Deductive and inductive reasoning

What is inductive reasoning?

• Drawing general conclusions from particular instances/examples.

• Probably, but not necessarily true

• E.g. extrapolation → all swans i have seen are white, so all swans are white.

What is deductive reasoning?

• Draw definite conclusions if tenets are true

• Based on formal logic

What is informal reasoning?

• ‘Everyday’ reasoning

• Based on relevant knowledge and experience

How do scientists use inductive reasoning in hypothesis testing?

• Generate hypothesis based on limited data

• Falsification of null hypothesis → evidence against hypothesis

• Popper

What is confirmation in hypothesis testing?

Gain evidence confirming hypothesis is correct

Can never fully support hypothesis → no matter how many white swans we may have observed, does not justify that all swans are white.

What is falsification in hypothesis testing?

Gain evidence to falsify hypothesis

Can prove hypothesis is wrong

What is Wason’s 2-4-6 task?

• Given 3 numbers → 2, 4 and 6

• Asked ppts to guess rule that generated these numbers

• Give three further numbers to test your hypothesis

What results have been shown in Wason’s 2-4-6 task?

• 21% correctly guess rule on first attempt

• 28% never guess rule correctly

• Actual rule → 3 numbers in ascending order of magnitude → e.g. 1-10-11

• Show confirmation bias → guess ‘goes up in twos’ → generate sequences conforming to this rule → fail to falsify hypothesis

How does Wason’s 2-4-6 task contribute to inductive reasoning?

Provides insight in inductive reasoning and how scientists reason.

How has Wason’s 2-4-6 task been criticised?

• Not real world → immediate feedback doesn’t often occur in real world, not always fully informative.

• Rule is very general → confirmation testing not appropriate

• Confirmation bias not always present

Do scientists hypothesis test?

• Often, but not always

• Unusualness heuristic → guided by unusual results

• ‘What if’ → hypothesis generation and simulation without experimentation.

What did Fuselgang et al (2004) find in study of molecular biology and experiments where 223/417 results were inconsistent with predictions and falsification?

• 88% inconsistent results blamed on methods rather than treating as falsifications of theory

• 12% modified theories based on discrepant results

• When discrepant findings replicated consistently → 61% change theory.

• Bayesian approach

What is conditional reasoning?

• Symbols stand for sentences (e.g. P= study, Q= good grade)

• Logical operators (e.g. if,and,or) applied to reach conclusions.

• E.g. if you study, you will get good grade → if P then Q

If P then Q, P= true, what is this?

Antecedents

If P then Q, P= true. Therefore Q,what is this?

Consequents

What is binary in conditional reasoning?

Either affirm or refute the consequent based on antecedents

What is Modus ponens in conditional reasoning?

If P then Q → P therefore Q

What is modus tollens?

If P then Q, not Q therefore not P

Which is more commonly refuted, modus ponens or tollens?

Modus tollens

What is denial of the antecedent?

• If P then Q → Not P therefore not Q?

How can denial of the antecedent be applied to studying and good grades (P and Q)?

• If you study hard (P) you will get good grade

• You don’t study hard → unlikely you will get a good grade

• But ‘unlikely’ is probab

How can logic construct false conclusions in conditional reasoning?

• E..g if Sarah is in Rio (P), then she is not in Brazil → Sarah is in Rio, therefore not in Brazil.

• Clearly false, but logically consistent

• Real world knowledge irrelevant in conditional reasoning

What did De Neys (2005) find in a study of conditional reasoning where they varied number of counterexamples → “if the brake is depressed, then the car slows down” then given counterexamples alternatives “e.g. running out of petrol” or disablers “a broken brake”?

• Modus ponens should be correct?

• If ppts exposed to more disablers, tend to decrease acceptance of valid conclusions

• Alternatives increase correct rejection of invalid conclusions → e.g. helps ppts see how wrong consequent is.

• Rely on real world knowledge and saliency in mind.

What did Markovits et al find in study where ppts given two statements both affirming consequent (1) If rock thrown at window, window will break. Window is broken therefore a rock was thrown and (2) If finger is cut, it will bleed. Finger is bleeding, therefore finger was cut. What was seen?

• More likely to accept (2) than (1)

• Real world knowledge → probability of relationship in real world, close 1 to 1 correspondence between P and Q in 2 than 1. Can’t think of many other reasons why finger would be bleeding??

• Generate counterexamples → window broken by bird, hammer, person, etc

What is the Wason selection task?

• Four cards a table: R, G, 2, 7

• Each card has letter on one side, number on the other

• Decide if this rule is correct → If R on one side, then 2 on the other

• Only turn over cards needed

What results are seen in Wason selection task?

• Only 5-10% choose correctly

• Perhaps because they use simple strategies (e.g. matching bias) or don’t understand rules (i.e. assume 1-to-1 correspondence between P and Q).

What is informal reasoning?

• Reasoning typically found in everyday life

• Based on knowledge and experience

• Probabilistic (80% chance in being correct)

• E.g. drug is safe because we have found no evidence it’s not vs ghosts exist because no one has proved they do not → many say 1 more likely than 2 despite identical logic.

What is the straw man fallacy?

• Focus on weaker points of opponent’s arguments to decrease probability of their view being correct.

• Your argument becomes relatively more probable.

What is myside bias in informal reasoning?

People evaluate statements with respect to one’s own beliefs

What did Stanovich and West find in a study of motivation and informal reasoning where ppts given two sentences: 1. college students who drink alcohol while in college are more likely to become alcoholic in later life and 2. the gap in slaary between men and women decreases substantially when they are employed in same position?

• Students who drank alcohol rate accuracy of 1 lower than those who didn’t drink alcohol

• Women rated accuracy of 2 lower than men.

What did Kahan et al find in study of climate change and informal reasoning?

• Big predictor of denial of climate change was cultural values

• Egalitarian communitarians vs hierarchal individualists

What did Howe and Leiserowitz find in study of climate change, informal reasoning and experiences of summer?

Those who were dismissive of climate change remembered previous (very hot) summer as colder than those concerned about climate change.

What is bounded rationality?

• Idea that we are rational, within limits of our cognitive capacity

• We produce workable solutions to real world problems in spite of limited processing resources.

• Hence correlation between performance in reasoning tasks and IQ, more processing capacity = better at reasoning.