Same-sex marriage and the fascinating “empty set problem”

… well, I find it fascinating! Not sure if anybody else will. lol

People who argue for same-sex marriage often, if not always, rely on what I call “the infertility argument.” This argument posits that because some opposite sex married couples do not bear children, this means that marriage is not procreative. This becomes the door, so to speak, that people use to justify same-sex marriage.

empty setThe argument has a really fascinating problem, one that is little-known. In fact, I’ve never seen it addressed so I think I am the first person to identify it. I call it, “the empty set problem.” The argument depends on a definite set of infertile opposite sex couples, but I will show how it is not possible to identify the actual members of the set. That is why I say it is an empty set. Let me be clear: the set of permanently infertile opposite sex couples exists. See the brackets on the left? The set is real. The problem is that its members cannot be identified with certainty.

Since all of the members of the set of same-sex couples have a literal 0% fertility, all of the members of the comparison set must also have a literal 0% fertility. To be fair and just, we must apply an equal standard to both sets. Unfortunately, proponents of the infertility argument are not careful in their thinking. They are content with theoretical members in their set of infertile opposite sex couples, members that they don’t have to actually identify. I also suspect that they would be content to have an unequal standard between the two sets, that they would be content to let the comparison set have something slightly above a literal 0% fertility, although I can’t prove this. I do know that they toss this set into the discussion, assuming it is full of members. But arguments depending on a set of real couples must have real, identifiable couples in the set and the standard for comparison must be equally applied.

Let’s do a thought experiment. Imagine a football stadium, filled with married opposite sex couples. Now, go through this set couple by couple and identify two characteristics about them:

  1. Which of them are, and will forever be until they die, 100% infertile.
  2. Which will have one spouse die at some point in the future, and the other spouse goes on to remarry and does not bear children in subsequent marriages.

A medical doctor trained in fertility could do the first task but not with 100% certainty across the entire population, and the second task can’t be predicted by anybody.

Quite naturally, these tasks apply to elderly couples. For example, we must predict, with 100% certainty, which actual elderly couples will have the wife die, and then the husband goes on to remarry a younger woman and not bear children. I can’t predict that. Can you?

Now, let’s remove the football stadium and apply this to the entire population. Plus, in real life across the world, new couples are entering the actual set of married, opposite sex couples all the time. Now do those tasks again.

We can’t cheat by using statistics or speaking in generalities, and we must apply the same standard to both sets. We are talking about real couples, so real couples must occupy the set. I don’t think we can identify the specific couples with 100% certainty, but I might be wrong. Perhaps somebody can. Even if it can be done by somebody, the number of members in the set will be dramatically less than people realize.

If the set of opposite sex couples who have a literal 0% fertility rate is empty, this discredits the argument. But even if the set has a tiny number of couples in it, this does not validate the argument. Why? Because we can step back and demand that the burden of proof–that same-sex marriage does not change the character of marriage–rests with those making the argument. Few realize that its more honest proponents have already admitted that same-sex marriage does change the character of marriage:

“Same-sex marriage is far more radical than interracial marriage. It challenges our basic understanding of the institution.” William Saletan of

“Fighting for gay marriage generally involves lying about what we’re going to do with marriage when we get there . . . The institution of marriage is going to change, and it should change.” Masha Gessen, biographer of Vladimir Putin, as quoted in National herring

Right on cue, once same-sex marriage became law we saw headlines like this: “California deletes ‘husband’ and ‘wife’ from marriage law.” No more husbands and wives in marriage is part of “gender ideology,” and it changes the character of marriage dramatically. I am so grateful that the Church categorically rejects this change.

The infertility argument was always a red herring based on a specious premise.


Author: everybodysdaughter

I'm an adult child of divorce, having been raised in multiple divorce/remarriage situations. I'm writing in order to shed light on the problems of divorce from the perspective of the child. I will also discuss problems with other non-triad family structures, since there is a lot of overlap. People often think that better parenting skills will overcome problems in non-triad arrangements. While I agree that parenting skills are important, they cannot overcome the problems I discuss such as fractured ontology and perpetual liminality. I converted to the Catholic faith in 2012, and will discuss Catholic things from time to time as well.

22 thoughts on “Same-sex marriage and the fascinating “empty set problem””

    1. Clare, this is not hatred. Once again, you try to redefine terms. You didn’t like how I used the word coitus, so you redefined it to make me wrong. You are doing the same thing here with the word hatred. If you continue to gaslight me on my blog, I will delete your comments.

      I beg you: engage the actual argument I made without making assumptions about my motives.


          1. I think you mean “doth protest”.

            Oh, right. Argument. Gay people form couples. The two become one flesh. Those couples should have the same rights as straight married couples. Christians in England have the right to hold marriage services for gay couples in the same manner as for straight couples, as a direct result of Christian lobbying of Parliament. Praise God!


  1. I think I get your point, although I don’t think it’s necessary for us to be able to identify members of the set of completely infertile couples for the argument to work. And wouldn’t a man without testes or a woman without a womb be completely infertile? Since these both exist, the set isn’t empty.

    The crucial difference is, that no matter how infertile a man and woman may be, it is conceivable, i.e. not a logical contradiction, that they might miraculously conceive; whereas for a same-sex couple to conceive is a contradiction of them being of the same sex.

    Liked by 1 person

    1. Thanks for the thoughtful comment. I am reasonably sure that since we are talking about real couples, we must have real couples in the comparison set. By real, I mean concretely identifiable. Your example of the man without testes is good. The woman without a womb can still, if she has her ovaries and Fallopian tubes, potentially experience pregnancy. That actually sounds scary to me but technically it is possible. Now if her ovaries are missing, then that’s like the man without testes–no pregnancy possible.

