psych exam 3

procedural information

knowledge about how to preform a task or skill, often acquired through practice and becoming almost automatic

different from declarative knowledge

skill learning three stages

1. cognitive

2. associative

3. automaticity

cognitive

declarative knowledge

commit facts to memory

rehearse

requires attention

associative

strengthens connection that lead to desired result, get rid of actions that lead to errors

feedback is important

automaticity

fast, executed with less attention

declarative knowledge is less important

less verbalization

feedback is less important

when aiming for the same performance level, consistent practice is still needed

power law of practice

improvement follows a power law:

skill increases with more practice

but, the rate of improvement diminishes with time

ACT-R

adaptive control of thoughts: separates procedural from declarative knowledge

procedural knowledge is represented in the form of production (if-then statements: if (condition) then (action))

proceduralization: take declarative knowledge and turn into products

(declarative knowledge of conditions A, declarative knowledge of action B; product: if condition A then perform action B)

composition: after you practice, you string those all together; take several productions and join them together into one (if condition A then, preform action B, then preform action C)

ACT vs modern view

ACT is one way to conceptualize motor skill development, but this is a bit old view --> modern view: we have multiple systems that are operating in parallel, we have the system that is more of a declarative system and another system that's more important for procedural learning, happening at the same time

fast learning system

Explicit/declarative, conscious, goal-directed, effortful, flexible

slow learning system

implicit/procedural

unconscious

automatic

inflexible

serial reaction time task (SRTT) evidence

a sequence of lights appear on a screen, press the corresponding key as fast as you can

explicit training: there's a pattern, think about that

implicit training: just react asap

performance on learning sequences the same irrespective training type

slow (implicit) learning system consciously learns patterns in the background, even without being aware of them

our brains can pick up unconsciously, people are learning the pattern (even if they are not aware of it)

plus-maze evidence from rats

train (find reward)

test (from opposite location)

route learning: implicit skill

tested either early on or after extended training:

early on in the learning: driven by place learning (explicit skill) "fast" learning, hippocampus

extended learning: driven by route learning (implicit skill) "slow" learning, basal ganglia

chain response

feedback from one movement triggers the next, start the second step after the first step is completed --> WRONG

anticipatory movements during typing

motor program evidence

not response chaining (too fast)

fast and doesn't require feedback

hierarchical structure: abstract high level, specific low level

composed of subprograms (less abstract representations of movement sub-parts)(much slower when have to say more words because you need to load those sub-programs before you begin)

ex: signatures: using different muscles - but you have your signature looks basically the same (evidence for abstract motor programs AND hierarchical representations)

hierarchical representation (finger tapping experiment)

empirical evidence for hierarchial representation:

rosenbaum experiment

• make a movement sequence (Lm, Rm, Lm, Li, Ri, Li, Ri)(m=middle finger)(i=index finger)

• it should take you long time to press the first one (Lm) (because you have to travel quite far down) but not a long time to press the next one (because you don’t have to travel as far)(but going from Lm to Li will take some time because you have a long ways to travel (in the hieracharical structure))

• rt time shows this (slow for the first button press then fast for the second, a but slower for the 3rd, etc)

• our motor programs are organized hierarchially

properties of language

communicative

symbolic - map symbols onto meaning

mostly arbitrary (same words in other language often do not resemble each other

some exceptions: like kiki vs bouba example)

generative - can come up with infinite new sentences

dynamic - constantly evolving (eg slang)

structured (hierarchical)

kiki vs bouba example

a psychological experiment demonstrating how people assign sounds to shapes, where 'kiki' is usually associated with a spiky shape and 'bouba' with a round shape,

across many different languages these results held true, this is because “kiki” is a very sharp sounding thing while “bouba” is a round sounding thing which matches with the physical appearances that people assign them to (out of the 2 given shapes) however depending on the language these results are not as clear cut

language levels

sentence (largest)

phrase

word

morpheme

phoneme (smallest)

phoneme

smallest unit of sound used to distinguish words in a given language ("atoms" of sound)

different phoneme is different languages

ie stranger: strynj + er

morpheme

smallest unit of meaning

syntax

a set of rules that determine the grouping and arrangement of words in phrases in sentences

ambiguity

words alone aren't enough to convey meaning

lexical ambiguity

same words has 2 or more meanings

syntactic ambiguity

words can be grouped into more than one phrase structure

phrase structure

same words can sometimes be grouped into phrases differently which changes meaning

context effects in lexical access

how do we access the meaning of a word when we encounter it in a sentence?

