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Chapter 3: Problem 76

If you are given an argument in words that contains two premises and a conclusion, describe how to determine if the argument is valid or invalid.

Short Answer

Expert verified
An argument is valid if the truth of the premises guarantees the truth of the conclusion. An argument is sound if it is valid and its premises are true. So, to determine if an argument is valid or invalid, first, identify the premises and the conclusion. Evaluate the logic that connects the premises to the conclusion. Finally, check the truth of the premises to determine if the argument is sound or unsound.

Step by step solution

01

Identifying the premises and conclusion

The initial task involves breaking down the argument's structure. Distinguish the premises and the conclusion of the argument. Premises are the preconditions or statements that supports or leads to the conclusion. The conclusion is the statement that is arrived at by the premises.
02

Assessing the Logic

The next step would be to evaluate the logic that connects the premises to the conclusion. If the truth of the premises implies the truth of the conclusion, the argument can be considered valid. This means the conclusion directly follows from the premises.
03

Checking for Soundness

A valid argument is sound if its premises are true. This requires some knowledge or facts regarding the subject matter of the argument in question. If the premises are indeed true and the argument is valid, you can conclude that the argument is sound and the conclusion is also true.
04

Final Validation

In the final step, you should evaluate the overall argument. An argument is really 'good' if it's both sound and valid. If the premises don't justify the conclusion, the argument is invalid. If it's valid but the premises aren't all true, it's unsound.

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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. 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 all people obey the law, then no jails are needed. Some people do not obey the law. \(\therefore\) Some jails are needed.

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 Tim and Janet play, then the team wins. Tim played and the team did not win. \(\therefore\) Janet did not play.

Use Euler diagrams to determine whether each argument is valid or invalid. All actors are artists. Sean Penn is an artist. Therefore, Sean Penn is an actor.

Under what circumstances should Euler diagrams rather than truth tables be used to determine whether or not an argument is valid?

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &(p \rightarrow q) \wedge(q \rightarrow p) \\ &\frac{p}{\therefore p \vee q} \end{aligned} $$
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