Logic: Hypothetical Syllogisms Quiz

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Questions and Answers

What is the name for a syllogism that uses only hypothetical statements?

  • Categorical syllogism
  • Disjunctive syllogism
  • Hypothetical syllogism (correct)
  • Conditional syllogism

In a hypothetical statement 'If P then Q', what is 'P' referred to as?

  • The subject
  • The predicate
  • The antecedent (correct)
  • The consequent

Which of the following accurately represents the structure of a pure hypothetical syllogism?

  • P → Q, Q → R, ∴ R → P
  • P → Q, Q → R, ∴ P → R (correct)
  • P → Q, R → Q, ∴ P → R
  • P → Q, P → R, ∴ Q → R

What type of categorical syllogism does a hypothetical syllogism of the form 'P → Q, Q → R ∴ P → R' correspond to?

<p>AAA-1 (B)</p> Signup and view all the answers

Hypothetical statements combine how many categorical statements?

<p>Two (C)</p> Signup and view all the answers

In a hypothetical statement, what is the term for the statement following 'then'?

<p>Consequent (B)</p> Signup and view all the answers

Which of the following best describes a mixed hypothetical syllogism?

<p>An argument combining hypothetical and categorical statements. (C)</p> Signup and view all the answers

What is the name for the valid argument form: If P then Q, P, Therefore Q?

<p>Modus Ponens (A)</p> Signup and view all the answers

Given the statements: If it rains, then the ground is wet. It is raining. Using Modus Ponens, what is the valid conclusion?

<p>The ground is wet. (B)</p> Signup and view all the answers

Which of the following represents the formal structure of Modus Ponens?

<p>$P \implies Q$, $P$, $\therefore Q$ (D)</p> Signup and view all the answers

Which of the following best represents the structure of a modus ponens argument?

<p>If P then Q; P; Therefore, Q (C)</p> Signup and view all the answers

Identify the conclusion in the following modus tollens argument: If it is raining, then the ground is wet. The ground is not wet. Therefore...?

<p>It is not raining. (D)</p> Signup and view all the answers

What error in reasoning is demonstrated by the fallacy of affirming the consequent?

<p>Assuming the truth of the antecedent based on the true conclusion. (B)</p> Signup and view all the answers

Which propositional logic symbol represents "not"?

<p>¬ (C)</p> Signup and view all the answers

Which of the following is a valid form of the argument called modus tollens?

<p>If P then Q; Not Q; Therefore, Not P (A)</p> Signup and view all the answers

Which logical fallacy is committed when one concludes that because the consequent is true, the antecedent must also be true?

<p>Affirming the Consequent (A)</p> Signup and view all the answers

What does the Latin term 'non sequitur' refer to?

<p>An argument where the conclusion does not logically follow the premises (B)</p> Signup and view all the answers

Given the statement: 'If it rains, the ground is wet,' which fallacy is demonstrated by concluding that 'Since it did not rain, therefore the ground is not wet'?

<p>Denying the Antecedent (B)</p> Signup and view all the answers

What is a key characteristic of the logical fallacies 'Affirming the Consequent', and 'Denying the Antecedent'?

<p>They are both examples of <em>non sequitur</em> arguments (C)</p> Signup and view all the answers

In a conditional statement 'If P, then Q', which argument structure is an example of 'Affirming the Consequent'?

<p>Q is true, therefore P is true (B)</p> Signup and view all the answers

Flashcards

Hypothetical syllogism

An argument that uses only "if...then" statements.

Antecedent

The first part of a hypothetical statement, following "if".

Pure hypothetical syllogism

A hypothetical syllogism with the form: If P then Q. If Q then R. Therefore, if P then R.

Categorical syllogism

A type of syllogism where all three propositions are universal affirmative. Example: All A are B, All B are C. Therefore, All A are C.

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AAA-1 categorical syllogism

A hypothetical syllogism can be translated into a categorical syllogism with this structure.

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Consequent

The 'then' part of a 'if...then' statement.

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Mixed Hypothetical Syllogism

A logic argument that combines 'if...then' statements with simple statements.

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Modus Ponens

A valid form of mixed hypothetical syllogism with this structure: If P then Q P Therefore, Q

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Fallacy of Affirming the Consequent

An argument that begins with a conditional statement ("If P, then Q"), then affirms the consequent (Q), and concludes that the antecedent (P) must be true.

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Modus Tollens

A valid argument form that uses a conditional statement ("If P, then Q"), then denies the consequent (Q), and concludes that the antecedent (P) must be false. The form is: If P then Q, not Q, therefore not P.

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Affirming the Consequent: A Fallacy

It occurs when the second premise affirms the consequent of the hypothetical statement in the first premise, leading to an invalid argument. This is a common logical fallacy.

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Hypothetical Argument

A type of argument that uses a conditional statement ('If P, then Q') as the first premise and either affirms the antecedent (P) or denies the consequent (Q) in the second premise.

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Affirming the consequent

An invalid argument form that assumes if a consequence (Q) is true, then the antecedent (P) must also be true. In reality, there could be other ways to reach the consequence.

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Denying the Antecedent

An invalid argument form that assumes if the antecedent (P ) is false, then the consequence (Q) must also be false. But, there might be other factors that can lead to the consequence.

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Non sequitur

A Latin phrase meaning 'it does not follow', indicating an argument is invalid. It highlights that the conclusion isn't logically connected to the premises, making it a non sequitur.

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Invalid Hypothetical Syllogism

A type of argument using 'if...then' statements, where the conclusion doesn't follow logically from the premises. It's invalid due to either affirming the consequent or denying the antecedent.

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Valid Hypothetical Syllogism

A valid hypothetical syllogism follows the form: If P then Q. If Q then R. Therefore, if P then R. It establishes a clear chain of logic.

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