The basis of the argument is, as with all natural law arguments, simple on the face of it. The details, and replies to potential objections, can become complicated, and when I was Catholic I wrote a couple dozen pages on this form of the argument. Here I’ll just show the argument itself, cite some of my sources, and then wait for replies.
A natural law argument for the evil of an act can be represented as
(Foundational Assumption) All human actions are oriented to an intrinsic end.
(Definition) An act is evil if it is intentionally carried out in a way opposed to its intrinsic end.
(Premise 1) Act X has the intrinsic end E.
(Premise 2) Intentionally committing X in a way that frustrates E forces X to be opposed to E.
(Premise 3) A possible component C included in X entails that X be committed in a way that frustrates E.
(Prop) Intentionally including C in X forces X to be opposed to E. [Premises 2 and 3]
(Conclusion) Intentionally including C in X makes that instance of X evil. [Prop, Premise 1, Definition]
All natural law ethics use arguments similar to this, as far as I know. The problem is that many forms of natural law do not agree on the premises, especially Premise 1. They don’t agree on the good of a given act, because they find the foundations to their natural law ethics in different places. We will explore changing Premise 1 only. The argument against contraception is very simple (T for traditional, premises as above).
(TP1) Sex has the intrinsic end of procreation.
(P2) Intentionally having sex in a way that frustrates procreation forces that instance of sex to be opposed to procreation.
(P3) Contraception in sex entails that sex be committed in a way that frustrates procreation.
(TC) Intentionally contracepting during sex makes sex an evil act.
Different acts can have a lot of ends. For example, sex produces friction and that results in heat. Sex as an end of producing heat, but that’s not the intrinsic end, because that’s not why people have sex. That’s not what makes sex good. But who is to say that procreation is the intrinsic good of sex? Maybe it’s just something that comes along for the ride. It doesn’t matter if procreation is connected to evolution and is necessary for species survival, because evolution is directionless (unless we are going to include religion with our natural law).
Rather, the natural place to look for the intrinsic end of an act is something that is generally entailed in each act by each actor, and something connected to what people generally want. Most times, food provides nourishment, so it seems that nourishment is the intrinsic good of eating. Regularly and intentionally eating while frustrating that intrinsic good is called bulimia, and natural law arguments would find bulimia to be immoral.
Most sex isn’t going to produce children, and producing children may not be in each individual’s best interest. Sex doesn’t generally result in babies. It only does so on the off chance (that’s why it has to be committed over and over). Also, having sex without having children doesn’t mean that you are “doing it wrong”. So sex can be seen to have a different intrinsic purpose. Maybe the purpose of sex is romantic pleasure for all partners involved. We’ll call this RP1. In that case:
(RP1) Sex has the intrinsic end of romantic pleasure for all partners involved.
(P2) Intentionally having sex in a way that frustrates pleasure for all partners involved forces that instance of sex to be opposed to that pleasure.
(P3) Contraception in sex does not entail that sex be committed in a way that frustrates romantic pleasure for all partners involved.
(RC) Intentionally contracepting during sex does not necessarily make sex an evil act.
There’s a very simple natural law argument (probably more in line with Hobbs’s ideas about natural law, or other non-Thomistic natural law theories). Its conclusion is that contraception isn’t intrinsically evil. It’s at worst morally neutral.
So that we don’t lose sight of what I’m arguing: I’m not arguing that contraception isn’t evil. I’m arguing that natural law by itself is too flexible to show that contraception is evil. Revelation, in the form of religion or some other source, is necessary in order to determine what the intrinsic ends of a given act are.
Natural law arguments, without the Catholic religion or some Christian religion to definitively reveal the intrinsic ends of human activity, tend to conclude that nothing is wrong with contraception.
Beis, Richard H. “Contraception and the Logical Structure of the Thomist Natural Law Theory.” Ethics 75.4 (1965): 277-284.
Grisez, Germain Gabriel. Contraception and the natural law. Bruce Pub. Co., 1964.
Pakaluk, Michael. “Is the New Natural Law Thomistic?.” The National Catholic Bioethics Quarterly 13.1 (2013): 57-68.