In studying arguments, it is often worthwhile to think about the most general form of the argument you are considering, as well as the general family of arguments of which it is a part. This often makes structural features more clearly; it can also point out problems or difficulties an argument might have that are common features of a whole family of arguments. This is particularly useful, I think, with the argument from evil.
Transcendentia or transcendentals are terms that are not confinable to a category; in a slightly stricter sense, the term is used to indicate terms that are not confinable to a category because they are coextensive with being, which is the generally considered the most conceptually fundamental transcendental term. Scotus, following a line of thought in Bonaventure, notes that there are divisions of being that are transcendental in this sense as divisions; the particular disjuncts are not transcendentally coextensive with being (although they may still be transcendental in the slightly broader sense of transcending any given category), but disjunctively they are. These are often called 'disjunctive transcendentals' today. Examples are one/many, infinite/finite, absolute/relative, dependent/independent simple/composite. necessary/contingent, true/false, and good/bad. There are many, many more.
The disjuncts of such transcendentals are in some sense opposed to each other, although the exact nature of the opposition can vary quite a bit (because there many ways you can divide being). The cases we'll be interested in are cases in which the opposition is at least purportedly exclusive, in the sense that the disjuncts are positive contraries. The premise in arguments from evil, of course, is always some version of the idea that good excludes bad; if we speak metaphorically, they 'push each other out'. The reasons given for this kind of exclusion vary a lot; in terms of basic structure, this does not matter, but arguing over these reasons makes up the greater part of almost any discussion of an argument from evil.
For our purposes, we also want cases in which the opposition has a particular sort of asymmetry, which traditionally was described as an asymmetry of 'nobility'. One of the disjuncts is what we would call higher, better, superior, whether this indicates that it is in some way more fundamental. In the case of arguments from evil, of course, good is treated as the nobilior disjunct. Pinning down an exact account of nobility in this sense is a tricky bit of metaphysics, but for our purposes, we can take the nobilior to be the one that is most obviously the kind of thing that is suitable for God.
Arguments from evil generally tend to make identifying the nobilior disjunct easier by cross-fertilizing disjunctive transcendentals. A very common way of doing this is to combine the good/bad transcendental with an infinite/finite transcendental. Thus, the arguments usually oppose not good and bad simply (which would give us a possible argument from evil, but one that would take an immense amount of argument to defend), but infinite good and at least finite bad. This doesn't fundamentally change the nature of the argument, but this cross-fertilization makes both the exclusive and the asymmetric opposition of the disjuncts much more vividly plausible. One might hem and haw over whether good is more fundamental than bad or whether good excludes bad as a contrary, but many people will assent immediately to the claim that infinite good is superior to and excludes merely finite bad.
Given all of this, we can characterize an argument from evil in the terms we have been using. The most general form one finds is:
(1) Some things are bad.
(2) Good would be more fundamental and opposed to bad.
(3) Therefore, there is no good.
This in its bare form is obviously not a popular one. More common would be a cross-fertilized kind, e.g.,
(1A) Some things are at least finitely bad.
(2A) Infinite good would be more fundamental and opposed to at least finite bad.
(3A) Therefore, there is no infinite good.
But, again, we could cross-fertilize good/bad with more, or with other, disjunctive transcendentals than infinite/finite, e.g.,
(1B) Some things are at least contingently bad.
(2B) Necessary good would be more fundamental and opposed to at least contingent bad.
(3B) Therefore, there is no necessary good.
In practice, though, there are other ways in which this basic argument-form might be varied. First, we might specify it to a particular domain (instead of talking good/bad in general, we might talk about natural, moral, intellectual, etc. good/bad). Second, we might break down the division in finer ways using some other distinction (e.g.,, we might want to make a distinction between gratuitous and nongratuitous bad). Third, we might treat the opposition as probabilistic rather than necessary (as is done in what are commonly called 'evidential arguments from evil').
Recognizing all of this, however, we can identify a general family of arguments that would work along the same lines of an argument from evil; that is, we can generate a large number of atheistic arguments. For instance:
Contingent beings exist; necessity would rule out contingency; therefore no necessary being exists.
Finite beings exist; infinite being would rule out finite being; therefore no infinite being exists.
Diverse, plural beings exist; being that is properly one would rule out diversity and plurality of being; therefore no being that is properly one exists.
Some things are potential; pure actuality excludes potentiality; therefore nothing is purely actual.
Some things are at least contingently false; necessary truth excludes at least contingent falsity; therefore nothing is necessarily true.
Composite things exist; simplicity would rule out composition; therefore no simple being exists.
Some things are relative; if something were absolute, it would exclude relativity; therefore there is nothing absolute.
We could, again, multiply these indefinitely. We certainly do find some of these arguments occasionally given (sometimes varied in the ways noted above), which we can take as confirmation that we are identifying the family correctly.
The most useful thing we gain by identifying the general family of an argument is seeing more clearly what problems and weaknesses it shares with the rest of the family; these usually indicates problems that are not really eliminable no matter how one tries to adjust the argument. When we look at the kinds of argument we get in generalizing from the argument from evil, we find that all such arguments have at least two immediate related problems, both of which arise for arguments from evil in general.
I. The disjuncts in such transcendentals are often not in fact opposed as contraries but as positives and privatives. Thus exclusion premise in such cases is false. The opposition between the disjuncts in disjunctive transcendentals is often (and perhaps always) one of privation, not contrariety. The less noble disjunct is distinguished from the more noble simply in lacking something that the more noble has. If this is the case, then the question of why the less noble exists in a given case is simply that something required for the more noble is missing; it arises from a defect, and not from some positive exclusion.
This is related to another, less obvious problem, which is that all arguments of this form treat a perfection or example of the nobilior as ruling out defective causes. But in general there is no reason to think that (e.g.) necessity in one thing rules out something being a source of a defect of necessity in another thing.
In the case of the argument from evil, arguing for the relevant kind of exclusion regularly runs into problems if we accept that (a) badness as such is merely a privation of good or (b) some causes are good that nonetheless can be sources of a lack of good in other things. (Both of these claims are in fact generally held, the latter especially in the case of free will, although there are other things, like corruptible or defectible goods, that can be used.) Similar problems arise, however, with other arguments in the family.
II. The less noble participates the more noble, being unable to exist without the nobler, so actually proves the existence, not nonexistence, of the nobler. That is to say, the asymmetry, while necessary for directing the argument in one direction, also works against the argument. We can sum it up in what might be called Scotus's Rule:
Positing the less noble in some being, we can conclude the more noble in some other being.
In the case of the argument from evil, the argument will always run into the difficulty that (on certain common accounts of badness) the existence of bad implies at least the existence of good, and, if one accepts Scotus's Rule in the case of infinite-good/at-least-finite-bad, the existence of infinite good. One could, of course, reject Scotus's Rule, but the point is that every argument from evil, as well as all the other atheistic arguments generated, can be turned into an argument for God's existence in this way.
Again, these problems will tend to be ineliminable. They are answerable, in that you could bite the bullet with each, arguing for a positive theory of evil, or rejecting possible defective causes, or denying the participation accounts that give one something like Scotus's Rule. But, given the structural issues, what this means is that these are really the points on which the acceptability and cogency of the argument from evil hang.
