Reasoning Flashcards
People may solve reasoning problems by using _____ rather than engaging actual reasoning processes
Simple heuristics (rules of thumb)
True or False?
People always solve reasoning problems by
engaging actual reasoning processes
False
People may solve reasoning problems by using simple heuristics (rules of thumb) rather than engaging actual reasoning processes
Why do people often make reasoning ‘errors’?
Because the use of language in formal logic differs from that of everyday life
True or False?
People often make “errors” because the use of language in formal logic differs from that of everyday life
True
Which framework provides an example of an algorithmic description of the
steps by which people reason?
The “Mental Models” framework
What is the ‘Mental Models” framework?
A framework which provides an example of an algorithmic description of the steps by which people reason
What are responses in reasoning tasks highly sensitive to?
List 2 things
- The framing of the task
- The participant’s background beliefs
The framing of the task and the participant’s background beliefs affects…?
Responses in reasoning tasks
What are the 2 types of reasoning?
- Inductive
- Deductive
What is inductive reasoning?
Reasoning that involves drawing general conclusions from particular instances
Reasoning that involves drawing general conclusions from particular instances
This is known as…?
Inductive reasoning
Sarah has fallen asleep in all Psychology lectures so far
Therefore, Sarah will always fall asleep in Psychology lectures
This is an example of…?
a.Deductive reasoning
b. Inductive reasoning
b. Inductive reasoning
Sarah always falls asleep in Psychology lectures
Sarah is in a Psychology lecture
Therefore, Sarah will fall asleep
This is an example of…?
a.Deductive reasoning
b. Inductive reasoning
a.Deductive reasoning
What is deductive reasoning?
Reasoning that involves drawing conclusions which follow necessarily from the premises
Reasoning that involves drawing conclusions which follow necessarily from the premises
This is known as…?
Deductive reasoning
What is the main problem about inductive reasoning?
The conclusions are not necessarily true
e.g. Sarah has fallen asleep in all Psychology lectures so far
Therefore, Sarah will always fall asleep in Psychology lectures
There is always the possibility that the next Psychology lecture will manage to hold your attention throughout.
The conclusions are not necessarily true
This applies to..?
a.Deductive reasoning
b. Inductive reasoning
b. Inductive reasoning
If we accept that the premises are true, and if the argument follows the rules of logic, then the conclusion has to be true, too
This applies to..?
a. Deductive reasoning
b. Inductive reasoning
a. Deductive reasoning
What are the 2 types of deductive reasoning?
- Propositional reasoning
- Syllogisms
- Propositional reasoning
- Syllogisms
These are the two types of ____ reasoning
a. Deductive reasoning
b. Inductive reasoning
a. Deductive reasoning
What are the 4 approaches to reasoning?
- Identifying simplifying strategies
- Interpretation of terms
- Process models
- Effects of framing and experience
What are syllogisms?
Comprised of two premises and a conclusion, and involve the quantifiers all, none, some, and some…not
Comprised of two premises and a conclusion, and involve the quantifiers all, none, some, and some…not
This is known as…?
Syllogisms
First premise: Relationship between A and B
Second premise: Relationship between B and C
Conclude something about: Relationship between A and C
This is an example of…?
Syllogisms
When presented with:
First premise: Relationship between A and B
Second premise: Relationship between B and C
What will we conclude, based on Syllogisms?
The relationship between A and C
ALL Psychologists (A) are Comedians (B)
ALL Comedians (B) are Tap-Dancers (C)
What can we conclude?
ALL Psychologists (A) are Tap-dancers (C)
This is an example of…?
Syllogisms
When presented with:
ALL Psychologists (A) are Comedians (B)
ALL Comedians (B) are Tap-Dancers (C)
What can we conclude?
What will we conclude, based on Syllogisms?
ALL Psychologists (A) are Tap-dancers (C)
When presented with:
ALL Psychologists (A) are Comedians (B)
ALL Comedians (B) are Tap-Dancers (C)
What can we conclude?
How many people predict ALL Psychologists (A) are Tap-dancers (C)?
88%
Such arguments in syllogisms may be valid or invalid
Validity is determined by …?
The structure of the argument
The relations between the premises and the conclusion
In syllogisms, what is determined by the structure of the argument/ the relations between the premises and the conclusion?
Validity or arguement
True or False?
