Logical reasoning

Question 1

What is rationality?

Answer 1

the ability to think and behave in a principled way
go beyond and understand the information we’re given and act on it
supposedly a defining human trait

Question 2

What is formal logic?

Answer 2

a set of rules for drawing valid conclusions from a true premise
valid means if you apply the rules to premises that are true then their conclusions will also be true.
these rules are ‘truth-preserving’ and generally applicable which is powerful as they enable us to go beyond a set of information by drawing inferences that are true about things we have’t observed
underlies modern computing

Question 3

What is modus ponens inference?

Answer 3

‘if p, then q’

p is true, so q (MP inference)
know that the premise is true so we are able to draw the valid conclusion, q.

Question 4

What is modus tollens inference?

Answer 4

‘if p, then q’

q is not true, so p is not true.
as the conclusion does not apply/ is not correct, the premise that necessarily entails that conclusion does not apply/ is not correct.

Question 5

what are the two types of valid conclusions we can draw from ‘if-then’ rules

Answer 5

modus ponens

modus tollens

Question 6

what are the two types of invalid conclusions we can draw from ‘if-then’ rules?

Answer 6

Affirmation of the consequent

Denial of the antecedent

Question 7

what is affirmation of the consequent?

Answer 7

‘If p, then q’

q is true, so p
logical fallacy
Doesn’t follow with certainty from the given information .’. invalid

Question 8

What is denial of the antecedent?

Answer 8

‘if p, then q’

not p, so not q
There are situations where it’s not true so can’t be concluded with certainty from the information given

Question 9

What is a descriptive theory?

Answer 9

A theory as to how people do in fact behave

e.g People do not in fact employ deductive rules of logic in their reasoning.

Question 10

What is a normative theory?

Answer 10

A theory as to how people ought to behave

e.g people ought to employ rules for drawing a valid conclusions

Question 11

What is Marcus and Rips’ (1979) Conditional Reasoning Experiment?

Answer 11

Gave subjects examples of reasoning and conclusions that you could draw from this information.
Participants were asked to if the conclusions necessarily follow from the information given various condition rules, such as “if the fish is red, then it is striped.”
They found that most people appropriately endorse modus ponens conclusions; only half endorse modus tollens conclusions and a significant proportion wrongly endorse affirmation of the consequent or denial of the antecedent.
Given these are the most basic forms of logical reasoning we can give people it seems unlikely that the brain naturally employs such rules when reasoning.

Question 12

What is Klauer et al’s (2000) Syllogistic reasoning study?

Answer 12

Syllogistic reasoning: a process in logic where two general statements lead to a more particular statement.
Subjects were given two premises and a conclusion .
Manipulated so that the conclusion was either valid or invalid or statements had been reorganised so that the conclusions were either believable or unbelievable.
Unbelievable statements do not fit with prior knowledge.
Told to assume the premises are true; so if applying general logic rules should identify statements as valid irrespective of whether or not they are believable; if employing prior knowledge believability should have an effect.

Results
main effect of validity
belief bias
Regardless of the quality of the reasoning, only endorsing conclusions as valid and following from the information provided if they fit with people’s expectations of prior knowledge

Question 13

What is Wason’s Card Sorting Task (1966)

Answer 13

Given a rule: “If p vowel on one side of the card, then q, even number on the other”
asked to select the exact cards which would need to be turned over in order to test the rule
There are four cards which represent the outcomes: ‘p’ e.g A (vowel) ‘not-p’ e.g K (consonant) ‘q’ e.g 4 (even number ) ‘not-q’ e.g 7 (odd number)
Logic would dictate that the two cards which should be turned over are the p and not-q cards.

Question 14

What did Oaksford and Chater’s (1994) meta-analysis of Card selection results find?

Answer 14

Collated about 30 experiments employing Wason-style selection tasks involving about 800 people.
Most people tend to turn over the ‘p’ card
people do not tend to turn over the ‘not-q’ card
but a significant number of people turn over the ‘q’ card
thus people do not seem to be applying logic rules in their reasoning

Question 15

What is the effect of training on performance in the Wason card selection task?

