Deductive Reasoning Patterns Module 3 Part 1

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Questions and Answers

What does a Venn diagram of a syllogism need to demonstrate for the syllogism to be valid?

It must include all terms in the premises.

It must exclude the possibility of the conclusion being false. (correct)

It must include a representation of the subject term.

It must demonstrate at least one true premise.

In the claim 'The only people admitted are people over twenty-one', which term is introduced by the phrase 'the only'?

The subject term. (correct)

The middle term.

The predicate term.

The minor term.

What type of syllogism involves reasoning from a general premise to a specific conclusion?

Argument by elimination

Hypothetical syllogism

Categorical syllogism (correct)

Argument from definition

When diagramming the argument 'All fish are swimmers. All bass are fish. All bass are swimmers', what area in the Venn diagram represents the conclusion 'All bass are swimmers'?

The area that is shaded for bass. Signup and view all the answers

How should claims about single individuals be treated in categorical logic?

As A-claims or E-claims. Signup and view all the answers

In a group exercise focused on propositional logic, what is the primary task of each individual member?

To formulate valid deductive arguments Signup and view all the answers

Which argument type specifically utilizes mathematical reasoning?

Argument based on mathematics Signup and view all the answers

What is the significance of translating claims into standard form in categorical logic?

It enables the use of the mechanism of categorical logic. Signup and view all the answers

What is the central focus of the group discussion exercise detailed in the content?

Creating valid deductive arguments from song lines Signup and view all the answers

What must be present in the Venn diagram to affirm that 'Some dogs are not brown' as a true statement?

There must be an unshaded area in the dogs circle. Signup and view all the answers

What is required for two claims to be considered equivalent?

They must be true under the same circumstances. Signup and view all the answers

How is each properly categorized argument evaluated in the group activity?

Each argument is worth one point for a total of five Signup and view all the answers

Which term is represented in the left circle of a standard Venn diagram for syllogisms?

Minor term. Signup and view all the answers

What is an example of an argument based on mathematics?

It takes more than eight minutes for the sun’s light to reach the earth. Signup and view all the answers

Identify the structure of a standard-form categorical claim.

All A are B. Signup and view all the answers

Which of the following statements is a categorical claim?

Some critical thinkers are philosophers. Signup and view all the answers

What type of argument is presented when a conclusion is derived from definitions?

Argument from definition Signup and view all the answers

In categorical logic, what is the term used for the claim structure that states 'No A are B'?

Universal negative Signup and view all the answers

Which of the following is NOT a valid term to use in a standard-form categorical claim?

Some red Signup and view all the answers

What kind of reasoning does an argument based on statistics employ?

Inductive reasoning Signup and view all the answers

Which option accurately describes the nature of categorical claims?

They relate different classes or categories. Signup and view all the answers

What is a hypothetical syllogism primarily characterized by?

Displaying a conditional statement in one of the premises Signup and view all the answers

Which pattern of deductive reasoning comprises a two-premise argument?

Hypothetical syllogism Signup and view all the answers

In a hypothetical syllogism, which of the following best describes modus ponens?

Affirming the antecedent followed by the consequent Signup and view all the answers

Which argument relies on mathematical reasoning to draw conclusions?

Argument based on mathematics Signup and view all the answers

What pattern of deductive reasoning is used when concluding an outcome from multiple conditional premises?

Chain argument Signup and view all the answers

Which common variety of hypothetical syllogisms asserts the consequent to reach a conclusion?

Affirming the consequent Signup and view all the answers

What does a categorical syllogism primarily involve?

Quantified statements Signup and view all the answers

Which argument is likely to be classified under the category of arguments from elimination?

Disproving alternative options to affirm one Signup and view all the answers

What should be done to handle ambiguity when placing 'x' in a segmented area?

Place 'x' on the border of the two regions. Signup and view all the answers

Which of the following statements is true regarding syllogisms?

No valid syllogism can have two negative premises. Signup and view all the answers

In a syllogism, which premise should be diagrammed first when one is universal and the other is particular?

The universal premise should be diagrammed first. Signup and view all the answers

What is a requirement for a term that is distributed in the conclusion of a syllogism?

It must be distributed in at least one premise. Signup and view all the answers

Which claim distributes its subject term?