A valid argument is one where, if one accepts the truth of the premises, then the conclusion is also true
True
ALL Psychologists (B) are Poets (A)
ALL Psychologists (B) are Acrobats (C)
What can we conclude?
SOME Poets (A) are Acrobats (C)
This is an example of…?
Syllogisms
When presented with:
ALL Psychologists (B) are Poets (A)
ALL Psychologists (B) are Acrobats (C)
What is the right conclusion?
SOME Poets (A) are Acrobats (C)
When presented with:
ALL Psychologists (B) are Poets (A)
ALL Psychologists (B) are Acrobats (C)
How many people concluded that SOME Poets (A) are Acrobats (C)?
8%
True or False?
Roberts and Sykes (2005) found that problems of the form: “all a are b; all b are c; what follows?” were correctly solved by 8% of participants (valid conclusion: “all a are c”).
However, given a problem of the form: “all b are a; all b are c; what follows?” 88% of participants correctly concluded that “some a are c” (or, equivalently, that “some c are a”).
False
Roberts and Sykes (2005) found that problems of the form: “all a are b; all b are c; what follows?” were correctly solved by 88% of participants (valid conclusion: “all a are c”).
However, given a problem of the form: “all b are a; all b are c; what follows?” only 8% of participants correctly concluded that “some a are c” (or, equivalently, that “some c are a”).
Who found that problems of the form: “all a are b; all b are c; what follows?” were correctly solved by 88% of participants and problems of the form: “all b are a; all b are c; what follows?” only 8% of participants correctly concluded that “some a are c”?
Roberts and Sykes (2005)
What does the atmosphere theory propose?
The mood of the premises influences judgments about what the mood of the conclusion should be
The mood of the premises influences judgments about what the mood of the conclusion should be
Which theory proposes this?
Atmosphere theory
What does “mood” mean in the atmosphere theory?
Whether the statement is affirmative or negative, and whether it is universal or particular
(E.g., “all…” is universal and affirmative, whereas “some are not…” is particular and negative).
Whether the statement is affirmative or negative, and whether it is universal or particular
(E.g., “all…” is universal and affirmative, whereas “some are not…” is particular and negative).
This is known as…?
“Mood”
How do we solve reasoning tasks using heuristics?
By referring to the “atmosphere” (quality and quantity) of premises shapes
conclusions
By referring to the “atmosphere” (quality and quantity) of premises shapes
conclusions
Which approach to solving reasoning tasks is this?
Heuristics (identifying simplifying strategies)
In heuristics, what does universal and affirmative mean?
All
In heuristics, what does particular and negative mean?
Some … Not
In heuristics, what does universal and negative mean?
No(t)
In heuristics, what does particular and affirmative mean?
Some
Some
a. particular and affirmative
b. particular and negative
c. universal and affirmative
d. universal and negative
a. particular and affirmative
All
a. particular and affirmative
b. particular and negative
c. universal and affirmative
d. universal and negative
c. universal and affirmative
Some…Not
a. particular and affirmative
b. particular and negative
c. universal and affirmative
d. universal and negative
b. particular and negative
No(t)
a. particular and affirmative
b. particular and negative
c. universal and affirmative
d. universal and negative
d. universal and negative
Describe Begg and Denny’s study on heuristics
Ps were given 64 reasoning problems comprising two premises and a choice of four conclusions.
e.g.
All a are b
All b are c
Choose one conclusion:
a. All c are a
b. Some c are a
c. No c are a
d. Some c are not a
There were 45 problems with “no valid conclusion”
In Begg & Denny’s (1969) study:
Ps were given 64 reasoning problems comprising two premises and a choice of four conclusions.
e.g.
All a are b
All b are c
Choose one conclusion:
a. All c are a
b. Some c are a
c. No c are a
d. Some c are not a
There were 45 problems with “no valid conclusion” so Ps who chose any of the four options constituted an error
What were the results when both premises were affirmative?
79% chose affirmative
In Begg & Denny’s (1969) study:
Ps were given 64 reasoning problems comprising two premises and a choice of four conclusions.
e.g.
All a are b
All b are c
Choose one conclusion:
a. All c are a
b. Some c are a
c. No c are a
d. Some c are not a
There were 45 problems with “no valid conclusion” so Ps who chose any of the four options constituted an error
What were the results when one premise was negative and one was affirmative?