many words have more than one meaning, but we don't usually get confused when we encounter them in context

swinney priming experiment (important come back to)

initially we access all possible meanings of a word (ANT, SPY),but very quickly (within a second) we narrow down the meaning and select the context-relevant one (ANT)

interaction of syntax and semantics

Active voice easier than passive voice sentences for semantically reversible sentences,

but not semantically irreversible sentences, suggests interaction of syntax & semantics

during comprehension

broca's aphasia

left frontal lobe

production difficulty

slow, halting speech (comprehension is intact)

ie what happened to you? - "stroke...sunday...hospital...bad"

wernicke's aphasia

left temporal lobe

comprehension difficulties

ie What happened to you? - "Boy, I'm sweating, I'm awful nervous, you know, once in a while I

get up, I can't mention the tarripoi, a month ago, quite ~~"

Fluent but make no sense

the neutral pathway for repeating a heard word

auditory cortex (receives incoming sound) to wernicke's area (processes MEANING of the received sound (comprehension)) to broca's area (converts the meaningful sound to a code for muscular movement required for speech production) to motor cortex (receives output from broca's area and initiates the muscular movement (mouth, lips, tongue))

the problem of language acquisition

language is complex:

need to learn how to distinguish language sounds from other sounds; need to break those sounds into phonemes; need to take phonemes, morphemes, and group them into words; need to figure out what the words actually mean; need to learn - how to combine words correct grammar

limited grammatical feedback when learning

adults typically do not correct grammar but do correct meaning; most adults don't say things like "No that's incorrect grammar" instead they might correct only when the meaning is wrong

linguistic universals

even when language is complex and there's limited feedback, we can still acquire language, general principles & innate

learning phenomes

phenome (smallest unit of language)

in 1st year infants can discriminate all phonemes from all languages

gradually they lose discriminations that are not important to their own language (narrowing)

motherese

infant-directed speech

when talking to infants (higher pitch, shorter sentences (slow rate), speak clearly and distinctly (exaggerated intonations))

exaggerated features help children understand boundaries between words or phrases

major stages of language development in children

1. holophrastic stage

2. telegraphic stage

3. learning syntax/rules/generalization

holophrastic stage

one word

no syntax yet

need context (gestures, affect) to understand

under/overgeneralization for first ~75 words

ie "dog" --> squirrels, rabbits, cats, etc

"dog" --> only to their poodle

telegraphic stage

two-words

begins to use correct use of word order (simple)

ie subject-action, action-object

"mommy go" "eat chocolate)

can convey lots of information succinctly

learning syntax/rules/generalization

start learning syntactic/grammar rules

examples: past tense, nonsense words

past tense- even if incorrect at first

ie "daddy goed" instead of "daddy went"

learning rules: past tense

U-shaped curve

at the beginning, children often use irregular past tense correctly (ie saying "did" instead of "doed")

then as they start to learn grammar rules, like adding '-ed' for the past tense they begin to overgeneralize ("saying "runned" instead of "ran")

finally they start to relearn the correct irregular forms as they build a more complete understanding of both the rules and the exception ---> curve goes back up

learning rules: nonsense words

learn general rules and apply them to new words (even if nonreal)

ie adding -s for plurals (eg "wug" to "wugs")

adding -ed for past tense "eg "rick" to "ricked")

language learning is generative: children create new forms based on rules they learned (not just imitating)

learning word meaning

children know massive amounts of words at a young age

will use clues from input from part/whole relationships (ie "this is a rabbit; these are his ears" --> "his" is a cue that the ears belong to the rabbit)

bias that new words refer to shape dimension (we have bias toward shape)

critical period effects

coptimal time window for language acquisition

people who learn languages after age 10-12 rarely acquire native fluency (regardless of how long they have lived in the country)

social isolation cases (children who were neglected (no social interaction unit 10) missed early exposure to language; even after rehabilitation couldn't reach native fluency)

this idea applies to both 2nd language and sign language

you can speak however you will never reach the proficiency as a native

problem

a problem consists of some initial state in which a person begins and a goal state that is to be attained, plus a non-obvious way of getting from the first to the second

well-structured/defined

clearly specified components

completely specified starting condition, goal state, and methods for achieving the goal (ie geometry proof)

ill-structured/defined

solvers need to define themselves

some aspects are not completely specified (eg writing the best novel, choosing a career, partner)

stages in problem-solving

form a representation, construct a (planning), execution (plan), checking/evaluation

problem representation

for many problems the repterm-51resentation many make it easier or harder to solve

