Extra Credit: Validity and Invalidity

For each of the statements below, provide an example that shows why the statement is either true or false. I will do it for the first one by way of illustration. You can post your responses here or email them to me for extra credit. 

1.    If an argument is valid then it has true premises and a true conclusion

To show that 1 is false, I need to show that it is possible for an argument to be valid and have either false premises or a false conclusion. For overkill I will give an example of both. 

Valid argument with false premises:

If grass is red, then it is cold.
Grass is red
Hence, it is cold

The premises of the above argument are false, but the argument is valid.

Valid argument with false conclusion

The biggest Indiana city north of Indianapolis is the capital of Indiana
Fort Wayne is the biggest Indiana city north of Indianapolis
Hence, Fort Wayne is the capital of Indiana

The conclusion of the above argument is false, but the argument is valid.

Thus, we know that it is possible for an argument to be valid while having either false premises or a false conclusion. Hence, 1 is false 


2.    If an argument is sound then it has true premises and a true conclusion

3.    All valid arguments have true conclusions

4.    All invalid arguments have false conclusions

5.    If an argument has true premises and a true conclusion then it is valid

6.    If an argument has true premises and a true conclusion then it is sound


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