Reasoning Flashcards
(26 cards)
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