*algebra problems easier as equations

*geometry problems easier graphically

*decision problems easier when laid out in a grid

problem space

whole range of possible states and operators (actions that move between states) only some of which will lead to the goal state

representation: nine dot problem

there are 9 dots arranged in a square below, using no more than 4 lines connect all dots without lifting your pencil

initial & goats states well defined

operators: 4 connected lines

presentation: graphical layout

problem space: all possible lines you can draw

go outside the imaginary box formed by the dots (most people assume they have to stay within the square but that's not actually a rule here)

shows the people often struggle with creating a good problem representation

removing constraints

representation: monk problem

text-based difficult

people imagine a single monk walking up & down the mountain --> misleading (this representation does not help solving the problem)

solution: modifying representation (imagine 2 monks instead of 1; who leave at the same time from different location at some point they must meet)

isomorph

isomorphic problems are equivalent underneath the underlying structure, even though the surface representation is different

ie 2 players, each draw 1 card at a time, first player to hold 3 cards sum to 15 wins can also think of this Sadako or tik tac toe

analogies

when we face a new problem, we often try to retrieve a similar problem we've solved in the past

people usually focus on surface similarities rather than deep similarities

duncker's ray problem

Real-world solution: use sub-lethal doses coming in from different directions.

10-20% of subjects came up with this spontaneously.

Would an analogy (isomorphic problem) help?

Gick & Holyoak (1980) first presented subjects with a story about a general (military problem)

participants were either asked to solve ray problem alone or after reading military problem (analog)

different surface, but similar deep structure

even though both problems have similar deep structures, participants couldn't connect the military ray when no hint was given (analogy, no hint 30%)

only after hint is given ("can you use the military problem to help you solve the ray problem") participants could connect --> 80%

top-down preconceptions

when we look at a new problem we tend to encode it in a way consistent with LTM

hinderance in problem solving: functional fixedness

we tend to assume that we can only use an object in a particular way

candle problem

can you fix and light a candle on the wall so the wax won't drip on the table below?

tacks outside or inside the box?

same materials, same goals but arranged differently

43% solved when tacks in box while 100% solves when tacks are loose

maier's 2 rope problem

2 ropes attached to the ceiling and the participants need to tie to the 2 ropes, there are other objects in the room

functional fixedness may make you think that the pliers function is only grabbing however if you think of pliers as creating a pendulum, rather than grabbing device, you can do the task

trains meeting problem

trains moving in opposite directions, bird flying from on train to another

trapped by familiar prespective

• most people take perspective of the bird

• some might use advanced mathmatics of infinite series and limits

• but just notice how long the trains will travel (1 hr)

• bird flying at 100 miles/hour, travels 100 miles

adopting the wrong frame makes it really hard to solve

stuck in set

a habit formed by solving earlier problems the same way

once we find a method that works, we tend to keep using it, even when simpler solutions exist

luchins water jar problem

This is a task used to study problem-solving. It's results demonstrated how people have a tendency to repeat solutions that worked in previous situations, even if a more efficient way is available (this is called a mental set)

first 5 the solution is the same however the 6th one give them an easier solution but people will be set in the same way they previously solved the problems; stuck in set

algorithms

completely specified sequence of steps guaranteed to produce answers

usually guaranteed to produce correct answer

but may be slower or laborious

heuristic

short cut/"rule of thumb"

never guaranteed to produce correct answer

but usually quick and easy

think-aloud protocol

people try different heuristics and short-cuts to solve things

try a lot of different things and then you might find something that seems like it might work, that becomes a heuristic and try all the different things that use that heuristic

people tend to adopt and start trying out differnet little rules of thumb, like finding a root word that in the scrambled word and trying those out, that’s what’s called a heuristic

protocols do not reflect all of the reasons why a person tried a specific configuration

difference reduction

a problem-solving method that involves reducing the difference between the present situation and the desired one

at any point, select the operators that move you closer to the goal state: is new state more similar to goal?