A-claim. Signup and view all the answers

How many negative claims must be present in the conclusion of a valid syllogism?

No negative claims. Signup and view all the answers

Which claim does not distribute any terms?

I-claim. Signup and view all the answers

What is necessary for at least one premise in a valid syllogism?

To distribute the middle term. Signup and view all the answers

Study Notes

Module 3 Pt. 1: Common Patterns of Deductive Reasoning

This module identifies common patterns in deductive and inductive reasoning
By understanding these patterns, you build familiarity with necessary inferential relations (deductive) and probabilistic inferential relations (inductive)

Common Patterns of Deductive Reasoning

This section explores 5 common patterns of deductive reasoning:
- Hypothetical Syllogism
- Categorical Syllogism
- Argument by Elimination
- Argument Based on Mathematics
- Argument from Definition

Hypothetical Syllogism

A syllogism is a two-premise deductive argument
In hypothetical syllogisms, one premise is a conditional statement (If A, then B)
Example: "If it rains, the streets get wet. It rained."
- This leads to the conclusion: "So, the streets are wet."
This pattern is known as Modus Ponens and it follows this structure:
- A conditional premise (If A, then B)
- A second premise asserting the antecedent (A) is true
- A conclusion asserting the consequent (B) is true

Other Common Hypothetical Syllogism Varieties

Chain Argument: Three conditional statements linked together
Modus Tollens (Denying the Consequent): If A, then B. Not B. Therefore, not A.
Denying the Antecedent: If A, then B. Not A. Therefore, not necessarily B.
Affirming the Consequent: If A, then B. B. Therefore, not necessarily A.

Argument Based on Mathematics

Conclusions rely heavily on mathematical calculations or measurements (often combined with non-mathematical premises)
Example: "Light travels at 186,000 miles per second. The sun is more than 93 million miles away from the Earth."
- This leads to the conclusion: "Therefore, it takes more than eight minutes for the sun’s light to reach the earth."
Arguments based on mathematics can also be inductive, utilizing statistics or generalizations from samples

Argument from Definition

The conclusion is presented as being "true by definition"
It follows directly from the meaning of a keyword or phrase used in the argument
Example: "Bachelors are unmarried men. Jose is an unmarried man. So, Jose is a bachelor."

Categorical Logic

Logic based on relations of inclusion and exclusion among classes (or "categories") stated in categorical claims
Categorical claims make statements about classes of things
Standard-Form Categorical Claims:
- A (All): "All _________ are _________. (All Lasallians are Career-oriented persons.)"
- E (No): "No _________ are _________. (No Muslims are Christians.)"
- I (Some): "Some _______ are _________. (Some Christians are Filipinos.)"
- O (Some are not): "Some ______ are not _____. (Some critical thinkers are not philosophers.)"

Important Notes about Categorical Claims

Terms: The words or phrases in the blanks are called "terms," with the first being the subject term and the second being the predicate term.
Standard Form: Translation is crucial to apply the mechanism of Categorical Logic

Testing Syllogisms for Validity Using Venn Diagrams

To test if a syllogism is valid, Venn Diagrams represent the premises and analyze the result.
If the premises eliminate the possibility of the conclusion being false, the syllogism is valid.
If the Venn Diagram represents the conclusion, the syllogism is valid.
Each syllogism uses three terms, so a Venn diagram needs three circles (minor, major, and middle terms).

Rules Method for Testing Validity

Based on two ideas:
- Affirmative and Negative Categorical Claims (A and I are affirmative, E and O are negative)
- Distribution: A term is distributed if the claim applies to EVERY member of that class, if not, it's undistributed
  - A-claims distribute the subject term
  - O-claims distribute the predicate term
  - E-claims distribute both terms
  - I-claims distribute neither term

Three Rules of the Syllogism

For a syllogism to be valid, ALL of these conditions must be met:
1. The number of negative claims in the premises must match the number of negative claims in the conclusion (no valid syllogism has two negative premises).
2. At least one premise must distribute the middle term.
3. Any term distributed in the conclusion must also be distributed in its premises.

Propositional Logic

This topic will be explored in more detail in future discussions.

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Description

Explore common patterns of deductive reasoning in this module. You will learn about various syllogisms and inferential relations that enhance your understanding of logical arguments. Recognizing these structures is crucial for effective reasoning in problem-solving scenarios.