The Scientific Method - Homework 1 - Validity and Soundness
Remember that a deductively valid argument is one that provides a guarantee that, if its premises are true, then its conclusion must be true too. We talked about three ways of showing an argument is not valid.
Test #1: Is there any possible way that the premises could be true, but the conclusion false? (Here it can help to imagine things someone could do to make the premises true and the conclusion false.) If there is such a possibility, then the argument doesn't guarantee that true premises will yield a true conclusion, so it is not valid.
Test #2: Pick some noun/verb/adjective in the original argument. Make up some other noun/verb/adjective to replace it with. Replace the first with the second, everywhere it occurred. Such substitutions cannot stop an argument from being valid. So if this substitution yields a clearly invalid argument (you might use test #1 to show this), then you know the original argument was not valid either. [Note: this test doesn't work on logical terms like 'if', 'and', 'is', 'or', 'all' or 'some'.]
Test #3: Draw a Venn Diagram in such a way that all the premises will be true, but the conclusion would be false. Much like Test #1, if you can do this, that shows that the premises are not enough to guarantee the truth of the conclusion. (Sometimes drawing a Venn diagram also puts you in a position to be able to clearly explain why an argument is valid -- e.g., if the premises guarantee that something will be inside one circle and that that circle will be fully inside a larger circle, then that's enough to guarantee that the something will be in the larger circle too.)
Remember also that a sound argument is an argument that is both valid and actually has true premises (and hence therefore must have a true conclusion too).
Homework: For each of the following arguments, specify whether or not the argument is valid, and whether or not the argument is sound. Explain your answers, using one of the three tests for invalidity in the cases where you think an argument is invalid. (If you think you don't have enough information to decide whether a particular argument is sound, explain what further information you would need.)
First hint: Premises can be true or false, but they can't be deductively valid or sound. Arguments can be valid or sound, but they can't themselves be true or false. If you ever call a premise "valid" or an argument "true" that's a clear sign you aren't understanding things.
Second hint: As far as validity is concerned, it doesn't matter whether the premises and conclusions are actually true and false - all that matters is whether there is a guarantee that if the premises were true, then the conclusion would have to be true (i.e., whether there is any possible way that the premises could be true and the conclusion false). If you say an argument isn't valid because one of the premises is false, that's a clear sign you aren't understanding things.
A1. All Republicans are white.
A2. Ben Carson is a republican.
A3. So Ben Carson is white.
B1. The sun has risen every day of my life.
B2. The sun has also risen every day of my mom's life.
B3. So the sun will rise tomorrow.
C1. There are just three hypotheses regarding the origins of species: Evolutionism, Creationism, and Pranksterism (the hypothesis that species were created by a powerful being who wanted to trick us into believing in evolution).
C2. Both Evolutionism and Pranksterism do better than Creationism at predicting fossils and imperfect designs.
C3. Evolutionism is simpler than Pranksterism.
C4. So Evolutionism is true.
D1. Einstein's theory entails that starlight would curve as it passes near the sun.
D2. Starlight does indeed curve as it passes near the sun.
D3. So Einstein's theory is true.
E1. Newton's theory entails that starlight would go straight as it passes near the sun.
E2. Starlight does not go straight as it passes near the sun.
E3. So Newton's theory is false.