      And you are correct that miraculous conceptions occur; at the very least, they might seem miraculous to the people who experience them.

      Liked by 2 people

      1. As a woman without a womb… let me just tell you that it really is 100% impossible to experience a pregnancy. Zero connection between the vaginal opening and the ovaries means there is no way for sperm and egg to ever touch each other. I agree with you that the infertility argument is a red herring, but maybe not for the reason you’re postulating. And I have ovaries- literally the only way my husband and I could ever reproduce is via IVF and a surrogate, but we’re against that on moral grounds.

        Liked by 1 person

  2. Also, it is important to know that I reject “sexual orientation” as a legitimate category. It is not based in science, and, as it is commonly understood, it strips people of their free will. While it is true that I have not stood up for gay marriage, I would absolutely stand up for somebody who experiences same sex attraction for many other reasons.For example, if they are a child of divorce I would stand up for them in that arena although their sexual urges play no part in why I care about that issue. If they experience violence because of their sexual attractions, I would condemn that violence but again, their sexual attractions aren’t why I would condemn it. And so forth. Please do not conflate my lack of support for same sex marriage as a lack of compassion for people who experience sexual attraction to members of the same sex.

    Liked by 1 person

  3. Moot point. God created human beings to love. There have been translations, upon translations of the Holy Bible. If you are a Christian it is because you believe Jesus Christ is the begotten (chosen < though that word IS missing in the current Catholic bible translation) son of God. Jesus did not condemn gays. In fact homosexuality as a whole was not even discussed in the bible, it wasn't important.

    Pope Francis is correct in stating The Church needs to apologize to homosexuals along with other marginalized (women…) groups of people.

    We are all to grow in love with God and study the teachings of Jesus Christ, without whom, there would be no "The Church".


    1. Well, sure, in one sense I agree with you about it being moot, since ssm is the law of the land. As I said, it is an interesting problem. I would appreciate it if you would address the substance of the argument.

      Would you like me to begin talking about gay people or gay sexual activity? If so, that’s not going to happen. I’ve never spoken against gay sexual activity, and I doubt I ever will. I defend what the Church teaches on marriage. I can do this as a stand-alone concept; I don’t need to talk about gay people or gay sexual activity to do it.

      Jesus did not condemn gays, and neither have I.


      1. Your article had a clear anti-gay leaning. I will defend what Pope Francis said – we owe homosexuals an apology. ~ God bless,


        1. You are adding to what I said. The issue is from a policy perspective, not an interpersonal one. I have never once spoken (or written) negatively about gay sexual activity. I don’t need to, because marriage is a stand alone issue.

          Have you apologized to gays?


          1. I have always stood up for homosexuals. I speak up to clergy also.

            I did not add to what you stated. You can’t post something like this and try to stand on the line. There is a clear leaning against homosexual relationships. That is fine, you may have your opinion. I posted, as a practicing Roman Catholic (mass daily) who chose to repeat the words of a very wise Pope.


            1. “You attacked your opponent’s character or personal traits in an attempt to undermine their argument.
              Ad hominem attacks can take the form of overtly attacking somebody, or more subtly casting doubt on their character or personal attributes as a way to discredit their argument. The result of an ad hom attack can be to undermine someone’s case without actually having to engage with it.”


            2. Your self-righteousness is ugly and offensive. And your attack in my character is wimpy shortcut. Have the courage to address my argument.

              I don’t see where it says in the Bible that I have to stand up specifically for homosexuals. Where is that? I’ll tell you: it’s not in there. It’s a made up sin you have found me guilty of committing. But don’t worry, because I have committed plenty of REAL sins, sins that are actually found in the Bible.

              You changed the goal posts. First I was against gays, and that was the sin you found me guilty of, the sin that justified you not responding to my argument. Then the sin became me not standing up for homosexuals–that became the sin that justified you not responding to my argument. You’re not focused on the merits of what I wrote, and have instead focused on these false sins you’ve created. Also, whether or not I have stood up for homosexuals is not relevant to my argument. Either my argument has merit, or it does not. If it doesn’t, explain to me why. I’ve taken time to craft intelligent arguments, and I do not respect your self-righteous shortcut. If you are a Christian, it is even worse. You’ve judged somebody of committing your false sin with almost no actual evidence of that false sin, found them guilty, and didn’t even give them the courtesy of addressing the substance of what they actually said.

              Liked by 1 person

              1. I have not attacked you, however you have clearly attacked me. You have your beliefs, I have mine. I am well with mine – as you appear to be with yours. I will pray for you and perhaps you will do the same for me.


                  1. After being insulted? Sure. I stated it is a moot point, it is. Statistics are open to interpretation. It doesn’t matter how many hetro couples are infertile. I see a hook for an argument where there should not be one. God made all of us in His image. Some are fertile, some are not, neither is a reason for or against marriage. Remember the old clause for annulment – you could annul your marriage in the Roman Catholic church if one partner was infertile. These are old idea’s and laws and they will change, though it will be over time. I didn’t really see any reason for an argument or insults – we can both be of different opinions. I am sure anyone reading our replies here has their own opinions too. Thank God He gave us intelligence and the ability to discern. – My lunch is over, back to work. Be well.


                    1. I don’t think you understand what I was saying. This might be due to me not being clear, or it may just be a difficult argument to understand.

                      For example, I specifically said that using statistics won’t work, since the set of infertile opposite sex couples must have actual identifiable couples in it, not theoretical couples. Also, the Church’s grounds for nullity due to infertility don’t change the argument. Those grounds just mean that some opposite sex couples are not in the comparison set since they aren’t validly married. They are like single people, and single people are not part of this argument.


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