sometimes you have to take a detour in order to be more efficient in solving a problem

description on how peoople solve things

means-end analysis

first identify the largest difference between current and goal state

set a subgoal (that reduces that difference)

find and apply an operator to reduce the difference

if the operator can’t be applied, new subgoal = remove obstacle that prevent applying the operator

EX

goal : take daughter to day care

the largest difference when current and goal state: distance

find a operator to reduce the difference: drive car to daycare

operator can’t be applied: car broke down

new subgoal: fix car

description on how people solve things

subgoaling

process of breaking down a complex problem/goal into smaller more manageable sub-goals that are easier to achieve

production system for means-end analysis

a framework that outlines the procedures and rules for applying means-end analysis to solve problems through a series of production rules and states

hobbits and orcs

the goal is to transport all 6 creatures across to the other side of the river

at not poitn on either side of the river can orcs outnumber hobbit

not possible to solve this one with difference reduction

people naturally want to do this difference reduction and if they get to an intermediate which looks like its not going towards the goal they tend to abadon it because they think they are doing the wrong thing (even though it necessary to get ot the goal)

working backward

transform goal state so it is more similar to the initial state (useful for maze-like problems)

means-end analysis cna involve working backwards

chess study

memorize where the chess pieces are on a chess board

and when you try to fill in the pieces and people that played chess a lot (had expertise) they were able to recall the positions more accurately due to pattern recognition and experience (was able to chunk)

however if you put the pieces in random position then the beginners are better than the experts because a lot of things on the random positioned board can’t happen in normal chess so they are dealing with functional fixness and top-down hinderance

practice

true that more practice is good and if you are an expert you probably have a lot of practice

depending on what domain you are looking at the number of hours of practice explain more of what’s called variance, can explain who’s gonna be better and worse in this professional class

depending on the domain practicce can explain quite a lot

power law of practice

the more times you spend the better you get

improvement dimishes with time

it takes VERY long to gain the small amount of improvementn that separates really good from great

expert problem solving

rich organized schema

• have lots of well-organized declarative and procedural knowledge

• more sophisticated representation

spend more time on representation

• experts take longer to srart solution, but less time to complete it

Less means-end analysis

• pre-sroted solutions in long term memory

• fewer demandds on working memory

Moving forward, not backwards

More reliance on long term memory, less on working memory

deterministic reasoning

deductive

conclusion necessarily follows from premises

the process of deriving predictions from general laws/theories

conlucsion follows from the premise (a//b, b//c --> a//c)

theory -> hypothesis -> observation -> confirmation (irgnore base rates)

ed: if it is cloudy it will rain, it is raining

probabilistic reasoning

inductive

conclusion does not necesaarily follow from premises

the process of developing hypothesis from fact/observations (observation -> pattern -> hypothesis -> theory)

ex: how a psychologist diagnose clients

ex: pavement is wet, so it's likely that it rained recently

normative theory

how people should reason (rules of logic)

normally you should think this way

current evidence

symptoms (ex: does katies have a cold or does she have ebola?)

dcotots need to devide if it's a cold or Ebola

they need to take into account base rate

probability of diagnosis (es: what is the rate of diagnosis for ebola in the US? pertty low so its probably not ebola)

descriptive theory

how people actually reason

describes how people actually reason

biases & heuristics

normative inductive reasoning

Base rate and current evidence

Mammogram example: Doctors confuse P(H|E) and P(E|H)

P(H|E) (positive predictive value) is refering to the probability of having breast cancer (given a positive mammogram result)

P(E|H) (sensitivity) is refering to the probability of a positive mammogram result (given breast cancer is present)

a mammogram has a 90% sensitivity (p(E/H)) and a 5% positive predictive value (p(H/E)). This means that if a woman has breast cancer, the mammogram has a 90% chance of detecting it. However, if a woman gets a positive mammogram result, there's only a 5% chance that she actually has breast cancer

Normative inductive reasoning - bayes

how do we update out beliefs based on the evidence?

