I'm generally glad your exploring this topic and posting about it, but I think you get the details wrong here in this opening paragraph (in a way that doesn't impede what follows but that still matters):
For logical positivists, deeming something a "social construct" is like signing its death-warrant. But really all it means is that the Litany of Tarski doesn't apply. If there is no underlying reality to the thing, we are allowed to decide what we want it to do for us, and with our thoughts make it so.
I'm not 100% sure I could pass the ITT for a logical positivist, but I think the "death warrant" framing gets their position wrong. Social fact that bottom out in observable behavior are fine for positivists because they can be verified same as other observations. So I think they'd happily accept much of social reality because it can be observed, and only throw up their hands at inferences that can't be verified (and only for so long as they can't be verified, assuming this is an information availability issue and not a fundamental issue).
I also don't think it follows that the Litany of Tarski doesn't apply. I could see that making sense if you buy into something like realism and consider social reality outside of what is so, but we can read the Litany as being just about what's so as experienced (since experience is the only source of signal about what is that we have), in which case it very much still applies to something we might construe to be a social contract, though obvious any notion of a contract is conceptualization applied to what is experienced.
That's fair; I'm trying to gesture at a certain cluster of rhetoric I sometimes come across, and I may be caricaturing or strawmanning by calling it "logical positivism":
A sentence like "The Congress of the United States shall consist of a Senate and a House of Representatives" is not "false", but it's not "truth-apt" either. It also wouldn't really make sense to apply the Litany of Tarski: "If the Congress of the United States shall consist of a Senate and a House of Representatives, then I desire to believe that the Congress of the United States shall consist of a Senate and a House of Representatives...". Maybe I think Congress should consist of one house, or three, or should be abolished, but this is unrelated to any belief about an underlying "reality" that this statement somehow fails to correspond to.
You can cash out "The Congress... does consist of..." into empirical observations, but I think people speaking imprecisely may confuse this with the "shall" version.
To give the analytic tradition its due, the concept of illocutionary acts was later developed to cover statements like this, but it would be hard to fit it into the framework of "classic" logical positivism (i.e. that everything is either an empirical fact, or a tautological relation of ideas, or else meaningless).
Yeah I agree it the idea of social constructs very much goes against the vibe of logical positivism, which is often what matters when talking with people who have it as their worldview. Logical positivism has long been shown unworkable, but many still cling to naive, intuitive versions of it, so I very much understand the impulse to push back on it (I've done the same myself many times!).
I wish we had a good name for the kind of strawman rationality that includes naive logical positivism that wasn't "strawman rationality" or "straw rationality" because it's not a fake position designed to be knocked down, but a real set of beliefs people hold that have to be argued against (especially among many people who are part of the rationalist scene).
We can go to Washington DC and observe Congress and see whether it does meet in two houses, and whether people do reliably call those houses the Senate and the House of Representatives. If we see that's actually what happens, then in what sense is the Constitutional provision not truth-apt? By learning what that provision says, we gain a correct prediction of what those people in DC actually do.
Occasionally, a law does become non-predictive. One example of this is selective enforcement, for instance the (real or purported) phenomenon of driving while black. The law says that anyone breaking the traffic laws gets a penalty. If the actual practice were that black drivers get penalties and white drivers don't, then the law would not predict the practice. This is why the courts have the ability to rule that a law may be constitutional as written but unconstitutional as applied.
[Followup to: We live in a society]
For logical positivists, deeming something a "social construct" is like signing its death-warrant. But really all it means is that the Litany of Tarski doesn't apply. If there is no underlying reality to the thing, we are allowed to decide what we want it to do for us, and with our thoughts make it so.
We have money, so we don't need to barter; we have language, so we don't need to point-and-grunt; and if one of those things isn't doing its job well, it's within our hyperstitious powers to change it.
