Cognition and Language (CaL) Week 9 Lecture: Thinking and Reasoning

Flashcards covering logic, deductive and inductive reasoning, conditional reasoning inferences (MP, MT, AC, DA), Mental Rules and Mental Models theories, Wason Selection Task, and Dual-Systems of reasoning based on Week 9 lecture notes.

What is the title of the Week 9 lecture for Cognition and Language (CaL)?

Thinking and Reasoning

Who is the lecturer for the Thinking and Reasoning session?

Dr Kevin Thomas

In which room is Dr Kevin Thomas's office located?

Room $P124$

According to the lecture, what is the definition of logic?

A set of standards for assessing the quality of arguments, propositions, or tasks and the objective analysis of statements.

What is logical (correct) reasoning?

Analysing arguments or propositions to draw or endorse correct conclusions by evaluating the supporting evidence presented.

For reasoning to be correct or logical, from where must conclusions follow?

They must follow logically from the supporting evidence.

What are the two synonymous terms for ‘reasoning tasks’ mentioned in the transcript?

Arguments or propositions.

What are the two primary components of a reasoning task?

Premises and Conclusion.

What is the definition of premises in a reasoning task?

Information that (supposedly) provides support for the conclusion.

In a reasoning task, what is the definition of the conclusion?

A statement that is claimed to follow logically from information contained in the ‘premises’.

According to the lecture, what is the only type of reasoning considered ‘truly logical’?

Deductive reasoning.

What is the definition of deductive reasoning?

Arriving at conclusions to propositions based on information presented in premises that is assumed to be true.

In deductive reasoning, from what is the nature of the conclusion derived?

The structure of the proposition or argument, not the content (i.e., premises).

In deductive reasoning, what occurs if the premises are true?

The truth of the conclusion is guaranteed.

Is it possible for premises to be true and the conclusion to be false in deductive reasoning?

No, there are no circumstances where this occurs.

Identify the first premise in the deductive cats example?

All cats are mammals.

Identify the second premise in the deductive cats example?

All mammals are warm-blooded.

What is the logical conclusion to the premises ‘all cats are mammals’ and ‘all mammals are warm-blooded’?

So, all cats are warm-blooded.

What is the definition of inductive reasoning?

Drawing or endorsing conclusions to propositions based on evidence that is not necessarily true.

Provide an everyday example where inductive reasoning is used.

When trying to solve crimes.

Does inductive reasoning guarantee the truth of a conclusion?

No, it only provides a likelihood of truth.

Name one way an inductive conclusion could be false even if based on premises.

Ignoring relevant evidence and using irrelevant evidence only.

Briefly describe the ‘journal article’ example of inductive reasoning.

A journal article based only on a study's data that fit with the study's hypothesis.

Briefly describe the inductive error in a ‘crime-suspect’ scenario.

A person wrongly convicted on the basis of false or incorrect eyewitness testimony.

In inductive reasoning, what do premises provide for the conclusion if they are true?

They provide support for the conclusion but do not guarantee its truth.

What does induction imply about the relationship between premises and conclusion?

The conclusion follows with a degree of probability or likelihood.

Identify the premises in the Jane ‘first’ class student example.

Premise $1$: Jane was a very good student; Premise $2$: Jane got a ‘first’.

What is the conclusion in the Jane ‘first’ example, and is it valid?

Conclusion: All very good students will get ‘firsts’; it is not certain/correct because some might fail a unit due to late submission.

What are the two properties used to judge if a proposition is logical?

Soundness and Validity.

What is the definition of Soundness in a proposition?

The conclusion follows logically from premises that are true.

What question forms the ‘soundness test’?

Are there any circumstances in which (or evidence to suggest that) information in the premises is false?

What is the definition of Validity in a proposition?

The conclusion follows logically from the premises, even if they are not true.

What question forms the ‘validity test’?

Does the conclusion follow logically from the information in the premises?

Can a proposition be valid but not true?

Yes.

Consider the proposition: ‘All lecturers are interesting. All interesting people are intelligent. Therefore, all lecturers are intelligent.’ Is it valid?

Yes, because the premises imply the conclusion.

