Problem Set 06


This problem set is due in class Thursday, 10/11. Again, I do not mind students working on the problem sets in groups--it is, in fact, encouraged--but your answers must be your own. If you have any question, puzzle, or require clarification, please do not hesitate to contact me (; 3976 office, 944-2756 mobile--texts strongly preferred).

Recall from class Thursday (10/4) that our response on behalf of Anselm's Ontological Argument for the Existence of God to Gaunilo's criticism was to point out that God's properties are very different from any properties Gaunilo's Island might possess. Indeed, "a being than which none greater can be conceived" seems altogether different than "an island than which none greater can be conceived." Where such a being's properties are, we might say, maximal. That is, there is nothing more powerful than an all-powerful being, nothing more knowledgeable than an all-knowing being, and nothing more good than a perfectly good being. An island, however imagined, could always stand to have another palm tree, or a nicer beach, or be larger, or what have you.

Yet these maximal properties may themselves be problematic. For consider,

The Problem of Evil
  1 If God exists, then God is omnipotent (all-powerful), omniscient (all-knowing), and omnibenevolent (perfectly good).  
  2 If God is omnipotent, omniscient, and omnibenevolent, then it is not the case that evil exists.  
  3 Evil exists.  
4 Either God is not all-powerful, God is not all-knowing, or God is not perfectly good. 2&3
5 God does not exist. 1&4

The idea is fairly intuitive. If you saw a small child about to wander into traffic, you would, doubtless, run and stop the child. Of course, you may not be able to, because you may not be able to run fast enough. But you are a good person, so you'll do your best to avert disaster.

What would we say of someone who stood by and watched as the child wanders into traffic to be struck and killed?

Because it's so hard to believe that somebody would just stand by and let it happen, we might first wonder whether the person was able to save the child. Perhaps this person, though standing, requires a cane to get around and knows that he can't get to the child in time to save it. Then we might be less inclined to hold him blameworthy for not saving the child. After all, we cannot be expected to do what is not in our power.

Yet suppose we find out this person was perfectly able to save the child. Then we might wonder, did he know that the child was about to wander into traffic? His attention might have been elsewhere. One cannot intervene in a situation if one doesn't even know the situation exists.

Suppose now that we discover the person did, in fact, know what was happening. He knew what was happening, he could have acted to prevent it, yet he did nothing. Our conclusion must be that he is morally, and perhaps legally, blameworthy for failing to save the child. At the very least, we would say that he is not a good person, because a good person who knew what was about to happen and could intervene would have done so.

God is in much the same position as this person we have been imagining. If God exists, then God can do anything, knows everything, and is perfectly good. It couldn't then be the case that children die in the thousands from starvation, abuse, and natural catastrophe every day, but it is. If God exists, then God watches, refusing to lift a finger.

So either God does not exist at all, or God is either not perfectly good, not all-powerful, or not all-knowing.

Using our newly acquired logic skills, and given the list of sentence letters (G, P, S, B, E), unpack the Problem of Evil argument above into two arguments: Premises 2 & 3, Conclusion 4, and Premises 1 & 4, Conclusion 5. Translate the two arguments into the Propositional Calculus and, using the method of Analytic Tableaux, show that they are valid.

Are the arguments sound? That is, are the premises 1, 2, & 3 true? In the span of a single page, explain which one of the premises you find most objectionable or most open to criticism. Regardless of your own views on the argument, what criticisms can you imagine being levied against the premise you've highlighted?