Reasoning Flashcards
inductive reasoning
involves drawing general conclusions from particular instances - conclusions are not necessarily true
e.g.,
- Sarah has fallen asleep in all lectures so far
- therefore Sarah will always fall asleep in lectures
deductive reasoning
draw conclusions which follow necessarily from the premises - if we accept that the premises are true, and if the argument follows the rules of logic then the conclusion has to be true,
e.g.,
- sarah always falls asleep in lectures
- sarah is in a lecture
- therefore, sarah will fall asleep
syllogisms
typically comprise 2 premises and a conclusions, and involve the quantifiers: all, no, some, and some … not
e.g.,
all lecturer have good social skills
george is a lecturer
george has impeccable social skills
syllogisms can be valid or invalid - above is valid
a valid argument
valid argument:
- if one accepts the truth of the premises, then the conclusion is also true
- one might not accept. the premises but that does not change the validity
atmosphere theory (syllogistic r)
- the mood of the premises influences judgements about what the mood of the conclusion should be
- “mood” meand whether the statement is affirmative or negative, and whether it is universal or particular
Begg and Denny (1969) - atmosphere theory study
task:
- gave participants 64 reasoining problems comprising 2 premises and a choice of 4 conclusions
- participants indicated which if any of the 4 conclusions followed from the premises
- 19/64 had a valid solution among the 4 options presented
- focussed on responses for the other 45
results:
- when both premises where positive, 79% of conclusions were positive
- when at least one premise was negative, 73% of chosen conclusions were negative
- when both premises were universal, 77% of chosen conclusions were universal
- when at least one premise was particular, 90% of conclusions were particular
interpretation of the terms (syllogistic r)
errors partly reflect differences between the use of language in formal logic and in everyday life
- can easily change ‘perceived’ validity
e.g., in logic “some” can mean all, while in everyday language “some” typically cannot mean all
syllogistic reasoning and language study block- Beraso and Provitera, 1971
task:
- presented wooden blocks and had people reason about their properties
- people given syllogisms suchas : all blocks with holes are red, all blocks with holes are triangular
results:
- only 1/40 people correctly identified “some red blocks are trianglular)
- when more explicit instructions laid out 27/40 got the correct answer
mental models framework
reasoning involves 3 stages:
- comprehension: use language and background knowledge to construct a mental model of the state of the world that is implied by the premises
- description: combine the models implied by the premises in to a composite, and use this to try to draw a conclusion that goes beyond re-iterating the premises
- validation: search for alternative models. If all of these are consistent with the inital conclusion, it is judged valid. If 1 or more of the new models contradict it, reject it and try to construct a valid alternative
- the more alternative models are considered, the more likley one is to draw the correct conclusion
- requires more effort
mental model example
all psychologists are comedians
all comedians are psychopaths
what follows?
model of first premise: each row representing a conjuction of items
psychologist comedian
psychologist comedian
model of second p:
comedian psychopath
comedian psychopath
next model:
psychologist. comedian. psychopath
one-model syllogism, other multiple-model syllogisms are more challenging
mental models study: Copeland and Radvansky, 2004
1 model - 87% correct, 25 s
2 model - 40% correct, 29 s
3 model - 34% correct, 33 s
more models = less accurate and slower
higher working memory = faster and more accuract
not direct evidence for model construction/validation
framing and experience - syllogistic reasoning
syllogistic reasoning is affecteed by the framing of problem and participants prior experiences
Evans et al. (1983)
- gave people valid and invalid syllogisms with believalbe and unbelieable conclusions.
- plausibility increased the judged validity of both valid and invalid statements
belief bias
the selective scrutiny hypothesis
- a heuristic approach to reasoning
- posits that people initially evaluate the plausibility of the conclusion.
- if it is reasonable they accept it without engaging in actual reasoning
- scrutiny of the logical connection only arises when the conclusion is unbelievable
however, we have seen people reject plausible arguments - evans et al., 1983
the misinterpreted necessity hypothesis
- people dont know how to respond when a conclusion is possible but not logically necessary
- in such cases they may use believability to make their decision
however, belief influences acceptance even when conclusions are deductively valid - not limited to indeterminate uncertainty
Klauer et al. 2000, framework on framing and experience
- people typically generate just 1 mental model because of capacity limits
- if the conclusion is believable, people attempt to construct a model that is consistent with this claim
- if the conclusion is unbelievable, they attempt to construct a model which refutes this claim
- when the attempt to contruct the “desired” model fails, the participant is in a state of uncertainty and will be somewhat swayed by their belief about the base-rate probability that the conclusion is valid
propositional reasoning
involves reasoning about propositions containing the conditionals: if, and, not, and or
e.g., if it is raining then I take the bus
modus ponens (MP)
e.g., if it is raining then I take the bus
- it is raining, conclude I took the bus
- valid
97%
denial of the antecedent (DA)
e.g., if it is raining then I take the bus
- it is not raining, conclude I did not take the bus
- error
- 56%
affirmation of the consequent (AC)
e.g., if it is raining then I take the bus
- if took the bus. conclude it is raining
- fallacy
- 64%
modus tollens (MT)
e.g., if it is raining then I take the bus
- I did not take the bus. conclude it is not raining
- valid
- 74.2%
four card selection task - Wason, 1968
cards : D K 3 7
“if there is a D on one side of any card then there is a 3 on its other side”
D = P, K = not P
3 = Q, 7 = not Q
correct answers D and 7 to check
- 1/34 chose this
initially attributed to condirmation bias - idea shown to be inadequate
propositional reasoning - heuristics
Evans and Lynch, 1973
Simply choosing items that are explicity mentioned in the problem statement - A “matching heuristic” - might be one simplifying strategy when faced with this kind of task
propositional reasoning - interpretation of terms
errors may reflect participants interpretation of the terms
Gebauer and Laming, 1997:
- the common selection of P and Q results from a pattern of understanding
- under the interpretation of “if” the participant would beed to turn over all 4 cards - or just the “p” and “q” cards if they think the rule applies to the visible faces of the cards
propositional reasoning - framing and experience
- easier to recognise rules in thematic versions, memory cuing
deontic reasoning: reasoning about obligations and permissilbe behaviours
cheater detection
familiarity cannot be whole explanation for superior performance in modified versions, as we see improvements with rules that are completely novel
Cosmides, 1989
- selection task that involved a fictional tribe
- 4 card selection
- task to see if rule is being broken
- when rules were framed as a social contract correct choices increased
conclusion: humans have an evolved sensitivity to violations of soicla contracts, which can be thought of as : “if u take benefit, u pay cost”
flawed:
- we see performance in areas that do not include social contracts, or cannot be described as one (no benefit, just action)
relevance and utility - propositional reasoining
Girotto et al, 2001
- the perceived relevance/ value of the ooptions has effect rather than the detection of rule-violations