Consider the proposition: ‘All lecturers are interesting. All interesting people are intelligent. Therefore, all lecturers are intelligent.’ Is it sound?

No, because the premises are not true (not all lecturers are interesting).

What defines a sound proposition or argument?

A valid argument with true premises.

If an argument is sound, what must be true about its conclusion?

The conclusion must be true.

Identify the status of a ‘valid argument with false premises that logically imply a conclusion.’

The argument is valid but unsound.

Is it logically possible for an argument to be sound and invalid?

No.

Consider the argument: ‘All grass is blue. Fern is a type of grass. Therefore, fern is blue.’ What is its validity status?

Valid.

Why is the ‘grass is blue’ argument unsound?

The first premise (all grass is blue) is untrue.

What is the focus of conditional reasoning?

How the words in connecting propositions (‘connectives’) influence inferential reasoning.

How do ‘connectives’ affect our thinking?

They affect drawing correct conclusions based on making inferences (going beyond evidence).

Name the three examples of ‘connectives’ provided in the lecture.

‘If’, ‘or’, and ‘not’.

What is the typical form of propositions in conditional reasoning?

The ‘if-then’ form.

What are the three components that typically comprise a conditional reasoning proposition?

$1$ premise (with $2$ parts), $1$ statement of factual information, and $1$ conclusion.

When is a conditional reasoning proposition considered valid?

If the conclusion follows logically from the premise given the information statement.

In the ‘if-then’ format, what is the ‘if’ clause called?

The antecedent part or clause.

In the ‘if-then’ format, what is the ‘then’ clause called?

The consequent part or clause.

What letter is used to represent the antecedent in logic?

$$P$$

What letter is used to represent the consequent in logic?

$$Q$$

In ‘If Kevin is smiling, then he is happy,’ what is the antecedent clause ($P$)?

Kevin is smiling.

In ‘If Kevin is smiling, then he is happy,’ what is the consequent clause ($Q$)?

He is happy.

Identify the parts of this proposition: ‘If it is raining, then I take an umbrella. It is raining. Therefore I take an umbrella.’

Antecedent: It is raining; Consequent: I take an umbrella; Info: It is raining; Conclusion: I take an umbrella.

How many distinct types of conditional reasoning inferences are mentioned?

$$4$$

Name the two logically-valid (correct) conditional reasoning inferences.

Modus ponens ($MP$) and Modus tollens ($MT$).

What is another name for Modus ponens?

Affirmation of antecedent.

What is another name for Modus tollens?

Denial of consequent.

Name the two logically-invalid (fallacious) conditional reasoning inferences.

Affirmation of consequent ($AC$) and Denial of antecedent ($DA$).

Briefly describe Modus ponens ($MP$).

Drawing a logically-valid conclusion by affirming the antecedent based on a statement of fact.

Provide the Modus ponens example involving a cat and a dog.

If the cat is sitting on the mat ($P$), then the dog will bark ($Q$). The cat is sitting on the mat. Therefore, the dog barks.

Briefly describe Modus tollens ($MT$).

Drawing a logically-valid conclusion by denying the consequent based on a statement of fact.

Provide the Modus tollens example involving a telephone.

If the telephone is working ($P$), then there will be a dialling tone ($Q$). There is not a dialling tone. So, the telephone is not working.

Briefly describe Affirmation of the consequent ($AC$).

Drawing a logically-invalid conclusion by affirming the consequent based on a statement of fact.

Provide the ‘cheating’ example of an $AC$ inference.

If you are cheating on me ($P$), then you will be out of the house a lot ($Q$). You are out of the house a lot. Therefore, you are cheating on me.

Why is Affirmation of the Consequent considered logically-invalid?

Just because one thing follows another ($If\,P\,then\,Q$), it does not logically follow that the reverse is true ($If\,Q\,then\,P$).

In the ‘cheating’ example, why is it incorrect to conclude the partner is cheating?

Because she could be out of the house for other reasons, like shopping or work.

Briefly describe Denial of the antecedent ($DA$).

Drawing a logically-invalid conclusion by denying the antecedent based on a statement of fact.

