Rationality Flashcards
What is formal logic?
drawing a set of rules for being able to draw valid conclusions. Fundamentally deals with certainty because you can know for sure if something follows.
What is probability theory?
sets of rules for judging likelihood. Deals with uncertainty.
What is Chater & Oaksford’s (1990) everyday reasoning thought experiment?
Able to give contrasting explanations in terms of logic or probability of human reasoning.
Logic or probability?
If I see Fred go past at 9am, then he’s off to buy his morning paper.
What do I conclude?
Logical terms: MP if p- then q
P is true, so q
Probabilistic: conditional probability, given p, q is probable
Maybe more reasonable to think about this thought process in terms of probability
Unlike logic conclusions can be changed based on other information
Likely BUT if other information is known, wouldn’t draw the same conclusion
What are the correct answers to the Wason’s card sorting task according to the probabilistic approach?
Turning over P.
Turning over the q card is an informative selection in the context of probability theory
What is Chater and Oaksford’s (1999) Informative selections thought experiment?
The rule: “If p (a pot falls in the kitchen), then q (there will be a clang)”
logic says that in order to prove this must turn over p and not-q cards
in real life this translates to observing pots fall and hearing clangs and checking to make sure no pot has fallen and not made a clang, every time there is no clang.
Ecologically invalid, waste of resources and deeply impractical in an ever changing world.
Probability theory says that every time the two relatively rare events of a pot falling and a clang sound coincide our belief that pots falling cause clangs increases. Thus it provides useful positive evidence that the two things are related.
(Could be modelled in terms of prediction and reward)
What is Oaksford & Chater’s (1994) Information gain hypothesis?
use bayes theorum as a model for belief updating where
P(hypothesis | data) = P(hypotheseis) * P(data | hypothesis) / P(data)
so that P(hypothesis | data) > P(hypotheseis)
if P(data | hypothesis) / P(data) > 1
it follows that a pot is much more likely to have fallen if a clang is heard given the pot falling causes the clang
ultimately explains why people choose the cards they do
What does Oaksford and Chater’s (1994) Optimal data selection model show?
Apply Bayes theorem to quantify how much information would you expect to gain by turning over each of the cards in Wason’s card selection task
Standardised measure
Observing two rare events together tells you that they’re probably related
Most informative: p card
Q card is more likely to be informative than turning over the not-q card.
Closely maps the selections people tend to make
Optimal data selection theory of what people are doing in the Wason’s card task
what criticisms are there of probability theory?
What about people who P & not-q
Is the ‘rarity assumption ‘ true
People are bad at probabilities too
What is the issue of monotonicity?
Logic is monotonic - no further information will change the conclusion
Problematic in the real world.
Our real life conclusions are never monotonic which is inconsistent with logic
Non-monotonic reasoning is natural and evident from a young age.
allows us to predict different outcomes given different combinations of information
what are the limitaitons of logic Oaksford & Chater (1991)?
Conclusions never deductively true?
New info can defeat old conclusion
Need to make many assumptions to reach any particular conclusion
Real-world knowledge in reasoning
General rules are not enough to allow us to draw sensible conclusions
Reasoning is adapted to an uncertain world
If we take reasoning in this context, Formal logic is the wrong natural theory because in the real world things are usually true but never definite, there are frequently exceptions to rules but it is fundamental to our survival that we are able to interact with the world despite irregularities and focus on the overarching principles
‘Constant conjunction’ - never observe causality
The right framework is probability theory
Why people fail - they don’t reason logically, they reason probabilistically.