p(H) = overall probability that hypothesis is true

= prior probability

= BASE RATE

normative inductive reasoning - Bayes example

in this village, 80% of the animals are dogs adn 20% are cats. one night you hear a strange animal sound near bushes

How likely is it that the sound came from a cat, given that we heard it?

p(H|E) using Bayes' theorem

H: the sound was from a cat

H\ : the sound was not heard from a cat- it was a dog

E: you heard an animal sound at night

We need 3 pieces of info

P(H|E) : probability of current evidence if hypothesis is true (what is the chance you’d hear this sound at night, if it really was a cat?)(lets say 90% of cats meave at night P(H|E) —> 0.9)

P(E|H\) : probability of current acidence if hypothesis is false (what is the change you’d hear this sound if it wasn’t a dog (was a dog barking))(10% of dogsbark at night P(E|H\) —> 0.1)

P(H) : probability of hypothesis independent of current evidence (base rate") how common are cats in this village?)(cats make up 20% if animal population → P(H) =0.2)(cats don’t make up 80% of animal population —> P(H\)=0.8)

descriptive inductive reasoning

inductive (probabilistic, specific —> general) (based on evidence (observations make conclusions)
descriptive (how people actually people reason; describes how people actually reason (biases/heuristics)

we often pay too much attention on base rates and not enough weight to current evidence

OR

we sometimes ignore base rates and we don’t use logical calculations of base rate & evidence

ALSO people ignore base rate when thinking of similarity (people tend to judge more ‘random looking’ sequences as being more likely)

50/50 poker example

there are 2 bags (one contains 70 red chips and 30 blue chips)(the other contains 70 blue chips and 30 red chips)

a person picks one bag ar random (each having an equal 0.5 probability of being chosen)

if they then pull a red chip, bayes’ theorem calculates the probability that the bag chosen was the predominantly red one getting 0.7, however people typically answer 0.6 showing they rely too heavily on the base rate and don’t give enough weight to the new evidence

an example of descriptive inductive reasoning

representative heuristic

we assume an outcome is more probable simply because it appears to fit our expectations (our intuition often tricks us into believing that patterns ressembling “true randomness” are more probably even when statistics say otherwise)

when people focus on superfical patterns instead of statistical principles, their reasoning becomes flawed

emphasis on similarity regers to the tendency of people to judge the likeluhood of an event based on how much it represents their mental prototype of that category rather than considering actual statistical probabilities

COIN EXAMPLE

you flip a coin 5 times

the 2 sequences are presented

HHHHH

HHHHT

people tend to judge the 2nd sequence as more likely because it looks more random even though both sequences have the same probability, this is an example of a representative heuristic, it ignores base rate when making judgements

BIRTH ORDER EXAMPLE

there are 2 different birth sequences

GBGBBG (72 families observed)

BGBBBB *seeking the estimated count)

statstically the probability of any specific birth sequence in a six-child family is the same (girl 50%; boy 50%) thus the number of families with BGBBBB shoudl also be 72 however people often use the representative heurisitc and assume patterns that look more random are more likely than clustered sequences

lawyer and engineers

representativeness

judge whether A has some characterisitc by relying on the similarity of A to other things iwth that characterisitc

problem: tend to ignore the base rate

in part 1 of the experiment: there was no description given so they could correctly assess the probability of whether A is an engineer or a lawyer based solely on the provided information

In part 2 there was a description that matched the description of an engineer which led participants to ignore the base rate and the statistics and assume higher probability of A being an engineer based on similarity rather than actual base rates

when there was a neutral description there was a tendency to ignore the base rate entirely and they assigned equal probabilities in both cases this shows that once people focus on an individual’s characteristics, they often disregard base statistical probabilities

similarity of istance to catergory

CS major exaple

base rate: % of grad students in humanities is much higher than CS

however when given a description that matches one of CS major people judge based on similarity and ignore the base rate and assume that Tom is a CS major even though the base rate says that much less likely

how representativeness explains doctor’s tendency to confuse P(E|H) and P(H|E)

P(M+|C) = 0.8 : probability of a positive mammogram given cancer

P(C|M+) = 0.07 : probability of cancer given a positive mammogram

Doctors tend to think, “A person with a positive mammogram is similar to a person with cancer.” This emphasis on similarity leads them to overestimate the likelihood that a positive mammogram indicates cancer. They neglect the base rate—the fact that cancer is rare in the general population—which drastically affects the actual probability.

