What is it for an argument to beg the question? I suggest that an argument begs the question if it is impossible to know one of the premises to be true without knowing that the conclusion is true. The simplest question-begging arguments are of the form
Clearly, every argument of this form is valid, and some arguments of this form are sound. It follows that an argument can be sound and yet probatively worthless. In plain English, no argument of the above form proves its conclusion in the sense of giving a 'consumer' of the argument any reason to accept the conclusion; it rather presupposes its conclusion. One cannot know the premise to be true without knowing that the conclusion is true.
Now consider a richer example: (P1) We are creatures; (P2) There is no creature without a creator; therefore, (C) A creator exists. This argument begs the question in that it is impossible to know that (P1) is true without knowing that (C) is true. For only if I know that a creator exists can I know that I am a creature. The argument is not probative because it presupposes in (P1) what it needs to prove. (Of course, I am assuming that one is not equivocating on 'creature' and that one is using it in the sense in which it must be used for (P2) to be true; if one is equivocating, then naturally the argument is worthless for this reason.)
Now it might occur to someone to wonder whether logical arguments from evil for the nonexistence of God also beg the question. Is there anything to this notion?
Logical arguments from evil start with a fact, the fact of evil. No doubt evils exist. But for evils to prove the nonexistence of the omni-qualified God of traditional Judaism, Christianity, and Islam, these evils must be gratuitous. A gratuitous evil is one that cannot be reconciled with the existence of the omni-qualified God, for example, an evil that God has no morally sufficient reason to permit, or an evil that God cannot prevent because it is the deed of a free agent. A gratuitous evil, then, is one the existence of which is logically inconsistent with the existence of God conceived in the traditional way.
Granted, evils exist. But only gratuitous evils are inconsistent with the existence of God. Only they pose a problem for the existence of an all-good God. Consider the pain of a just punishment, the pain of imprisonment, say, that convinces a miscreant, an armed robber for example, to reform his life. (Few penal punishments are truly rehabilitating, but certainly some are.) The pain of punishment is evil. But in my example, it is necessary for the achievement of a greater good. Thus the evil in question is not gratuitous.
How do we know that there are gratuitous evils? To know this, we would have to know that God does not exist. Thus we would have to know the conclusion of the LAFE to be true in order to know that its key premise -- Gratuitous evils exist -- is true. But this is the very definition of begging the question.
Therefore, it seems that LAFE begs the question. To appreciate my point, compare:
1. If there are gratuitous evils, then God does not exist.
2. If creatures exist, then a creator exists.
Both of these propositions are analytically true. So if one knows that there are gratuitous evils, then one knows that God does not exist. Likewise, if one knows that creatures exist, or that the physical universe is a creation, then one one knows that a creator exists. But how does one know either of these things? Suppose I witness a brutal and unprovoked physical assault on a human being by another human being. Witnessing this, I witness an evil. But by what mark do I recognize the gratuitousness of the evil? By no empirical mark since what I observe is consistent both with the assault's being gratuitously evil and with its being nongratuitously evil.
Something similar holds for (2). How do I know that what I see, mountains and valleys, cacti and sky is creation or created nature as opposed to uncreated nature? By what mark do I know that nature has the status of having been created? By no mark.
Return to the brutal assault. Imagine it to be perpetrated against a loved one. Atheists will naturally take such crimes as 'proof' that there is no God. But it is no more 'proof' than the existence and order of nature is 'proof' of an intelligent creator. Both athetist and theist interpret the data in the light of a worldview that precedes the data and is imposed upon them. Each can fit the data into his scheme. But fitting data into a scheme is not the same as data proving a scheme. Thus the brutal assault fits the atheist's scheme but does not prove it, and the existence and order of nature fits the theist's scheme but does not prove it.
So here is my challenge to Peter and others: explain how LAFE does not beg the question against the theist.