Lecture 10: Types of reasoning and the cognitive science of logic

Deductive reasoning and critical thinking:

• Formal fallacies

• The Wason selection task

The structure of the scientific method:

• A non-deductive process of slow confirmation

• A deductive argument involving falsification

What are the 2 types of human reasoning?

• deductive reasoning

  • formalized by logic

• non-deductive reasoning

  • inductive reasoning

  • abductive reasoning

limited dataset used to make generalizations → non-deductive reasoning

• chat gpt

What is an important type of human reasoning?

Using a series of claims to reach a new claim – conclusion

How are deductive arguments evaluated?

validity and soundness

What is an advantage of deductive reasoning?

advantage: the conclusion is 100% certain

What is the structure of deductive arguments and what formal tool is used?

Premise 1: If A then B

Premise 2: A

Conclusion: B

If the premises are true and the argument is valid, the conclusions necessarily follows

Formal tool: formal Logic

What is a disadvantage of deductive reasoning?

disadvantage: very limited information deductively follows from the premises (what is contained in the premises)

Premise 1: Every 1st year CSAI student has to take programming

Premise 2: Michael is a 1st year CSAI studnet

Conclusion: Michael has to take programming

• conclusion doesn’t go beyond the info in the premises

  • we don’t gain much new information

What is non-deductive reasoning? is the notion of validity applicable?

the premises support the conclusion to some degree, but the conclusion does not necessarily follow

• the notion of validity is not applicable to non-deductive arguments and instead the notion of the argument’s strength is considered

Example 1:

• premise: 1 student told me that understanding the base rate fallacy is hard

• conclusion: understanding the base rate fallacy is hard

Example 2:

• premise: 50 students told me that understanding the base rate fallacy is hard

• conclusion: understanding the base rate fallacy is hard

List the formal tools used, advantage and disadvantage of non-deductive reasoning

Formal tools: probability theory, statistics, some logical frameworks

Advantage: Possible to make many more conclusions

Disadvantage: 1. Uncertainty, 2. The problem of induction

What are the 2 types of non-deductive arguments?

• inductive reasoning

• abductive reasoning

What is inductive reasoning?

moving from a number of particular instances to a generalization

• example: 50 students think that the base rate fallacy is hard, therefore all students think its hard

• ex. all the ravens i’ve seen are not white therefore all ravens are not white

*non-deductive argument

What is abductive reasoning?

moving from a claim (premise) to a claim that explains the best conclusion given the available knowledge → inference to the best explanation

• occam’s razor

• example: my bike is not where I left it, therefore someone stole it

*non-deductive argument

What is the connection between deductive, inductive, and abductive reasoning?

• we will treat them as independent

• formal logic models for deductive reasoning

• probability theory models for inductive and abductive reasoning

• Hume’s problem → can we base induction on deduction

What is the connection to ai with the 3 ways of reasoning?

trying to mechanize human reasoning, we can try to automate:

• deductive reasoning → symbolic ai, logical methods

• inductive reasoning → data science, machine learning

• abductive reasoning → can that be automated? can a computer jump to the best explanation as we can?

Understanding human reasoning is important to understanding ai

What is the connection to scientific thinking regarding inductive and deductive reasoning?

Scientific method 1: confirmation of a general hypothesis by many instances = inductive reasoning

• problem of induction for confirmation

Scientific method 2: only a process of falsification of hypothesis (popper) = deductive reasoning

What is formal fallacy?

a fallacy in reasoning based on misapplication of logic

What are 2 important formal fallacies?

• affirming the consequent

• denying the antecedent

What’s the argument structure of: the formal fallacy affirming the consequent?

premise 1: If A then B

premise 2: B (here you affirm the consequent of the conditional)

invalid conclusion: A

example: If someone rides a bike at night without lights they will get a fine. Michael got a fine. Therefore, Michael rode his bike without lights.

What’s the argument structure of: the formal fallacy denying the antecedent?

premise 1: If A then B

premise 2: not A (here you deny the antecedent of the conditional)

invalid conclusion: not B

example: If Maria eats a lot of meat, then she has high cholesterol. But she is a vegetarian. So, she does not have high cholesterol.

Why is learning formal logic useful?

To be more aware of the 2 formal fallacies, affirming the consequent and denying the antecedent

What are the 2 valid argument forms?

• Modus Pones

• Modus Tollens

What’s the argument structure of: Modus Pones

premise 1: If A then B

premise 2: A

valid conclusion: B

What’s the argument structure of: Modus Tollens?

premise 1: If A then B

premise 2: not B

valid conclusion: not A

The Wason selection task, which cards do you check?

check d and 7

• you check 7 bcs of the contrapositive form where not 7 implies not D

What is the contra-positive and converse of the conditional A → B?

Conditional: A → B

contra-positive: ~B → ~A

• ex. if you are not in the Netherlands, you are not in Tilburg

converse: B → A

• ex. if you are in the Netherlands, you are in Tilburg

What are 2 important things to note about conditionals regarding their contra-positive and converse forms?

• every conditional is logically equivalent to its contra-positive form

• conditionals are not logically equivalent to their converse form

What does the Wason selection task depend on?

its content

• Psychologists have noticed that the content of the conditional influences the ability to get the right answer.

• But, from a formal logic perspective, the content does not matter.

• This strongly suggests that humans don’t directly implement logic rules in their reasoning.

Why is the Watson selection task so hard for humans?

Cognitive psychologists have proposed a bewildering number of theories to explain why people are so much better at solving such versions of the selection task compared with other, formally equivalent variations, like the original card version. The most generally cited of these theories, due to Leda Cosmides (1985, 1989), is that humans have evolved a specialised algorithm (or procedure) for detecting cheaters in social contracts.

The algorithm has the general form: If you accept a benefit, then you must meet its requirement

• we’re sensitive to the content

Deductive conditional reasoning

• Psychologists still argue what exactly is going on.

• But, its clear that people constantly fail to note the equivalence between a conditional and its contrapositive form.

• Sometimes its super easy:

  • “If students get above 5.5 in the final, they pass the course.”

  • I didn’t pass the course!

  • Oh, you got a bad result in the final...

• In abstract and scientific contexts, the equivalence can be much harder to detect (remember the ravens from the tutorial?)

What is an advantage and disadvantage of inductive arguments?

advantage: an easy way to get from evidence (observations) to general statements

disadvantage: the conclusion is never 100% certain (unlike deduction)

What is an advantage and disadvantage of abductive arguments?

advantage: an easy way to draw conclusions about an uncertain world

disadvantage: is it even rational? why should we be confident in the conclusion?