Reasoning

Wason Selection task: abstract vs concrete information

-Participants see four cards, two with a drink and two with an age. All four cards have either an alcoholic or non alcoholic drink on one side, and an age, either over or under 21, on the other. -Concrete rule: If someone is drinking beer, then they must be 21 or over. -To determine if the rule is being followed: --Affirm the antecedent-see if beer card has an age over 21 on the other side. --Deny the consequent-see if card with an age under 21 is drinking something non alcoholic. -3/4 of college participants were able to solve this problem correctly If a rule is concrete, people are better at figuring out how to test it and are less vulnerable to confirmation bias.

Syllogism example

-Some psychology majors are friendly people. -Some friendly people like dogs. -Therefore, some psychology majors like dogs. Invalid-when both premises are quantified by "some" there is never a valid conclusion.

Why people are bad at conditional reasoning tasks

1. If p then q is not the same as if q then p. --If today is Thursday, then I have my pottery class. --If I have my pottery class, then today is Thursday. 2. The Confirmation bias 3. Difficulties reasoning with abstract information.

Summary deductive reasoning

1. People are bad at using abstract logical rules. 2. Rather than strictly adhering to the rules of logic, we are easily swayed by our beliefs and actively seek to confirm what we believe to be true. 3. People are much better at conditional reasoning when content is meaningful.

Conditional reasoning

A form of deductive reasoning. An "if...then" statement is followed by a conclusion that is logically valid or invalid. Antecedents and consequents

Premise

A statement, from which others are inferred, that helps to establish what is already known about a problem.

The propositional calculus

A system for either affirming or denying antecedents and consequents in a particular conditional statement to determine logically valid and invalid arguments.

Valid arguments-conditional statements

Affirming the antecedent Denying the consequent

The Wason Selection Task

Also known as four-card task. Participants see four cards, two with a shape and two with a number. They are told all four cards have a shape on one side and a number on the other. Participants are given a rule: "If a card has a circle on one side, then it must have an even number on the other." Participants are told to turn over the cards that would allow them to determine if the rule was true. Correct answer is to turn over the card with a circle on it (affirming the antecedent) and to turn over the card with an odd number on it (denying the consequent).

Snyder & Swann (1978)

An example confirmation bias in inductive reasoning Participants asked to conduct interviews to determine interviewee's personality traits. Led to expect either an extrovert or an introvert. Given a set of questions to select from: -½ framed for extroversion ("what would you do to liven up a party?") -½ framed for introversion ("what do you dislike about loud parties?") Participants tended to choose questions from the list that served to confirm their beliefs about the interviewee.

permission schema

Can be used to explain the results of the Wason selection task. Knowledge about rules that govern thoughts and actions. If a person satisfies a particular condition, that person can carry out a particular action.

Example of propositional calculus (denying antecedent and consequent)

Conditional statement: If Julie is a psychology major, then she is a student. -Julie is not a psychology major. -Therefore, Julie is not a student. --Invalid-denying the antecedent. OR... -Julie is not a student. -Therefore, Julie is not a psychology major. --Valid-denying the consequent.

Example of the propositional calculus (affirming antecedent and consequent)

Conditional statement: If today is Thursday, then I have my pottery class. -Today is Thursday. -Therefore, I have my pottery class. --Valid-affirming the antecedent. OR... -I have my pottery class. -Therefore, today is Thursday. --Invalid-affirming the consequent.

Cosmides & Tooby (1992)

Created unfamiliar situations where cheating could occur. -Example: If a man eats a cassava root, he must have a tattoo on his face. Participants performed well. Evidence that a "cheater detector" is part of the human cognitive apparatus. Allows for detection of rule violation in even unfamiliar contexts.

Invalid arguments-conditional statements

Denying the antecedent Affirming the consequent

evolutionary adaptation to reasoning rules

Do humans have a built-in program to detect cheating in social exchanges? -Someone unable to detect cheating would be at a big disadvantage in any society so perhaps a "cheater detector" is part of the human cognitive apparatus. -Drinking problem version of the Wason selection task asks participants to look for violations of a social contract (cheating).

Deductive Reasoning

Drawing conclusions from a set of premises using principles of logic; reasoning from the general to the specific.

