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Chapter 3: Problem 75

Describe what is meant by a valid argument.

Short Answer

Expert verified
In logic, a valid argument is where, if the premises are true, then the conclusion must be true. The validity of the argument does not depend on the actual truth or falseness of its premises or conclusion, but whether the argument is logically coherent.

Step by step solution

01

Define a Valid Argument

In the context of logic and reasoning, a valid argument is a type of argument where if the premises are true, then the conclusion must also be true. In other words, the truth of the premises logically guarantees the truth of the conclusion. It is important to remember that an argument's validity is independent of the truth of its premises or conclusion.
02

Clarify with an Example

To illustrate this concept further, consider the following example: Premise 1: All birds can fly; Premise 2: A penguin is a bird; Therefore, the conclusion is: A penguin can fly. The argument is valid because if the two premises were true, then the conclusion would be true. Yet the conclusion is false because not all birds can fly - for example, penguins.

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Most popular questions from this chapter

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. Having a college degree is necessary for obtaining a teaching position. You do not obtain a teaching position, so you do not have a college degree.

This is an excerpt from a 1967 speech in the U.S. House of Representatives by Representative Adam Clayton Powell: He who is without sin should cast the first stone. There is no one here who does not have a skeleton in his closet. I know, and I know them by name. Powell's argument can be expressed as follows: No sinner is one who should cast the first stone. All people here are sinners. Therefore, no person here is one who should cast the first stone. Use an Euler diagram to determine whether the argument is valid or invalid.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I watch Schindler's List and Milk, I am aware of the destructive nature of intolerance. Today I did not watch Schindler's List or I did not watch Milk. \(\therefore\) Today I am not aware of the destructive nature of intolerance.

Determine whether each argument is valid or invalid. No \(A\) are \(B\), some \(A\) are \(C\), and all \(C\) are \(D\). Thus, some \(D\) are \(B\)

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If we are to have peace, we must not encourage the competitive spirit. If we are to make progress, we must encourage the competitive spirit. \(\therefore\) We do not have peace and we do not make progress.
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