This bias can lead to unnecessary anxiety, further testing, or even overtreatment to patients who recieve false-positive results

availability heuristic

used when estimating the frequency or probability by the ease with which instances or associations could be brought ot mind

evaluate the probability or likelihood of na event by judging how easy relevant instances come to mind

accuracy of estimates compared to actual retrieval is pretty good (russian novelists/flower example)

because flower are more available in your memory, you estimate that you could name more of them - and you actually can

factors other than frequency that can affect retrievability

Tversky & Kahneman’s experiment: “famous names”

people say that the list had more female names than male names, B/c famous names are more available in your memory, you think that the list had more female names when asked to list 20 famous female names and 20 generic male names

frequency of lethal events experiment

each of the follow pairs of lethal events, judge which one is the more frequently occuring worldwide

people are often wrong about which is the more lethal event due to which one is more widely discussed in media and health campaigns, emotional impact, and which has more vivid dramatics event associated with it (as those are easier to retrive)

household chore experiment

asked couples to estimate the percentage of household chore they and their partner did, teh resulrs showed that each partner tended to overestimate their own contribution with the combined percentage often exceeding 100%, people are more likely to recall the instanced they themselves performed, leading to overestimate their contribution

biases due to retrieval (r____ word vs __r__ words; ____ing words vs _____n_ words)

most people say that more words that start with r_____ because its easier to recell them; but actually more english words have R as the 3rd letter

same for ___ing and __n_ every "-ing” word must also have an “-n-” at some point meaning that “-n-” words are at least as frequent or more frequent however because “-n-” do not come to mind as easily people would say more words end with “ing” than “-n-”

simulation heuristic

base judgment on how easily you can stimulate (how things will turn out in the future; how things would turn out in different circumstances (what if))

Mr Crane and Mr. Tees’s emotional reaction

Mr. Cane his flight left on time and he was late, while with Mr. Tees the flight was delayed

easier to image “if only I had left 5 min earlier” mental simulation for flight delayed

predicting daughter/mother eye colors (cause and effect scenarios)

Given that her mother has blue eyes, what’s the probability that a daughter has blue eyes? VS Given that her daughter has blue eyes, what’s the probability the mother has blue eyes?

both are mathmatically the same but people find the 1st one easier, b/c they can mentally stimulate the inheritancepath from parent to child, SAME for height example

causal links between action and actor: ease of simulating avoidance of accident

casual reasoning, is how people infer links between actions and outcomes, for a situation that describes a near collision but leaves the reason for its aviodance ambigious it prompts the reader to supply an explanation, most people attribute the accident avoidance to an agent’s action however alternative explanations exist

conjunction fallacy

occurs when people mistakenly believe that a conjunction of events (hot and sunny) is more probable than a single event (sunny)

which is more likely sunny and hot or just sunny?

people say “sunny and hot" but logically this cant be probable (subset)

caused by availability

if ‘hot and sunnny’ days are more vivid in you memory, they feel more likely

caused by causal reasoning

‘if it’s sunny, then it will be hot” even though that’s not always true

caused by representativeness

match the scenario to a stereotype - like ‘typical summer day’

linda the femisinst bank teller example

orignially posed by Tversky and Kahneman describe linda as a 31 year old, single, outspoken, and very bright with a background in philosophy and activitsm for social justice, participants are more likely to choose “linda is a bank teller and active in the feminist movement” even though it is mathmatically less likey this is b/c linda’s description fits the stereotype of a feminist activist more than a generic bank teller, leading people to overestimate the probability of the conjunction of 2 events, however the probability of the 2 events occuring together is always equal to or less than the probability of either event occuring alone

how a problem is frammed

same information presented in different forms can lead to differnet decisions

disease experiment

the wording where it makes it so people will be saved is more likely to be picked over the one that insinutates that people will die (even if the later option is the better of the 2)

gain frame —> risk averse

loss frame —> risk seeking

positive frame/risk avoidance/conservatism vs negative frame/risk seeking

negative frame: people are less likely to choose even if it means the same thing as the positive frame just wordered differently

why use non-normative heurisitics

simplify the mental task involved in reasoning

mental shortcuts that help people make desicions quickly and efficiently, can lead to errors

sunk cost fallacy

tendency to continue an endeavor if we have already invested time, effort, or money into it, even if the cost outweigh the benefits

types of deductive reasoning problems

quantifier (categorical syllogisms)

some A are B

all B and C

then some A are C?