So what does this vacuous-sounding statement "society is a social construct" mean? It's really just a restatement of Arrow's Theorem, which (to recap) says that there is no objectively correct way of aggregating the preferences of a group of people into a choice function that behaves in the way a rational actor would. Therefore, when we make statements like "Society prefers X" or "Y is bad for Society", our precise meaning is to some degree arbitrary. Granted, we can speak objectively about Pareto efficiency (i.e. making at least somebody better off, and nobody worse off); but by the time someone is talking about "the social good" we know we must already have run out of Pareto-improvements because those can be justified through individual appeals alone. Therefore statements about "Society" contain an embedded definition (perhaps a utilitarian calculation) about how individuals' conflicting preferences can be traded off in order to say what "Society" wants.
Edgy-teenage-me noticed this, and also noticed that such statements are invariably paired with the implicit value judgement "...and you should act in the interests of Society (as I've defined it)."
Perhaps, according to someone's definition of Society, one might disagree with that value judgement. Unfortunately, edgy-teenage-me didn't understand these issues well enough to say that. Instead, he decided to reject the enterprise of "defining Society" altogether. If, as Arrow shows, there is no objectively correct definition, then I don't have to accept any, and so I don't - so there!
As I explained, that attitude was somewhat wrong-headed. In Social Construct Land, we can define anything however we want. The question should really be: Can I come up with a definition of Society such that I would agree with the value judgement?
Let's start by scaling back our ambitions drastically. Forget trying to define a social choice function for a nation of 350 million; forget even small towns and villages. Instead let's consider (you guessed it) voluntary associations, guilds, corporations, all that kind of thing. This should be a lot easier. Firstly, the preference-aggregation function (i.e. some kind of deliberation and voting procedure which, if followed, defines the "will" of the organization) is explicit and clear, and we can refine it as needed. Secondly, because the association is voluntary and not just a random selection of people, we are starting with a group whose interests are at least somewhat aligned. And thirdly, in any event we are not requiring that anyone surrender their individuality in toto to the greater whole; the organization exists for a particular purpose, and outside of that scope there is no need for the aggregation to apply. (We are looking for business partners, not life partners.)
Given that, we can set about summoning our "egregore". It will not always behave perfectly rationally (as per Arrow's Theorem), but this is no great concern, since one can perfectly well derive benefit from a being that acts with less-than-perfect rationality (animals, children, adults...). The gamble each member makes, therefore, is that the egregore will act in one's interest most of the time (such that the good outweighs the bad), and that by the power of cooperation and supra-linear scaling it will do so more effectively than anyone acting alone.
As a general rule, majoritarian decision-making works well so long as the group members' views on various issues are distributed fairly independently, such that everyone can expect to be in the majority most of the time. Of course, this doesn't work in highly factionalized groups where there is a persistent minority that is in the minority most of the time. Such people will quickly realize that the arrangement is not in their self-interest, and drop out to do their own thing. So, again we need to fall back on the voluntary and scope-bounded nature of the association - majoritarianism can work if there is some alignment as to the overall goals of the group, even if imperfect. And just to be sure, it also helps to temper the majoritarian principle with some rules enabling exchange of opinions and protecting the basic rights of the minority, so that the entity can strive to act in the interests of as many of its members as possible.
So, to summarize: A group of people can summon an egregore into existence by following certain self-created bureaucratic procedures; this is what we call a guild (or association, society, whatever). The guild can be effective if its members are generally aligned to its purpose and if it focuses on things which are better done collectively than alone. And thus each member can find it in their own interest to play along with the social construct and keep the egregore alive, even if it sometimes acts irrationally or against one's interest.
If you've never seen this in action before, it may superficially resemble a cult of the classic type - a whole bunch of people performing strange rituals and getting invested in some "fictional" entity, perhaps even identifying themselves with it. But this is more of a sign of our impoverished vocabulary than anything else. In a society full of guilds, none of this is at all out of the ordinary, and nobody feels that their whole identity is being swallowed up in any one egregore, because there are plenty of others to choose from. It's a tall order, but we can push through the strangeness and start rebuilding this culture here and now, one guild at a time.