reasoning
TRANSCRIPT
Reasoning
http://www.toothpastefordinner.com/012408/circular-reasoning.gif
Types of Reasoning
Deductive Reasoning
deductive validity
Inductive Reasoning
inductive strength
Types of Reasoning
Deductive Reasoning Syllogistic reasoning
Basic syllogism:
Premise 1: All A are B.
Premise 2: All B are C.
Conclusion: Therefore, all A are C.
Types of Reasoning
Deductive Reasoning Syllogistic reasoning
Syllogism example:
All red books are astronomy books.
All astronomy books are large.
All red books are large.
Types of Reasoning
Deductive Reasoning Syllogistic reasoning
Categorical syllogisms
Conditional syllogisms
1. All Beagles are dogs
All dogs have fur.
Therefore:
2. Some teachers are women.
All women are human.
Therefore:
3. No elephants are carnivorous.
Some dogs are carnivorous.
Therefore:
4. Some cats are grey.
Some cats like dogs.
Therefore:
5. All ghost stories are scary.
No jokes are scary.
Therefore:
6. No documentary films make money.
No nonfiction books make money.
Therefore:
Types of Reasoning
Deductive Reasoning Principles of validity and truth in syllogisms
Principle 2: the validity of a syllogism is determined only by its form, not its content.
All birds are ants.
All ants have four legs.
Therefore, all birds have four legs.
Types of Reasoning
Deductive Reasoning Principles of validity and truth in syllogisms
Principle 1: if two premises are true, the conclusion of a valid syllogism must be true.
All birds are animals.
All animals eat food.
Therefore, all birds eat food.
Types of Reasoning
Deductive Reasoning Using Euler circles to determine validity
Types of Reasoning
Deductive Reasoning Studying Syllogisms
Normative Approach
Descriptive Approach
Types of Reasoning
Deductive Reasoning Studying Syllogisms
Normative Approach
Descriptive Approach
Illustrations of possible meanings of “Some bers are sabs.”
Reasoning Performance Premise phrasing
Illustration of possible meanings of “All daxes are wugs.”
Reasoning Performance Alternation of premise meaning
Failure to consider all possibilities
Reasoning Performance
Believability effects
Reasoning Performance
All of the students are tired.Some tired people are irritable.Some of the students are irritable.
All of the men are tired.Some tired people are women.Some of the men are women.
All of the students are tired.Some tired people are irritable.Some of the students are irritable.
All of the men are tired.Some tired people are women.Some of the men are women.
Types of Reasoning
Deductive ReasoningConditional syllogisms
An example of a logical argument
Premise p q If “p,” then “q”
Existing condition p p is true
Conclusion qtherefore, q is true
Types of Reasoning
Deductive ReasoningFormal Logic
Inference rulesModus Ponens (valid)
p q If “p,” then “q”
p p is true
¬ p therefore, q is true
Types of Reasoning
Deductive ReasoningFormal Logic
Inference rulesModus Tollens (valid)
p q If “p,” then “q”
¬ q q is not true
¬ p therefore, p is not true
Types of Reasoning
Deductive ReasoningFormal Logic
Fallacies Denying the antecedent (invalid)
p q If “p,” then “q”
¬ p p is not true
¬ q therefore, q is not true
Types of Reasoning
Deductive ReasoningFormal Logic
Fallacies Affirming the consequent (invalid)
p q If “p,” then “q”
q q is true
p therefore, p is true
Summary of Conditional Syllogisms
Type of Syllogism
2nd Premise Conclusion Valid?
Modus Ponens p q Yes
Modus Tollens Not q Not p Yes
Denying the antecedent
Not p Not q No
Affirming the consequent
q p No
Wason’s selection task (or four-card task)
Types of Reasoning
Deductive Reasoning
$35
Check 1
Check 4Check 2
Check 3
no initialsinitials
$20
Types of Reasoning
Inductive Reasoning
Types of Reasoning
Inductive Reasoning Analogical
reasoning
Examples of verbal and pictorial analogies.
Example of a matrix completion problem.
Types of Reasoning
Inductive Reasoning Analogical
reasoning
Types of Reasoning
Inductive Reasoning Hypothesis testing
Confirmation bias
Approaches to Studying Reasoning
Fallacies in ReasoningEquivocation Illicit contrastArgument by innuendoLoaded questionFallacy of the continuumFallacy of composition