Provide the ‘socialist’ example of a $DA$ inference.

If you are a socialist ($P$), then you are in favour of the welfare state ($Q$). You are not a socialist. Therefore, you are not in favour of the welfare state.

Why is Denial of the Antecedent considered fallacious?

Just because the antecedent is false (not $P$), it does not mean the consequent (not $Q$) is also false; other factors could make the consequent true.

In the ‘socialist’ example, why is the conclusion logically incorrect?

You could be a benevolent capitalist who still believes all people are entitled to free healthcare.

According to Evans et al. ($1998$), what percentage of participants endorsed Modus ponens ($MP$)?

$$98\%$$

According to Evans et al. ($1998$), what percentage of participants endorsed Affirmation of the consequent ($AC$)?

$$77\%$$

According to Evans et al. ($1998$), what percentage of participants endorsed Modus tollens ($MT$)?

$$60\%$$

According to Evans et al. ($1998$), what percentage of participants correctly endorsed/spotted Denial of the antecedent ($DA$)?

$$59\%$$

Why is performance typically worse for Modus tollens than Modus ponens?

Due to the presence of negation (the word 'not') in the information statement of $MT$ inferences.

What is the ‘presence of negation’ problem?

It is harder for people to judge the logic of arguments when they contain words such as ‘not’.

Who proposed the Mental Rules theory, and in what year?

Rips ($1994$).

What is the first principle of Mental Rules theory?

The mind contains ‘mental logic’.

How are premises represented according to Rips ($1994$)?

In a language-like way.

According to Mental Rules theory, which rule do we possess and which do we lack?

We have a rule for Modus ponens, but not for Modus tollens.

What are the three stages of Mental Rules theory?

$1$. Represent underlying logical form; $2$. Access appropriate rules; $3$. Evaluate argument components.

Why does Modus tollens take more effort in Mental Rules theory?

One has to deconstruct the Modus ponens version ($P\,then\,Q$) before analysing the Modus tollens version ($P\,then\,not-Q$).

Who proposed the Mental Models theory, and in what year?

Johnson-Laird ($1983$).

What is the key assumption of Mental Models theory regarding ‘mental logic’?

The mind contains no ‘mental logic’ (mental rules).

According to Johnson-Laird, why do reasoning errors occur?

Due to failure to keep track of mental models.

What are the three stages of Mental Models theory?

$1$. Comprehension of premise; $2$. Draw conclusion; $3$. Search for counter-examples.

What specifically occurs during the ‘Search for counter-examples’ stage in Mental Models theory?

Searching for alternative models where the conclusion is false.

Why is Modus tollens harder than Modus ponens according to Mental Models theory?

It requires generating more models and ‘fleshing-out’ the basic Modus ponens mental model ($if\,P\,then\,Q$).

In Mental Models theory, what does ‘fleshing-out’ mean?

Generating a more complex mental representation of the argument by searching for counter-examples.

Who devised the Wason Selection Task ($WST$), and in what year?

Peter Wason ($1966$).

What components are used in the original Wason Selection Task?

$4$ playing cards, each with a vowel or consonant on one side and an odd or even number on the other.

What is the common rule used in Wason’s vowel/even number selection task?

If a card has a vowel on one side, then it has an even number on its other side.

What were the labels on the four cards in Wason’s original ($1966$) experiment?

$E$, $K$, $4$, and $7$.

In the original $WST$ study, which two cards did ~ $70\%$ of participants typically choose?

The $E$ and $4$ cards.

Map the card labels ($E$, $K$, $4$, $7$) to their logical components ($P$, $not\,P$, $Q$, $not\,Q$).

$E=P$; $K=not\,P$; $4=Q$; $7=not\,Q$.

Is choosing the ‘$E$’ and ‘$4$’ cards the logically correct choice in the $WST$?

No.

Why is choosing the ‘$E$’ card logically correct?

It permits affirmation of the antecedent ($MP$).

Why is choosing the ‘$4$’ card logically incorrect in the $WST$?

It does not check the truth of the proposition because it doesn't permit denial of the consequent ($MT$); it only confirms the rule.