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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?
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?
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?
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?
Which of these statements about categorical syllogisms is incorrect?
In a standard form categorical syllogism, what must happen with respect to the middle term?
In a standard form categorical syllogism, what must happen with respect to the middle term?
Which of the following describes subcontrary claims in the Square of Opposition?
Which of the following describes subcontrary claims in the Square of Opposition?
Which rule is NOT a rule for testing categorical syllogisms?
Which rule is NOT a rule for testing categorical syllogisms?
What type of argument is a categorical syllogism classified as?
What type of argument is a categorical syllogism classified as?
What type of reasoning does the following argument exemplify? 'If it rains, the streets get wet. It rained, therefore the streets are wet.'
What type of reasoning does the following argument exemplify? 'If it rains, the streets get wet. It rained, therefore the streets are wet.'
Which of the following statements represents a sweeping generalization?
Which of the following statements represents a sweeping generalization?
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.'?
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.'?
Which of the following phrases is an example of an inductive indicator word?
Which of the following phrases is an example of an inductive indicator word?
What is the primary characteristic of deductive reasoning?
What is the primary characteristic of deductive reasoning?
Which of the following is NOT an example of a syllogism?
Which of the following is NOT an example of a syllogism?
What is the conclusion in the following deductive argument? 'All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.'
What is the conclusion in the following deductive argument? 'All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.'
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.'?
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.'?
What does modus tollens propose regarding a conditional statement?
What does modus tollens propose regarding a conditional statement?
Which of the following describes an argument by elimination?
Which of the following describes an argument by elimination?
A truth table is primarily used to:
A truth table is primarily used to:
Which logical form is considered a non-reliable reasoning method?
Which logical form is considered a non-reliable reasoning method?
In propositional logic, the statement 'If the robot is blue, then it works' is an example of:
In propositional logic, the statement 'If the robot is blue, then it works' is an example of:
Which of the following is represented by an 'E' categorical claim?
Which of the following is represented by an 'E' categorical claim?
How should the claim 'Only senior students can enroll in this course' be translated in categorical logic?
How should the claim 'Only senior students can enroll in this course' be translated in categorical logic?
The conclusion of an argument based on mathematics relies on which of the following?
The conclusion of an argument based on mathematics relies on which of the following?
What conversion is necessary for past tense claims in categorical logic?
What conversion is necessary for past tense claims in categorical logic?
Which of the following is an example of affirming the consequent?
Which of the following is an example of affirming the consequent?
A categorical claim's structure includes which elements?
A categorical claim's structure includes which elements?
Which option illustrates a standard form 'O' claim?
Which option illustrates a standard form 'O' claim?
Which logical reasoning does not ensure correctness when the premises are true?
Which logical reasoning does not ensure correctness when the premises are true?
If 'All cats are pets' is a categorical claim, which of the following assertion can be true?
If 'All cats are pets' is a categorical claim, which of the following assertion can be true?
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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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