Are we logical?

Errors in logical reasoning are common, but systematic. Real world knowledge interferes with logical reasoning (belief and confirmation bias). We tend to reason most effectively on problems whose content we have experience with.

Syllogism

Form of deductive reasoning A type of logical argument that contains two or more premises, completed with a conclusion that may or may not follow from the premises.

Rips (1974)-diversity

Hawks have digestive enzyme Y. Robins have digestive enzyme Y. Therefore, all birds have digestive enzyme Y. vs. Sparrows have digestive enzyme Y. Robins have digestive enzyme Y. Therefore, all birds have digestive enzyme Y. More inductive strength in argument involving hawks: -Greater difference between hawks and robins than between sparrows and robins --More likely the feature thus pertains to the entire premise category

Validity vs. Truth

If a person likes pizza, then they are a very bad dancer. Judy likes pizza. Therefore, Judy is a very bad dancer. Valid argument but no real world truth. If one is the president, then one lives at the White House. Donald Trump lives at the White House. Therefore, Donald Trump is the present. Real-world truth, but invalid argument.

Belief bias

If a syllogism's conclusion happens to be something we believe to be true, we're likely to judge that conclusion to be valid (e.g. Evans, 2012). Explains why people are so prone to making errors in regards to reasoning about syllogisms.

Deductive validity

If premises are true and reasoning proceeds according to logical rules, the conclusion cannot be false.

Inductive strength

Inductive reasoning leads to uncertain conclusions-conclusions are not necessarily true given the premises. a strong argument is one in which the truth of the premises increases confidence in the conclusion. --arguments are strong if it is improbable for the premises to be true and then for the conclusion not to be as well.

The Wason Selection test results

Less than 10% of people get this right (turned over the right two cards)! 1. People assume the conditional is bidirectional. --If there's a circle there must be an even number is not the same as if there's an even number, there must be a circle. 2. The confirmation bias: people try to confirm a hypothesis rather than disprove it. --Evidence that confirms relationship of rule relates to circles and even numbers on cards-people turn over cards with these items. --People do not try to disprove the hypothesis and turn over cards with odd numbers.

Wason (1966, 1968)

Participants were given a number series (ex. 2, 4, 6) that conforms to a rule. Participants must discover the rule by offering their own number series (experimenter answers, "yes that follows the rule" or "no that doesn't follow the rule"). Participants had difficulty discovering the relatively simple rule (numbers that increase). -This is because they tended to develop a general idea of the rule and then construct examples that follow the rule. -They did not test their rule by constructing a counterexample (a triplet that, if their rule is correct, would not receive a "yes" from the experimenter). Example of confirmation bias in inductive reasoning: -Participants only try to confirm their hypotheses instead of trying to test their rule.

Abstract vs. concrete information

People reason much more effectively with concrete rather than abstract information.

Why is it easier to reason with real world content?

Permission schema? An evolutionary adaptation?

Inductive reasoning

Reasoning about conclusions that are likely given some set of premises; reasoning from the specific to the general.

Rips (1974)-typicality

Robins have ileated bones. -Therefore, all birds have ileated bones. vs. Turkeys have ileated bones. -Therefore, all birds have ileated bones. More inductive strength in argument involving robins: -Robins are more typical birds than turkeys. -Robins share more features with other birds than turkeys. -Less willing to project features belonging to turkeys as belonging to all birds.

Chapman & Chapman (1959)

Showed that people are remarkably bad at reasoning about syllogisms. Presented participants with the following syllogism: -All A's are B's. -All C's are B's. -Therefore, all A's are C's. 81% of participants falsely believed this conclusion was valid.

Antecedent

The Conditional: "If P then Q." -P The proposition that comes first, following if; the condition.

Consequent

The Conditional: "If P then Q." -Q The proposition following then; the result.

Inductive Reasoning: Diversity

The more premise categories differ from each other, the stronger the inference.

Inductive reasoning: typicality

The more typical the premise category, the stronger the inference to an inclusive category.

Reasoning

The process of drawing conclusions from given information

Confirmation bias

The tendency to seek out information that confirms a hypothesis.

Conclusion

What we evaluate in the process of reasoning