Deductive and inductive reasoning

What is the key difference between Inductive Reasoning and Deductive Reasoning?

Inductive Reasoning involves drawing general conclusions from particular instances, which are probably, but not necessarily true. Deductive Reasoning involves drawing definite conclusions if the initial tenets are true, and is based on formal logic

Describe Inductive Reasoning and give an example?

Inductive Reasoning is drawing general conclusions from particular instances or examples. These conclusions are probably, but not definitely, true. An example given is: "All swans I have seen are white, so all swans are white"

How do scientists use inductive reasoning?

Scientists use inductive reasoning for hypothesis testing, where they generate a hypothesis based on limited data. Most science is thought to be 'Popperian', focusing on falsification of the null hypothesis

In hypothesis testing, what is the difference between Confirmation and Falsification?

Confirmation involves gaining evidence confirming a hypothesis is correct9. Falsification involves gaining evidence to prove a hypothesis is wrong. Confirmation can never fully support a hypothesis, but falsification can prove a hypothesis is wrong

Describe Wason's 2-4-6 task.

Participants are given three numbers, 2-4-69. They must guess the rule that generated these numbers (generate a hypothesis) and then give three further numbers to test their hypothesis

What were the typical results of Wason's 2-4-6 task?

Only 21% correctly guess the rule on the first attempt. Worryingly, 28% never guess the rule correctly

What was the actual rule for Wason's 2-4-6 task?

The actual rule was simply "three numbers in ascending order of magnitude"

What is Confirmation Bias, as illustrated by Wason's 2-4-6 task?

Confirmation bias is the tendency to guess a rule (e.g., "goes up in twos") and then generate sequences that conform to this rule, thereby failing to falsify the hypothesis

What are some limitations or critiques of Wason's 2-4-6 task?

It is "not real world". Immediate feedback doesn't often occur in the real world, and feedback in the real world is often not fully informative. The rule was very general, making confirmation testing inappropriate. Confirmation bias is not always present in real-world hypothesis testing

Do scientists always use formal hypothesis testing?

No, they often do, but not always. They may sometimes be guided by an "unusualness heuristic" or use "What if" hypothesis generation and simulation without experimentation

Summarize the findings of Fuselgang et al. (2004) regarding how molecular biologists dealt with results inconsistent with predictions.

In a study, molecular biologists had many results (223 out of 417) inconsistent with predictions. They blamed 88% of these inconsistent results on methods. Only 12% modified their theories based on these discrepant results

According to Fuselgang et al. (2004), when were scientists more likely to change their theories?

When discrepant findings were replicated, 61% of scientists changed their theory. The source notes this might be a sensible strategy if they had a strong prior belief in the previous theory (Bayesian perspective)

What is Conditional Reasoning?

Conditional reasoning is a type of deductive reasoning that uses symbols to stand for sentences (e.g., P, Q) and applies logical operators (e.g., if, and, or) to reach conclusions. It typically follows an "If P then Q" structure

What are the components of a conditional reasoning argument?

The initial statements are the antecedents (or premises) (e.g., If P then Q, and P is true). The result is the consequent (or conclusion) (e.g., Therefore Q). Conditional reasoning is considered binary; you either affirm or refute the consequent based on the antecedents

Describe the Modus Ponens form of conditional reasoning.

Modus Ponens is a valid form: If P then Q, and P is true, therefore Q

Describe the Modus Tollens form of conditional reasoning.

Modus Tollens is a valid form: If P then Q, and Q is not true, therefore not P. The source notes that people tend to refute Modus Tollens more often than Modus Ponens

Describe the Affirming the Consequent fallacy.

Affirming the Consequent is an invalid form: If P then Q, and Q is true, therefore P?. This is a common error people make.

Describe the Denial of the Antecedent fallacy.

Denial of the Antecedent is an invalid form: If P then Q, and P is not true, therefore not Q?

How does Denial of the Antecedent relate to real-world reasoning versus formal logic?