73% chose negative
In Begg & Denny’s (1969) study:
Ps were given 64 reasoning problems comprising two premises and a choice of four conclusions.
e.g.
All a are b
All b are c
Choose one conclusion:
a. All c are a
b. Some c are a
c. No c are a
d. Some c are not a
There were 45 problems with “no valid conclusion” so Ps who chose any of the four options constituted an error
What were the results when both premises were universal?
77% chose universal
In Begg & Denny’s (1969) study:
Ps were given 64 reasoning problems comprising two premises and a choice of four conclusions.
e.g.
All a are b
All b are c
Choose one conclusion:
a. All c are a
b. Some c are a
c. No c are a
d. Some c are not a
There were 45 problems with “no valid conclusion” so Ps who chose any of the four options constituted an error
What were the results when one premise was particular?
90% chose particular
True or False?
The “atmosphere” (quality and quantity) of the premises does not shape beliefs about the validity of different possible conclusions
False
The “atmosphere” (quality and quantity) of the premises shapes beliefs about the validity of different possible conclusions
In Begg and Denny’s (1969) study, what % of the time do Ps correctly identify that there is no valid inference?
29 - 40% of the time
Focus on interpretation of the terms
Which approach to reasoning is this?
Comprehension
“Errors” in syllogistic reasoning partly reflect differences between …?
The use of language in formal logic and in everyday life
Differences between the use of language in formal logic and in everyday life affect…?
“Errors” in syllogistic reasoning
How do we reduce “error” rates in reasoning tasks?
By clarifying premises
“All A are B…”
“Some A are B”
vs.
“All A are B, and vice-versa” “Some, but not all, A are B”
This is an example of how _____ affects reasoning
Comprehension
“All A are B…”
“All B are C”
What is the valid conclusion?
All A are C
“All A are B…”
“All C are B”
What is the invalid conclusion?
All A are C
Describe Ceraso and Provitera’s (1971) study on how comprehension affects reasoning
List 5 points
- Ps were presented with wooden blocks and had to reason about their properties
- In the “traditional” version of the task, people were given syllogisms such as:
All blocks with holes are red
All blocks with holes are triangular
- Ps had to identify the valid conclusion: “Some red blocks are triangular”
- In a modified version of the task, Ps were given more explicit instructions about the interpretation of the premises, such as:
Whenever I have a block with a hole it is red, but not all red blocks have holes
Whenever I have a block with a hole it is triangular, but not all triangular blocks have holes
- Ps had to identify the valid conclusion: “Some red blocks are triangular”
In Ceraso and Provitera’s (1971) study:
- Ps were presented with wooden blocks and had to reason about their properties
- In the “traditional” version of the task, people were given syllogisms such as:
All blocks with holes are red
All blocks with holes are triangular
- Ps had to identify the valid conclusion: “Some red blocks are triangular”
- In a modified version of the task, Ps were given more explicit instructions about the interpretation of the premises, such as:
Whenever I have a block with a hole it is red, but not all red blocks have holes
Whenever I have a block with a hole it is triangular, but not all triangular blocks have holes
- Ps had to identify the valid conclusion: “Some red blocks are triangular”
What were the results of the study? List 4 points
- In the “traditional” version of the task, only 1 out of 40 Ps correctly identified “Some red blocks are triangular”
- More than half said “All red blocks are triangular”, which is what we’d expect if they take “All A are B” to imply “All B are A”
- In a modified version of the task, 27 out of 40 Ps correctly responded “Some red blocks are triangular”
- Across a number of such problems, people scored an average of 58% correct with the traditional format but 94% correct with the modified versions.
What did Ceraso and Provitera (1971) argue about syllogistic reasoning errors?
These errors arise because people don’t properly
apprehend the premises in the way that the experimenter intends
However, it is unlikely that
premise misapprehension accounts for the full spectrum of performance on this kind of task
Who developed the Mental Models framework?
Philip Johnson-Laird
What framework did Philip Johnson-Laird develop?
The Mental Models framework
What is step 1 of the Mental Models framework?
Construct a mental model of world implied by premises
What is step 2 of the Mental Models framework?
Make a composite model and draw a conclusion
What is step 3 of the Mental Models framework?
