A successful counterexample must have the same argument form as the argument to

Question

A successful counterexample must have the same argument form as the argument to which it is put forward as a counterexample. It is impossible for a valid argument form to allow a substitution instance with all true premises and a false conclusion. Therefore, if the proposed counterexample has the same argument form, and if it has all true premises and a false conclusion, then the counterexample is sufficient to show that the original argument's form is invalid Consider the following argument and argument form: Given Argument All dangerous situations are either causes for concern or reasons for action. Some dangerous situations are causes for concern. Therefore, some dangerous situations are reasons for action. Given Argument's Form P1: All D are either C or R. P2: Some D are C C: Some D are R. Below are three proposed counterexamples that purport to prove that the given argument's form is invalid. Determine the truth values of each sentence in the counterexample. Put a "T" or "F" in the spaces provided to indicate the truth value of each statement. Then, based on these truth values, indicate whether each proposed counterexample succeeds in proving that the given argument and its argument form are invalid. Proposed Counterexample A All dogs are either cats or fish. Some dogs are cats. Some dogs are fish Truth Value? P1: P2: C: 0 Based on these truth values, is Proposed Counterexample A a successful counterexample to the given argument form? Yes Pages

Explanation / Answer

A successful counter example prove original arguement by giving an example of same form where premise are true but conclusion is false.

In this case , truth table

1) all dogs are either cat or fish. (True)

2) some dogs are cats (true)

3) some dogs are fish (false) because there is possibility that all dogs are cats and no daogs are cat.

So this counter example is successful as it proves main arguement in the same form as invalid.

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