Many explanations of the term “social construct” are severely lacking. Let me explain what I personally mean when I call something a social construct. Largely, it means that we could have done it differently.
Gender is a social construct. Our ideas of which things are for men and which are for women has differed over place and time. Little boys used to wear dresses, women used to be considered mentally unfit to own property, gender nonconforming people (like women wearing pants) used to be shunned by their community. And that is just Western countries over the past century, without considering different millennia or cultures. We could change our current notions of gender without the gods coming down to interfere with our ambitions.
Money is a social construct. By choosing to redistribute or not, we shape the role of money and the way it influences the rich and poor. Same for (dis)allowing usury, theft or private ownership of the means of production, to name a few socially constructed aspects of private property and thus of money. Every facet of money is constructed through a social process, but the resulting structure can impact a person’s life as much as the law of gravity.
Mathematics is a social construct.1If you’re a platonist, read this as “our practice and understanding of mathematics.” I refer to the mathematics we know, not the mathematics that can be. There is no linear “tech tree” forcing people to develop Euclidean geometry before graph theory or predator/prey models. No law of nature tells pure mathematicians to abhor the thought of their work finding practical use. Instead of sorting computational problems into various Turing degrees,2Computable problems have the lowest Turing degree. The halting problem has a higher Turing degree. There are infinitely many other Turing degrees, some of which are higher or lower than the halting problem and some which are incomparable we could have been doing something useful instead. Peer reviewers use their own judgement to decide whether a result is novel, interesting and proven with enough rigor, no objective measurement devices involved. The choice of what is Real Mathematics and what is not is similarly arbitrary.
I tell people that a thing is socially constructed when I want to remind them that they could be different. When they’re talking about the thing as if it is a fixture of life and I want to invite them to imagine how it could be changed. Because no matter your philosophy of mathematics or external reality, the way we understand and value various ideas is always different among individuals and communities.