Logic Arguments and Types

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Questions and Answers

In a syllogism, what is the term that appears in both premises but not in the conclusion called?

Contradictory term

Middle term (correct)

Minor term

Major term

Which rule states that the number of negative claims in the premises must match the number in the conclusion of a categorical syllogism?

Faculty FIU Rule 2

Kay Sir Rule 1 (correct)

Rule of Validity

Rule of Distribution

What is true about A (universal affirmative) and E (universal negative) claims in the Square of Opposition?

They can both be true at the same time.

They are contrary claims and cannot both be true. (correct)

They can both be false at the same time.

They can both be true or false simultaneously.

Which of these statements about categorical syllogisms is incorrect?

A syllogism consists of one premise. Signup and view all the answers

In a standard form categorical syllogism, what must happen with respect to the middle term?

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

Which of the following describes subcontrary claims in the Square of Opposition?

They can both be true but cannot be both false. Signup and view all the answers

Which rule is NOT a rule for testing categorical syllogisms?

At least one premise must be affirmative. Signup and view all the answers

What type of argument is a categorical syllogism classified as?

Deductive argument Signup and view all the answers

What type of reasoning does the following argument exemplify? 'If it rains, the streets get wet. It rained, therefore the streets are wet.'

Hypothetical syllogism Signup and view all the answers

Which of the following statements represents a sweeping generalization?

That dog is a pit bull; it’s mean for sure. Signup and view all the answers

In propositional logic, which of the following best describes the logical structure of 'If we don’t stop for gas soon, we’ll run out of gas; if we run out of gas, we’ll be late for the wedding; therefore, if we don’t stop for gas soon, we’ll be late for the wedding.'?

Chain argument Signup and view all the answers

Which of the following phrases is an example of an inductive indicator word?

Probably Signup and view all the answers

What is the primary characteristic of deductive reasoning?

It offers a conclusion that is guaranteed to be true if the premises are true. Signup and view all the answers

Which of the following is NOT an example of a syllogism?

If I study, I will pass the exam. I didn't study, so I failed. Signup and view all the answers

What is the conclusion in the following deductive argument? 'All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.'

Socrates is mortal. Signup and view all the answers

Which logical fallacy is demonstrated in the statement, 'If it is getting dark, the lights are on; the lights are on, therefore it is getting dark.'?

Affirming the consequent Signup and view all the answers

What does modus tollens propose regarding a conditional statement?

If p, then q; not q, therefore not p Signup and view all the answers

Which of the following describes an argument by elimination?

One assertion denies another, leading to a conclusion Signup and view all the answers

A truth table is primarily used to:

List potential outcomes for logical variables Signup and view all the answers

Which logical form is considered a non-reliable reasoning method?

Denying the antecedent Signup and view all the answers

In propositional logic, the statement 'If the robot is blue, then it works' is an example of:

A conditional statement Signup and view all the answers

Which of the following is represented by an 'E' categorical claim?

No are Signup and view all the answers

How should the claim 'Only senior students can enroll in this course' be translated in categorical logic?

All enrolled students are senior students Signup and view all the answers

The conclusion of an argument based on mathematics relies on which of the following?

Mathematical calculations and assumptions Signup and view all the answers

What conversion is necessary for past tense claims in categorical logic?

They are rewritten in present tense Signup and view all the answers

Which of the following is an example of affirming the consequent?

If it rains, the streets are wet; the streets are wet, therefore it rains Signup and view all the answers

A categorical claim's structure includes which elements?

Subject and predicate Signup and view all the answers

Which option illustrates a standard form 'O' claim?

Some birds are not parrots Signup and view all the answers

Which logical reasoning does not ensure correctness when the premises are true?

Denying the antecedent Signup and view all the answers

If 'All cats are pets' is a categorical claim, which of the following assertion can be true?

Some pets are not cats Signup and view all the answers

Study Notes

Modus Tollens

A type of deductive argument
Form: If p, then q. / Not q. / Therefore, not p.
Example: If we don’t stop for gas soon, then we’ll be late for the wedding. / We are not late for the wedding. / Therefore, we stopped for gas.

Argument By Elimination

Logic is used to systematically eliminate possibilities until only one remains.
Example: Either Joe walked to the library or he drove. / Joe didn’t drive to the library. / Therefore, Joe walked to the library.

Argument Based On Mathematics

Conclusions are based on mathematical calculations or measurements.
Example: Light travels at the rate of 186,000 miles per second. / The sun is more than 93 million miles away from the earth. / Therefore, the sun’s light takes more than eight minutes to reach the earth.

Argument From Definition

The conclusion follows directly from the definition of a term.
Example: Bachelors are unmarried men. / Jose is an unmarried man. / So Jose is a bachelor.

Propositional Logic

Deals with propositions (statements) that can be either true or false.
Example: True: The robot in question is blue. / False: The robot is some other color.

Truth Tables

Used to represent all possible truth values of logical variables in a formula.
Determine if the formula is true or false based on the combinations of truth values.

Categorical Logic

Studies relations among classes or categories of things.
Focuses on categorical claims, which make assertions about classes, requiring nouns.

Categorical Claims - Standard Form

A: All (subject) are (predicate).
E: No (subject) are (predicate).
I: Some (subject) are (predicate).
O: Some (subject) are not (predicate).

Square of Opposition

Contrary: A and E claims cannot be both true.
Subcontrary: I and O claims cannot be both false.
Contradictory: A and O claims (and E and I) have opposite truth values.

Categorical Syllogisms

Two-premise deductive arguments where each premise is a categorical claim.
Each term appears exactly twice in the argument, across exactly two claims.
Major Term (P): Predicate term of the conclusion.
Minor Term (S): Subject term of the conclusion.
Middle Term: Term that appears in both premises but not in the conclusion.

Rules for Testing the Validity of Categorical Syllogisms

KAY SIR:
- Rule 1: The number of negative claims in the premises must equal the number of negative claims in the conclusion.
- Rule 2: The middle term must be distributed in at least one premise.
- Rule 3: Any term distributed in the conclusion must be distributed in its premise.
FACULTY FIU:
- Rule 1: The middle term must be distributed in at least one premise.
- Rule 2: Any term distributed in the conclusion must be distributed in its premise.

Induction

Reasoning from specific observations to general conclusions.
Conclusions are likely but not certain.

Deduction

Reasoning from general principles to specific conclusions.
Conclusions are guaranteed if the premises are true.

Sweeping Generalizations

A type of inductive argument that uses a specific instance to make a sweeping generalization about a whole category.
Example: That dog is a Pit Bull, it's mean for sure. / All Pit Bulls are mean.

Hypothetical Syllogism

A syllogism where one premise is a conditional statement.
Modus Ponens: If p, then q. / p. / Therefore, q.
Chain Argument: If p, then q. / If q, then r. / Therefore, if p, then r.

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Description

Explore various types of deductive arguments including Modus Tollens, Argument By Elimination, Argument Based On Mathematics, and Argument From Definition. Learn how each argument type is structured with specific examples to clarify these logical concepts.