PSY270 Lec 10

Reasoning

the process used to draw conclusions and make inferences from available facts, evidence, or premises

Deductive reasoning

involves using general knowledge to reason about specific examples

valid

Drawing conclusions via deductive reasoning means that when an argument's premises are assumed to be true, the conclusion is guaranteed to be true, or ____

sound

If the premises are actually true in the real world and the argument is valid, then the argument is _______

syllogism

a deductive argument composed of a set of statements (premises) that lead to a logical conclusion

categorical syllogism

We can infer properties about one member of a broader class

Premise A (p): All deciduous trees shed their leaves annually

Premise B (q): Maples are deciduous trees

Conclusion: Therefore, maple trees shed their leaves annually

conditional syllogisms

Syllogism with two premises and a conclusion, like a categorical syllogism, but whose first premise is an "If . . . then . . ." statement.

e.g., If it rains, then the sidewalk will be wet.

Antecedent (p): If it rains...

Consequent (q): then the sidewalk will be wet

Modus ponens (p is true)

If p is true, then q MUST be true - aka affirming the antecedent

Premise 1: If it rains, then the sidewalk will be wet

Premise 2: It rained (confirms p)

Conclusion: The sidewalk is wet (confirms q)

Modus tollens (q is false)

If q is false, then p MUST be false - aka denying the consequent

Premise 1: If it rains, then the sidewalk will be wet

Premise 2: The sidewalk isn't wet (disconfirming q)

Conclusion: It didn't rain (disconfirming p)

Affirming

______________ the consequent doesn't entail the antecedent being true

Premise 1: If it rains, then the sidewalk will be wet

Premise 2: The sidewalk is wet (q)

Conclusion: It rained -> INVALID

Denying

_____________ the antecedent doesn't entail the consequent being false

Premise 1: If it rains, then the sidewalk will be wet

Premise 2: It didn't rain

Conclusion: The sidewalk isn't wet -> INVALID

Wason Selection Task

highlights how we consistently commit deductive reasoning errors (<10% of participants got it correct)

If a card has an A on one side, it has a 3 on the other

Most selected A (valid) and 3 (invalid)

Social context version

Cosmides & Tooby (1992) reframed the task in a social context. Social contracts now give this task a concrete goal to detect the cheater, thus bypassing abstract reasoning.

If you are drinking alcohol, then you must be over 19. 75-90% of participants got it correct

Inductive reasoning

involves making generalizations about a broader group based on specific examples. The conclusions are probabilistic, meaning they are likely but not guaranteed to be true, even if the premises are correct.

strong

If the conclusion follows from the premises with high probability, it is a ________ argument

weak

If the conclusion follows from the premises with low probability, it is a _____ argument

cogent

If the premises are actually true in the real world and the argument is strong, then the argument is _______ (logical and convincing)

property induction

a form of inductive reasoning where we generalize properties from one exemplar of a category to other members of the category

(e.g., Crows have an anatomical part called slabido. Do all birds have slabido? → most likely to say yes when the exemplar is a crow)

Premise-conclusion similarity

high similarity between premise and conclusion entails a stronger argument

Premise typicality

premises that are more representative of the category lead to stronger inductions (e.g., crow vs. penguin)

premise diversity

the principle that an inductive argument is stronger when the examples come from diverse subcategories within a broader category. More varied examples suggest the property applies across the whole category, not just a narrow subgroup.

premise monotonicity

the principle that adding more premises (examples) that share a property strengthens an inductive argument, increasing confidence that the property applies to the broader category.

confirmation bias

the inclination to favour evidence in support of our beliefs, expectations, or hypotheses in the process of reasoning

Causal Reasoning

our ability to understand the relationship between a cause and effect

directionality

Causal relationships have _____________, where causes precede effects (e.g., A causes B)

(Red ball hits blue ball (A) -> Blue ball rolls away (B)

Causal launching

Causation associated with a direction

In an animated display, the perception that one moving stimulus causes a stationary one to move (or "launch") when it collides with it

