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Chapter 3: Problem 86

Write an original argument in words that has a true conclusion, yet is invalid.

Short Answer

Expert verified
An example of a true but invalid argument would be: 'All birds can fly. Therefore, the sun rises in the east.' The conclusion is true, but it does not logically follow from the premise, making the argument invalid.

Step by step solution

01

Identify the Premise

First, let's start by identifying a premise. For an argument to be valid, it needs to be totally impossible for all of the premises to be true and the conclusion to be false at the same time - that must not be the case here. A potential premise could be 'All birds can fly.'
02

Propose an Invalid Conclusion that Still Holds True

Now, we need to come up with a conclusion that is true, but does not logically follow from our premise. A possible conclusion could be 'The sun rises in the east.'
03

Create the Argument

'All birds can fly. Therefore, the sun rises in the east.' This is our argument. The conclusion is independently true - the sun does rise in the east. However, it's not guaranteed by the premise. The ability of birds to fly has nothing to do with the sun's rising, making the argument invalid.

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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 he was disloyal, his dismissal was justified. If he was loyal, his dismissial was justified. \(\therefore\) His dismissal was justified.

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'm tired, I'm edgy. If I'm edgy, I'm nasty. \(\therefore\) If I'm tired, I'm nasty.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \leftrightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore \sim r \rightarrow \sim p \end{aligned} $$

In this section, we used a variety of examples, including arguments from the Menendez trial, the inevitability of Nixon's impeachment, Spock's (fallacious) logic on Star Trek, and even two cartoons, to illustrate symbolic arguments. a. From any source that is of particular interest to you (these can be the words of someone you truly admire or a person who really gets under your skin), select a paragraph or two in which the writer argues a particular point. (An intriguing source is What Is Your Dangerous Idea?, edited by John Brockman, published by Harper Perennial, 2007.) Rewrite the reasoning in the form of an argument using words. Then translate the argument into symbolic form and use a truth table to determine if it is valid or invalid. b. Each group member should share the selected passage with other people in the group. Explain how it was expressed in argument form. Then tell why the argument is valid or invalid.

Use Euler diagrams to determine whether each argument is valid or invalid. All professors are wise people. Some wise people are actors. Therefore, some professors are actors.
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