EX

some businessmen are wealthy

all wealthy people are powerful

therefore some businessmen are powerful

are difficult

comparative (linear syllogisms)

A is stronger than B

B is stronger than C
A is stronger than C

conditional (wason task)(if-then logic)

if run, they you will be happy

you run

you will be happy

modus ponens:

if A —> B

and is A is true, then B must be true

syllogisms

ARE DIFFICULT

common reasoning errors

validity effect: we are biased towards syllogims that “look” valid

content effect: familiar topics (like dogs vs dinosaurs) make us likely to think something is valid

atmosphere effect: we like when the conclusion "matches” the language of the premise (eg some/some of all/all)

figural effect: we prefer when things are in simple, linear form (eg some A’s are B’s, some B’s are C’s)(more likely to accept syllogism when terms are in linear order)

conversion effect: we mistakenly believe the reverse must be true (eg All A’s are B’s —> all B’s are A’s)(all pets are animals —> all animals are pets ((INVALID))

all dogs are animals

some animals are pets

some animals are pets

therefore soe dogs are pets

all dinosaurs are animals

some animals are pets

therefore some dinosaurs are pets

both INVALID (but people endorse the first as valid)

some A’s are B’s

some B’s are C’s

therefore all A’s are C’s

INVALID

some B’s are A’s

some C’s are B’s

therefore some A’s are C’s

INVALID

wason selection task

conditional reasoning (if-then)

“if a card has a vowel on one side, then it must have an even number on the other” —> which ones do you need to flip over to test the rule

you have cards E, F, 4, 7

most people say: E and 4

correct answer: E and 7

you flip E to see if there’s an even number

you also flip 7- because if a vowel is hiding behind the 7, then the rule is broken

example of the content effects: the words “vowel” and “even number” lead our thinking in the wrong direction

if converting this to a bar scenario example (checking ID and age) people do much better - isomorphic change

formal rule theories

intuition: people are logical, but make sense (if A is true, and A implies B, then B must be true)

assumption: formal rules of logic are built in (reason by proof: apply rules until reach conclusion)

explanation of errors

1. misinterpret premise

2. some rules are unavailable

3. can’t find proof for conclusion

theoretical problems

1. if deduction depends on formal (content-free) rules, then why does content matter?

2. why would formal rules be built in, when they only apply to infrequent tasks (deducation)?

mental model theory COME BACK TO

people constrcut mental models (representations) that correspond to the premises, describe them, and then try to flasify conclusions by constructing alternative models (mental pictures)

can i think of a counterexample that falsifies the conclusion?

all of the artists are beekeepers

some of the beekeepers are clever

some of the artist are clever? not necessarily (b/c we weren’t given information about whether the clever beekeepers include artist (not all beekeepers are artist))

explanation of errors

we often mess up b/c of WM limitations (we can’t hold onto too many mental pictures)

syllogism that require more models are harder

theoretical problems

contrstructing counterexamples is a very complex process that is specific to deduction, would subjects with no training use it?

verbal reasoning theory

repeatedly use linguistic processes to try to extract more information from problem statement

• rather than applying formal rules or searching for counterexamples

read the problem, and we keep rephrasing it in our minds, trying to get the gist of what it says and reasoning to understand the problem better.

• we sometimes mess up because this process it built for communication not logical precision

• that’s why we sometimes

  • addd in information that wasn’t really there

  • or miss information that was deductively valid

intuition: without training, subjects don’t have deduction-specific strategies

they do have sophisticated language comprehension processes

assumptions: repeatedly use linguist processes to try to extract more information form problem statements (rather than apply formal rules of searching for counterexamples)

explanation of errors

errors arise because linguistic processes are adapted to demands of communication, not deduction

in communication, we construct a plausible representation of the gist

• includes inferred ifnromation that may not be deductively valid

• may exclude deductively valid ifnromation that wasn’t emphasized