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A more serious argument: The problem of evil

In this article, we look at a more serious and complex argument and test it for formal validity.
A volcano spouts hot ash into a darkened sky
© Image by Adrian Malec

In this step we’re going to look at a more serious and challenging argument.

One reason the argument is challenging is simply the number of basic sentences involved. We’ll look at how that challenge can be addressed.

The argument presents a version of what is called the Problem of Evil. Here it is:

  • If God is willing to prevent suffering, and unable to do so, then God is not omnipotent. If God is able to prevent suffering, and unwilling to do so, then God is not loving. And if God were both willing and able to prevent suffering, then there could not be any. There is suffering. Therefore, God is not both loving and omnipotent.

Let’s look at this argument to see if it’s formally valid. The first thing to do is to try to identify the basic sentences. Look through the argument and see if you can construct a list of the basic sentences. Note that you’ll probably need to paraphrase at some points. Have a go at this before you read on.

OK. Here’s a list of the basic sentences that seem to be involved. We’ve defined sentence letters here to use in the next step.

  • S: There is suffering
  • W: God is willing to prevent suffering
  • A: God is able to prevent suffering
  • O: God is omnipotent
  • L: God is loving

The next thing we need to do is work out the structures of the premises. Again, have a go at this before you read on. (If you’re puzzled by the structure of the English sentences, there’s a hint in the next paragraph.)

Hint: The first premise is a conditional with an antecedent that is itself a complex sentence.

OK. Here’s are the premises and conclusion in our formal language:

  • ((W & ~A) (rightarrow) ~O)
  • ((A & ~W) (rightarrow) ~L)
  • ((W & A) (rightarrow) ~S)
  • S
  • ~(L & O)

We’re going to work out whether this argument is formally valid, using truth-table methods. But before we press on with that, let’s think about exactly how we’re going to do it.

© University of York
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Logic: The Language of Truth

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