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Chapter 3: Problem 79

Write an original argument in words for the transitive reasoning form.

Short Answer

Expert verified
An example argument using transitive reasoning: All dogs are mammals (A is B), all mammals are animals (B is C), therefore all dogs are animals (A is C).

Step by step solution

01

Identify Statements

The first step is to identify three statements that can be logically connected in a transitive way. For example: Statement A - All dogs are mammals. Statement B - All mammals are animals. Statement C - Therefore, all dogs are animals.
02

Formulate the Connection

Next, formulate the connection between these statements following the principles of transitive reasoning. Here, because 'dogs' are related to 'mammals' in Statement A, and 'mammals' are related to 'animals' in Statement B, 'dogs' can therefore be logically connected to 'animals'. This connection forms Statement C.
03

Confirm Logical Transitivity

Finally, it's important to confirm that your argument follows the principle of transitive reasoning. This requires ensuring that if A is related to B, and B is related to C, then A must be related to C. So, given Statement A and Statement B from the previous steps, 'dogs' (from A) are indeed logically connected to 'animals' (from C), confirming that the argument adheres to transitive reasoning.

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Most popular questions from this chapter

Use Euler diagrams to determine whether each argument is valid or invalid. All insects have six legs. No spiders are insects. Therefore, no spiders have six legs.

Use Euler diagrams to determine whether each argument is valid or invalid. All writers appreciate language. All poets are writers. Therefore, all poets appreciate language.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. "I do know that this pencil exists; but I could not know this if Hume's principles were true. Therefore, Hume's principles, one or both of them, are false."

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \wedge \sim q\) P____ \(\therefore \sim q\)

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