Contrast the following two tidy little arguments, one of which has vexed philosophers and theologians for thousands of years, while the other has not:

Argument I

If God were willing to prevent evil, but unable to do so, then He would be impotent. If He were able to prevent evil, but unwilling to do so, then He would be malevolent. Evil can exist in the world only if God is either unwilling or unable to prevent it. Surely there is evil in the world. Yet if God exists, then He is neither impotent nor malevolent. Therefore, God does not exist. [W,A,I,M,E,G]

Argument II

If God were unable to prevent evil, then He would be impotent. If He were unwilling to prevent evil, then He would be malevolent. Evil can exist in the world only if God is either unwilling or unable to prevent it. Surely there is evil in the world. Yet if God exists, then He is neither impotent nor malevolent. Therefore, God does not exist. [A,I,W,M,E,G]

That is, one of these arguments is truth-tropic, or valid, while the other is not! Given our work in the class so far, you now possess the analytical skills to determine which is which.

Using the sentence letters in their recommended order, respectively, i) translate Argument I and Argument II into the Propositional Calculus (PC) and ii) test each argument by the Method of Analytic Tableaux to determine which one is valid and which one is not. Hint: You'll need two pages of paper, one for the translation and tree for Argument I, another for the translation and tree for Argument II. Sign and take a picture of each page. You'll attach these pictures to your completed essay to be emailed to me. For the valid argument, indicate that it is so by clearly indicating how each and every branch dies. For the invalid argument, clearly indicate the still-living branch or branches.

Since one of these arguments is valid, it follows that we have proven that God does not exist if the argument is also sound--that is, if it also has all true premises.

Does it?

Write an essay of not less than 500 words and not more than 750 words (as per the instructions), to be copied and pasted as the body of an email to me, in which you either defend each premise if you think the argument is sound or explain which premise or premises you reject and why you reject them. Do not forget to attach the pictures of your Analytic Tableaux before sending me the essay!

To be sure, this is your first foray into genuinely philosophical analysis. I strongly recommend you spend time in discussion with one or more of your classmates to clarify your ideas before writing the essay. Note that what you may find obvious may not be so obvious to others!