Deductive Reasoning and Arguments

Thought- Reasoning

• A sequence of thoughts is organized in a proposition.
• An argument is a proposition that includes reasons (premises) for a claim (conclusion).
• The claim can report on the certainty or probability of a fact.

Different Reasoning Goals

• Deductive Reasoning: Aims for certainty.
• Inductive Reasoning: Aims for probability.

Deductive Reasoning Examples

• Example 1:
  • No addictive things are inexpensive.
  • Some cigarettes are inexpensive.
  • Therefore, some addictive things are cigarettes.
• Example 2:
  • No addictive things are inexpensive.
  • Some cigarettes are inexpensive.
  • Therefore, some cigarettes are not addictive.

Syllogism Example

• All humans are mortal.
• Aristotle is human.
• Therefore, Aristotle is mortal.
• Unicorns don't fly.
• I don't fly.
• Therefore, I am a unicorn. (Note: this is a flawed example).

Deductive Reasoning: Logical Rules

• Deductive validity: If premises are true, the conclusion cannot be false.
• Example: Penguins are black and white. Some old TV shows are black and white. Therefore, some penguins are old TV shows. (Note: this is a flawed example).

Deductive Reasoning: Difficulty and Errors

• The more rules an argument requires, the harder it is and the more likely errors will be made.
• People take longer to make correct decisions with more complex arguments.

Deductive Reasoning: Effects of Content

• Belief Bias: People often judge a logically invalid conclusion as valid if it seems plausible.
• Content of propositions affect the rules used.
• Pragmatic rules, less abstract but relevant to everyday problems.
• Mental models help to represent situations.

Wason Selection Task

• If a card has a vowel on one side, it has an even number on the other side.
• Which cards would you turn over to determine if the claim is correct? (E, K, 2, 7)

Pragmatic Rules Example

• If a person is drinking beer, he/she must be over 18.
• Cards: BEER, COKE, 22, 16
• The content of a problem affects whether a pragmatic rule is activated.

Deductive Reasoning: Content Sensitivity

• Applying pragmatic rules and creating mental models depend on the problem's content.

Inductive Reasoning Example

• Sam qualified in accounting at college.
• Sam now works for an accounting company.
• Therefore, Sam is an accountant.

Deductive vs. Inductive Reasoning

• Deductive reasoning uses general premises to form a specific conclusion.
• Inductive reasoning uses specific premises to form a general conclusion.
• Inductive reasoning generates hypotheses (not certainties).
• Inductive strength is about probability.

Linda's Problem (Kahneman & Tversky)

• Linda is 31, single, outspoken, bright, majored in philosophy, concerned with discrimination.
• Estimate probabilities: Linda is a bank clerk; Linda is a bank clerk and active in the feminist movement.

Inductive Reasoning: Probability Rules

• Base-rate rule: The probability of something being in a class is higher if there are more members in that class.
• Conjunction rule: Probability of a proposition cannot be less than the probability of that proposition combined with another proposition.

Inductive Reasoning: Heuristics

• Heuristics are mental shortcuts that are easy to apply but not always reliable.
• People use heuristics in everyday life.

Inductive Reasoning: Tversky & Kahneman

• Tversky and Kahneman showed that people often violate basic probability theory when making inductive judgments.

Daniel Kahneman

• Nobel Prize winner for behavioral economics research.
• Integrated psychological insights into economic science.
• Research on human judgment and decision-making under uncertainty.

Inductive Reasoning: Similarity Heuristic

• People base judgments on the similarity between current situations and prototypes or stereotypes.

Inductive Reasoning: Availability Heuristic

• People base judgments on information that readily comes to mind.

Inductive Reasoning: Causality Heuristic

• People estimate the probability of a situation based on the strength of the causal connections between events.

Reasoning and Decision Making: Effects and Biases

• Framing effects: The way information is structured can influence decisions.
• Belief bias: Abandoning logical rules in favor of personal beliefs.
• Confirmation bias: Favoring evidence that confirms existing beliefs.

Neural Basis of Reasoning

• Different parts of the brain are activated during deductive and inductive reasoning.

Reasoning at a Glance: Deductive Thinking

• Start with general principles.
• Assess if they fit the specific case.
• Conclude on the specific case.

Reasoning at a Glance: Inductive Thinking

• Start with specific facts.
• Formulate a general principle.
• Collect and evaluate facts.