The Denial of the Antecedent often feels appropriate in the real world. For example, "If you study hard (P) you will get a good grade (Q) - You don't study hard - unlikely you will get a good grade". However, this is probabilistic in the real world, whereas formal logic is binary

Can formal logic produce false conclusions?

Yes, logic can construct false conclusions if the initial premises are false, even if the logical structure is consistent. The example given is: "If Sarah in Rio (P), then she is not in Brazil – Sarah is in Rio therefore not in Brazil". In formal conditional reasoning, real-world knowledge is irrelevant

What did De Neys (2005) investigate regarding counterexamples in conditional reasoning?

De Neys varied the number of counterexamples presented, which logically should be ignored in formal reasoning. He distinguished between Alternatives (other ways the consequent could happen, e.g., running out of petrol instead of applying the brake) and Disablers (factors that prevent the consequent from happening despite the antecedent being true, e.g., a broken brake)

What were De Neys' (2005) findings regarding the effect of counterexamples on conditional reasoning acceptance?

Disablers decreased acceptance of valid Modus Ponens conclusions. Alternatives increased correct rejection of invalid Affirming the Consequent conclusions

Describe the task used by Markovits et al. (2013) to study conditional reasoning.

Participants evaluated the validity of two arguments with the same invalid structure (affirming the consequent). Example 1: "If a rock is thrown at a window, the window will break. A window is broken, therefore a rock was thrown." Example 2: "If a finger is cut, it will bleed. A finger is bleeding, therefore the finger was cut"

What was the key finding of Markovits et al. (2013)?

Participants were more likely to accept the invalid conclusion in argument (2) (finger/bleed) than in argument (1) (rock/window)

What were the proposed reasons for the difference in acceptance in Markovits et al.'s (2013) study?

Reasons include the perceived probability of the relationship in the real world (closer 1-to-1 correspondence between P and Q in the finger/bleed example). It might also relate to the ability to generate counterexamples (easier to think of other ways a window could break than a finger could bleed without being cut)

What does the source conclude about human ability in conditional reasoning based on these studies?

We are not very good at conditional reasoning and often use real-world knowledge inappropriately when trying to solve formal logic problems

Describe the Wason Selection Task.

Participants are shown four cards with a letter on one side and a number on the other: R, G, 2, 7. They must decide which cards to turn over to test the rule: "If R on one side, then 2 on the other"

What percentage of people typically choose correctly in the Wason Selection Task?

Only about 5-10% choose correctly

What are some reasons for people's poor performance on the Wason Selection Task?

People may use simple strategies like matching bias, where they select the cards mentioned in the rule (R and 2). They may also not fully understand the rules, assuming a 1-to-1 correspondence between P and Q

What is Informal Reasoning?

Informal reasoning is the type of reasoning typically found in everyday life. It is based on knowledge and experience, unlike formal logic

How does Informal Reasoning differ from Deductive Reasoning in terms of certainty?

Deductive reasoning is binary (true or false). Informal reasoning is probabilistic (e.g., there's an 80% chance of being correct)

What is the Straw-man fallacy in Informal Reasoning?

The Straw-man fallacy involves focusing on weaker points of an opponent's argument to decrease the perceived probability of their view being correct, making one's own argument seem relatively more probable

What is Myside Bias, according to Stanovich & West (2007)?

Myside bias is the tendency to evaluate statements with respect to one's own beliefs

How did Stanovich & West (2007) demonstrate Myside Bias in college students?

Students who drank alcohol rated the accuracy of a statement linking college drinking to later alcoholism lower than those who didn't drink. Women rated the accuracy of a statement about the salary gap decreasing in the same position lower than men

What did Kahan et al (2012) find was the best predictor of climate change denial?

The best predictor was cultural values ("egalitarian communication" vs "hierarchical individualists"), having little to do with actual scientific evidence or scientific literacy

What is Bounded Rationality?

Bounded rationality is the idea that humans are rational, but within the limits of our cognitive capacity. We produce workable solutions despite having limited processing resources

How does Bounded Rationality relate to performance on reasoning tasks?

a correlation between performance in reasoning tasks and IQ, suggesting that more processing capacity potentially leads to better reasoning within the bounds of our limitations