Validate by searching for alternative models and checking they don’t contradict the conclusion
Which step of the Mental Models framework does this apply to?
a. Step 1
b. Step 2
c. Step 3
Make a composite model and draw a conclusion
b. Step 2
Which step of the Mental Models framework does this apply to?
a. Step 1
b. Step 2
c. Step 3
Validate by searching for alternative models and checking they don’t contradict the conclusion
c. Step 3
Which step of the Mental Models framework does this apply to?
a. Step 1
b. Step 2
c. Step 3
Construct a mental model of world implied by premises
a. Step 1
Which framework posits a sequence of processing steps?
The ‘mental models’ framework
The steps you take in your head to solve reasoning problems is known as…?
The ‘mental models’ framework
How many stages are there in the ‘mental models’ framework?
3 stages
When presented with these premises:
All Psychologists are comedians
All Comedians Are psychopaths
What happens in step 1 of the ‘mental models’ framework?
We construct a mental model of world implied by remises
e.g.
Psychologist Comedian
Psychologist Comedian
Comedian Psychopath
Comedian Psychopath
When presented with these premises:
All Psychologists are comedians
All Comedians Are psychopaths
What happens in step 2 of the ‘mental models’ framework?
We make a composite model and draw a conclusion
e.g.
Composite: Psychologist = Comedian = Psychopath
Conclusion:
All psychologists are psychopaths
When presented with these premises:
All Psychologists are comedians
All Comedians Are psychopaths
What happens in step 3 of the ‘mental models’ framework?
We validate by searching for alternative models and checking they don’t contradict the conclusion
e.g.
Conclusion: All psychologists are psychopaths
In this case there are no other models consistent with the premises, so accept the conclusion
Comprehension, Description and Validation are the 3 steps included in…?
The ‘mental models’ framework
What is the comprehension step of the ‘mental models’ framework?
Using language and background knowledge to construct a mental model of
the state of the world that is implied by the premises
What is the description step of the ‘mental models’ framework?
Combining the models implied by the premises into a composite, and use this to try to draw a conclusion that goes beyond re-iterating the premises.
What is the validation step of the ‘mental models’ framework?
Searching for alternative models
If all of these are consistent with the initial conclusion, it is judged valid
If one or more of the new models contradict the conclusion, reject it and try to construct an alternative which can then be validated
Conclusion: All psychologists are psychopaths
In this case there are no other models consistent with the premises, so accept the conclusion
Which step of the ‘mental models’ framework is this?
a. Comprehension/ step 1
b. Description/ step 2
c. Validation/ step 3
c. Validation/ step 3
Composite: Psychologist = Comedian = Psychopath
Conclusion:
All psychologists are psychopaths
Which step of the ‘mental models’ framework is this?
a. Comprehension/ step 1
b. Description/ step 2
c. Validation/ step 3
b. Description/ step 2
Mental Model:
Psychologist Comedian
Psychologist Comedian
Comedian Psychopath
Comedian Psychopath
Which step of the ‘mental models’ framework is this?
a. Comprehension/ step 1
b. Description/ step 2
c. Validation/ step 3
a. Comprehension/ step 1
True or False?
One-model syllogism should be relatively easy to solve
True
Why is one-model syllogism relatively easy to solve?
Because there is only one model that is consistent with the premises
Why are multiple-model syllogisms more challenging to solve?
Because there are several possible ways of combining the information in the premises
How do we solve multiple-model syllogisms using the ‘Mental Models’ framework?
e.g. Premises
No Artists are Bakers
All Bakers are Candlestick-makers
List 3 points
- We propose Model 1
Which would lead to the preliminary conclusion that “No Artists are Candlemakers” (or that “No Candlemakers are Artists”).
However, searching for alternative models during the validation step reveals that a second model is possible
- We propose Model 2
This model acknowledges the possibility of an artist-candlemaker, which refutes the initial conclusion.
A new conclusion, consistent with both of the models, is that “Some Artists are not Candlemakers”
However, a third model can also be constructed
- We propose Model 3
Again, this refutes the previous conclusion
The only conclusion that is consistent with all three mental models is that “Some Candlemakers are not Artists”
The more alternative models are considered, the ____ likely one is to draw the correct conclusion
a. More
b. Less
a. More
The more alternative models are considered, the more likely one is to …?
Draw the correct conclusion
People are more likely to draw the correct conclusion when …?
Alternative models are considered
True or False?
Considering alternative models requires more time, effort, and mental capacity
True
True or False?
