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.
Dual-Process Models of Reasoning
- System 1 – Fast cognition, associative process, outside consciousness
- Pragmatic reasoning
- Prone to errors - System 2 – Slow cognition, rule based and logical
- Allows us to try to apply rules of logic!
- But, limited by working memory
Why do people make errors in problem solving tasks according to the dual-process model?
They’re relying on System 1 instead of System 2”
- Because it’s easier, faster, and requires less cognitive resources
Problem
Any situation in which a person has a goal that is not yet achieved
Well-Defined Problems
Clearly defined goal state and constraints
Ill-Defined Problems
- Unclear goal state and constraints
- Difficult to create mental representations and identify a solution
Information Processing Approach
Problem-solving = “searching” through a space consisting of all possible states of the problem
Information Processing of Problem-solving
- Create a PROBLEM SPACE to represent the problem. Include the initial state, goal state, instructions, constraints, and relevant info from long-term memory.
- Select OPERATORS – actions that will transform the initial state.
- Implement the operators – results in a new current state within the problem space.
- Evaluate the current state – if it corresponds to the goal, a solution is reached
General Problem Solver (GPS)
Computer program based on information processing framework
- Remarkable similarity between GPS algorithm & what human participants report out loud while solving a problem
How to select operators to solve a problem?
Algorithmic Vs. Heuristic Strategies
Algorithms
Methods that are guaranteed to lead to the solution, if followed correctly
- E.g., mathematical rules ( 998 / 21 = ? )
- But sometimes can’t use them, due to memory constraints or other processing limitations
Heuristics
Methods or strategies that often lead to the solution
- But, not guaranteed to always succeed!
Means-End Analysis
- Compare the CURRENT STATE with the GOAL STATE.
- If there are differences, solve the LARGEST DIFFERENCE.
- Select an OPERATOR that will solve the difference.
- Apply the operator. If it cannot be applied, set a new goal (i.e., a SUB-GOAL) to reach a state that will allow the application of the operator.
- Solve this sub-goal by REPEATING 1-4
Analogy
PRIOR EXPERIENCES and BACKGROUND KNOWLEDGE can be helpful
- Classify and understand the problem
- Automatize some problem-solving steps
- Draw analogy from past experiences
1) Surface similarity
2) Structural similarity
Insight
the solver feels like they suddenly arrive at the solution (“Aha!”)
- Usually requires looking at the problem in a different way from the usual way
Incubation Effect
Insight can occur even when you’re not consciously thinking about the problem
What blocks insight?
- Self-imposed constraints
- Functional fixedness