Both adults and children (even infants) perceive the stills as a sequence of events demonstrating causal launching

Cause-effect relations

depict causal relationships which allows us to assign probabilistic weights to the strength of the relation

Probabilistic weight

the strength of a relation between 0 (no causal relation) and 1 (guaranteed causal relation)

causal induction

We learn cause-effect relationships through observations through ________ ____________ (inferring causal relationships) We consider many cues such as covariation, temporal order, intervention, prior knowledge

covariation

the likelihood that two events covary, or occur together

e.g., Being happy (A) -> Sleeping 7+ hours a night (B) vs. Sleeping <7 hours a night (C)

A has a higher covariation with B

Temporal Order

the arrangement of events over time. causal features are more important because earlier features are seen as the underlying basis that generates the rest of the chain, making them more essential for category membership.

e.g., Eats fruit (A) -> Has sticky feet (B) -> Builds tree nests (C)

People view A as more important than C

Intervention

considering an external independent cause to an event sequence, rather than simply observing the event sequence as is (e.g., considering weather as a factor in the relationship between ice cream sales and murder rates)

prior knowledge

our background knowledge influences how we determine the causes of events (e.g., Roosters crowing at sunrise provides covariation and temporal order cues, but we do not infer that the rooster causes the sunrise)

Illusory correlations

making connections between variables that have no relation to each other (e.g., superstition: You have a "lucky" shirt you wear for your favourite team's playoff games because you were wearing it when they won last time)

Counterfactual reasoning

we often think about alternative scenarios when trying to understand why something happened (e.g., would i have gotten the midterm questions about attention right if i attended lecture 2?)

Bayesian inference

allows us to estimate the probability of a hypothesis being true based on the evidence we have and our knowledge of the world

Bayes Theorem

The probability of an event occurring based upon other event probabilities.

P(H|E) = P(E|H) x P(H) / P(E)

Posterior Probability

P(H|E) = the probability that a hypothesis H is true after consideration of the E evidence

likelihood

P(E|H) = if the hypothesis is true, how likely is this evidence?

Prior Probability

P(H) = How likely was this before I saw any evidence?

probability, evidence

P(E) = _________ of the ________ you have

Bayesian estimation

updating probabilities based on new evidence, combining prior beliefs with observed data to estimate the likelihood of outcomes (e.g., perception, causal reasoning, predictions like sports or disease spread).

Problem solving

concerns finding ways to obtain one's goals, whether the agent is a person, animal, or machine

goal state

where the agent wants to be

actions/operators

agent uses _______/________ to move from current to goal state

routine problems

A problem that is familiar and has a known solution (e.g., how many $20 bills in $80)

nonroutine problems

unfamiliar problems with no clear solution. the current and goal states are clear but the actions are not (e.g., how can we get more people to eat more vegetables?)

well-defined problems

contain clear, specific given/goal states and actions/operators (e.g., 1019 + 21903)

ill-defined problems do not (e.g., How can I be happier in my life?)

Insight

the process of suddenly gaining a solution to a problem, like an aha moment

Transfer

learning how to solve one problem generalizes to solving others (e.g., writing skills from one class can transfer to many others)

random trial and error

randomly selecting and applying different solutions until the problem is solved (might eventually work for a Rubik's cube, but is often unsuccessful for more complex problems)

means-ends analysis

being specific about goals and subgoals to find moves that solve the problem (Ideally, you don't write a research paper in one sitting. Instead, you break it up into smaller steps: select the topic, do a literature review, write a section, and address multiple rounds of feedback at each stage)

Expert problem solving

Experts organize knowledge around deep underlying principles, allowing them to recognize meaningful patterns and solve problems efficiently. In contrast, novices focus on superficial features. Expertise is domain-specific and develops primarily through experience and practice.

Chess expertise

Shows that experts can recall real game positions better than novices because they use chunking. In random positions, experts lose this advantage because there are no patterns to chunk