If a reasoner fails to consider all of the alternative models, they are more likely to draw the correct inference – so multiple model syllogisms will be easier than single-model ones
False
If a reasoner fails to consider all of the alternative models, they are less likely to draw the correct inference – so multiple model syllogisms will be harder than single-model ones
Why do multiple-model syllogisms take longer to solve?
Because considering more models will require more time, effort, and processing-capacity
People with greater working memory, or those with more time/inclination to work on the task, will do better in…?
a. Multiple model syllogisms
b. Single-model syllogisms
a. Multiple model syllogisms
Who is better at multiple model syllogisms?
People with greater working memory, or those with more time/inclination to work on the task
What did Copeland and Radvansky (2004) do in their study on mental models?
List 3 points
- Ps completed a working memory span assessment
- Ps were presented with syllogisms:
“All cyclists are coffee drinkers
“All coffee drinkers are surgeons”
- Ps were presented with all 9 possible conclusions
(the 8 combinations of the two end terms “Cyclists” and “Surgeons” with the four quantifiers “All”, “None”, “Some” and “Some…not”, plus the option “no valid conclusion”)
In Copeland and Radvansky’s (2004) study:
- Ps completed a working memory span assessment
- Ps were presented with syllogisms:
“All cyclists are coffee drinkers
“All coffee drinkers are surgeons”
- Ps were presented with all 9 possible conclusions
(the 8 combinations of the two end terms “Cyclists” and “Surgeons” with the four quantifiers “All”, “None”, “Some” and “Some…not”, plus the option “no valid conclusion”)
What were the results of the study when there was only one-model?
87% of Ps got the correct conclusion
The average response times were 25 seconds
In Copeland and Radvansky’s (2004) study:
- Ps completed a working memory span assessment
- Ps were presented with syllogisms:
“All cyclists are coffee drinkers
“All coffee drinkers are surgeons”
- Ps were presented with all 9 possible conclusions
(the 8 combinations of the two end terms “Cyclists” and “Surgeons” with the four quantifiers “All”, “None”, “Some” and “Some…not”, plus the option “no valid conclusion”)
What were the results of the study when there were two-models?
40% of Ps got the correct conclusion
The average response times were 29 seconds
In Copeland and Radvansky’s (2004) study:
- Ps completed a working memory span assessment
- Ps were presented with syllogisms:
“All cyclists are coffee drinkers
“All coffee drinkers are surgeons”
- Ps were presented with all 9 possible conclusions
(the 8 combinations of the two end terms “Cyclists” and “Surgeons” with the four quantifiers “All”, “None”, “Some” and “Some…not”, plus the option “no valid conclusion”)
What were the results of the study when there were three-model?
34% of Ps got the correct conclusion
The average response times were 33 seconds
What did Copeland and Radvansky (2004) conclude about multiple models in their ‘mental models’ study?
When there are more possible models, conclusions are less accurate and the response times are slower
What did Copeland and Radvansky (2004) conclude about working memory in their ‘mental models’ study?
People with higher working memory are faster and more accurate at reasoning tasks, regardless of how many models there are
When there are more possible models, conclusions are ______ and the response times are ________
a. More accurate, Faster
b. More accurate, Slower
c. Less accurate, Faster
d. Less accurate, Slower
d. Less accurate, Slower
People with higher working memory are _____ and _____ at reasoning tasks, regardless of how many models there are
a. Faster, More accurate
b. Faster, Less accurate
c. Slower, More accurate
d. Slower, Less accurate
a. Faster, More accurate
People with higher working memory are faster and more accurate at reasoning tasks, regardless of how many models there are
What is one problem about Copeland and Radvansky’s (2004) conclusion?
It is not direct evidence for model construction/validation
True or False?
Problems with more possible mental models were solved more accurately, consistent with people sucessfully considering all of the possible states implied by the premises
False
Problems with more possible mental models were solved less accurately, consistent with people failing to consider all of the possible states implied by the premises
True or False?
Problems with more possible models were solved progressively more slowly, consistent with it taking time to construct each model and check the validity of preliminary conclusions
True
True or False?
Ps with higher working memory span were more accurate and faster at the
reasoning tasks, particularly for more complex syllogisms, consistent with model construction being a resource-intensive activity
True
Analysis of the response choices showed that they were better predicted by ______ than by _______
Better predicted by the mental models theory than by simple heuristics such as the “atmosphere” approach
Model construction is a ____ and ____ demanding activity
Time and Resource