PhilosophyLesson 1 of 1 in the course Logic and Reasoning

Logical Conditionals and Universal Affirmative Statements

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Conditionals express relationships between propositions and help make arguments precise. In this lesson, you will learn to identify the parts of a conditional, distinguish necessary from sufficient conditions, and use counterexamples to test conditional claims.

A conditional is a statement that expresses an if–then relationship. Its general form is “If XX, then YY.” The part following “if” is the antecedent; the part following “then” is the consequent.

All flashcards

What is a conditional?
A statement expressing an if–then relationship between propositions.
What are the antecedent and consequent?
The antecedent follows “if”; the consequent follows “then.”
What is a necessary condition?
A condition that must be true whenever another specified condition is true.
What is a universal affirmative statement?
A claim that every member of one group belongs to another group.
What is a counterexample to a conditional?
A case where the antecedent is true and the consequent is false.

Quiz questions

  1. “You can have pudding only if you eat your meat.” What condition does this make necessary for having pudding?Answer: Eating your meat.
  2. What does “All A are B” claim about members of group B?Answer: It does not claim that every B is an A.
  3. Which conditional is logically equivalent to “All A are B”?Answer: If something is A, then it is B.
  4. If no counterexample has been found to a universal claim, what follows from that alone?Answer: The search has not produced a disproof.
  5. What would disprove “All A are B”?Answer: A case that belongs to A but not to B.

Based on Introduction to Philosophy by Nathan Smith (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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