Answer 15

Cheng & Holyoak et al, (1986)
At university lots of students take an introductory course to logic
Compared start vs end of the course
Told its a psychology experiment rather than a test in formal logic
Can argue that they get a bit better, no dramatic increase even after a whole term of training in formal logic and reasoning

Question 16

What did Grigg’s and Cox (1982) familiar rules study show?

Answer 16

The rule: “If a person is drinking beer, then they must be over 18 years old’
Asked to reason about a social rule or law
Given a card selection tasks where p or q could be true or false
Same logical structure of the task as in the wason’s card task
More intuitive than abstract rule in terms of what to turn over and not
Compared to the original <10%, 73% of participants correctly identify which cards to turn over (specific definition of correct according to the laws of logic)

Question 17

What did Cheng and Holyoak’s (1985) Thematic material study show?

Answer 17

Extended this idea to show that people perform better if they are given rules that are meaningful, even if they are not familiar with them.
Thematic: understandable and has a real world context, but not necessarily everyday
The rule: “If the form says ‘entering’, then the other side must list ‘cholera’.”
Manipulation
No rationale
Rationale - imagine border guard checking whether people are entering the country or merely in transit. On the other side is the inoculations they’ve had, must have one for cholera.
92% - almost perfect
People are reasoning in terms of pragmatic reasoning schemas - learned rules for dealing with, in this case, permissions or obligations.

Question 18

What is Cosmides Social contracts hypothesis and study (1989)?

Answer 18

Our reasoning abilities have evolved in the context of humans being social
Important aspects of lives as humans is that we enter into social contracts, which are critical to our ability to function in the social world around us.
Very good at detecting violations to these social contracts so we’re good at detecting cheats
Showed that people are good at reasoning if the problem is framed as a cheat detection problem, even in unusual contexts.
Wason Card selection task with the rule “If a man eats cassava root, then he must have a facial tattoo”
Manipulation
control group told that this is a geographical rule regarding southern islanders who have face tattoos and eat a lot of cassava.
Cheat defection group told that it is a social rule where men get face tattoos when they are marries and only married men can eat aphrodisiac cassava
Results
Control: 45%
Cost-benefit: 80%
Accuracy nearly doubles

explanation: its a social exchange problem (cost=marriage; reward = aphrodisiac) which we have evolved to understand easily.
Wason’s tasks are difficult because we don’t have generally applicable logic rules (content independent)
Evolved to be social creatures, an inherent aspect of society is social rules, we therefore are able to automatically notice violations of social contracts
Content dependent circuitry

Crit: more explicit why someone without a face tattoo would not be eating cassava rather than people understanding the idea that only married men should have aphrodisiacs
Just under stand rule better ‘cheat’ aspect is not relevant

Question 19

What is Ermer & Kiehl’s (2010) violating social contracts study

Answer 19

Support for the idea that our mechanisms for reasoning are closely tied to the rational demands of social creatures
Cases where people’s attuning to social contracts breaks down in the absence of other general cognitive problems
Characterisations of psychopathy
Psychopaths are characterised as being intelligent but insensitive to the normal moral standards that bind most of us most of the time to appropriate social behaviours.
If we have these modules/ context dependent circuitry, perhaps they can go wrong (psychopathy)
Gave different forms of reasoning problems and Wason card selection tasks to people who were diagnosed with psychopathic traits in prisons
Psychopathy: intelligent but immoral
Descriptive rules that don’t imply social contracts: If from California, then patient.
Social: If you borrow someone’s car, then you should fill it with petrol before you return it.
Results
Non-psychopathic visitors benefit from social rule versions of the task compared with the descriptive rules
Psychopaths: much smaller benefit of the social rule framing because they are insensitive to social contracts.

Question 20

What are the problems with cheat detection?

Answer 20

Can it explain all successes
If you clear up spilt blood, then you must wear rubber gloves. (Manktelow & Over, 1991)
No obvious cheat detection interpretation
Is it a general account of reasoning?
What about other if-then rules?
Seem to underlie the every day reasoning we engage in / inferring causality
Worry about implications for what it says we can’t reason about
Are people really irrational?