- Series of incremental inferences to arrive at undesirable conclusion
- E.g. If we allow gay marriage, the next thing we know, people will want to marry their dogs, or their cats, or what about their pigs?
Mental Models of Reasoning
People create, combine, and evaluate specific possibilities
- Premises are stored in a concrete, meaning-based format, rather than in an abstract logical way
- Premise 1: All birds are animals
- Premise 2: Some animals are large
- Conclusion: Some birds are large
- Invalid
Why do people make reasoning errors according to mental models?
People did not consider enough possibilities (mental) models
- Limited by working memory capacity
Bayesian (Probability) Models of Reasoning
- People make judgments based on probabilities, rather than engaging in pure deductive reasoning
- When people answer incorrectly on reasoning tasks, it’s because they treat them as probability tasks
An Example of Inference Based on Probability: Dog and Fur
- Premise 1: There’s a high probability that a dog has fur
- Premise 2: Some don’t, but it’s a pretty good guess
- Conclusion: Therefore, Rover has fur
- When you hear “Rover is a dog”, you assume that Rover has fur.
