A few related thoughts on abstraction: 1) One classic way to think about abstraction is as the process of forgetting stuff on…
A few related thoughts on abstraction:
1) One classic way to think about abstraction is as the process of forgetting stuff on purpose. You look at a concrete situation, in all its infinite complexity, and say “ok, for the given problem I’m trying to solve, which of these details do I have to worry about and which can I ignore?” You then pick some to keep and “forget” the rest, and there you have an abstraction. This is both very powerful and very dangerous.
One reason abstraction is powerful is that it can turn intractable problems into tractable ones. The human mind can’t possibly keep account of every minute detail of a situation, so if you want to get anything done you have to select a few to focus on and leave the rest for later. A problem that without abstraction would be utterly unsolvable can become manageable with abstraction. As an aside, for this reason, abstraction is also unavoidable. We’re abstracting things all the time in our everyday life, and we simply wouldn’t be able to process the world around us without doing that. There are people who don’t like abstraction, because of the various dangers in it (which I’ll get to), but to those people you kinda have to say: tough luck. Abstraction is the bread and butter of human cognition. Or something like that.
Another reason abstraction is powerful is because it allows you to generalize. If you can pick out the salient details in a situation and focus your analysis only on those, then guess what: that analysis will also be useful in all the other situations in which those salient details are the same. Since the minutiae of basically everything differ, if you refuse to abstract at all, you’ll be forced to analyze every new question totally from scratch. Abstracting allows you to pass over reasoning from one situation into another, or to reason generally about many situations at once. I hope it goes without saying that this is very useful. It’s also another argument for the necessity of abstraction: there are simply too many possible situations, too many questions, for us to think through each one separately with no overlap. Even in a very mundane sense, we need to make generalizations like “chairs can usually be sat on”, “bread is usually edible” and so forth to get through the day. Generalization is a prerequisite for thinking about and interacting with the world basically at all. And abstraction is necessary for generalization.
But, ok, abstraction is also very dangerous. It’s very dangerous because you’re forgetting things on purpose! You’re purposely choosing to ignore certain details! What if those details turn out to be relevant? What if ignoring them leads you to terribly wrong conclusions, or totally handicaps your ability to solve your problem? These dangers are not just hypothetical, they often come to pass when we’re abstracting. And this is very troubling. This is why some people think we should avoid abstraction, and why they can’t be easily dismissed. If abstraction is this incredibly powerful tool, indeed if it’s this unavoidable thing that we do, then the fact that it comes with significant inherent dangers is inconvenient, to say the least.
2) So abstraction is this sort of eldritch power, that we’d like to bring to bear on our various questions about the world, but which comes with inherent epistemic risks. What can be done about this? Well, I think one of the principle factors in the success of the sciences is that they’ve found really good methods of reining in abstraction, of keeping it on a leash, which allows them to apply it in ever more delicate situations where unmitigated abstraction would fail spectacularly.
For instance, take mathematical formalism (not the philosophical school, but formalism as in “a formalism"—i.e. rigor). Mathematical formalism is, I think, maybe the single most powerful leash on abstraction that humanity has ever devised. In mathematics, we take these incredibly out-there ideas about logic and space and structure, and translate them into a formal game of symbols that we can play on a page. Big questions about the nature of reality are turned into small questions about pluses and sigmas and epsilons. And even when mathematicians are thinking post-rigorously—using abstraction in its full power—this formalism acts as a check on just how much it can run amok.
Mathematical formalism is so powerful, in fact, that it rules out the vast majority of abstractions we make in everyday life. "Chairs can usually be sat in”, and “bread is usually edible” don’t stand up to its very high standard. In fact, no empirical observations stand up to its very high standard! Once this formalism has been applied, only the abstractions that we can really control remain, those bound indelibly by logic. Everything else is blasted away. This lets us apply abstraction in ever more complex ways in mathematics, where in other fields we’d lose control of it. So we tend to think of mathematics as a very abstract field, but I think this framing leaves the most important part out! Mathematics might be better understood as a field that could become very abstract while staying productive, because its abstraction-leashing tools are so powerful.
In contrast (I know this sounds contentious, but hear me out), I think philosophy is what happens when you give yourself no abstraction-leashing tools at all. And, look, I like philosophy a lot (in fact, I’m doing philosophy right now!), but the thing about philosophy is that it’s really easy for philosophy to be bullshit. There’s a lot of really great philosophy out there, but there’s also a lot of… total nonsense. Words on page. Just absolute blabber. Why? Well, maybe one reason is that a lot of philosophy seems to set up some abstractions and then let them totally run amok, ride them wherever they go, just go wild with it. And this is really fun, it’s what like half of my posts are. But it often leads to nonsense, to just saying a bunch of words that mean almost nothing at all. You’re out in abstraction land and your connection to the real world has been totally severed.
Perhaps that’s another way to think about abstraction-leashing, as a sort of tether between the abstraction and the real world. You need some kind of wire, hooking your abstractions way up in the sky to concrete things here on the ground, so that all the convolutions going on way up there can be translated into something actionable down here. Without some sort of tether, some translation scheme to turn abstract into concrete and vice-versa, your abstraction doesn’t do much good. It just floats around up there, disconnected, not able to actually say anything. And because you’re a concrete being who ultimately can only take concrete actions (of which even thought is a subset), I’m tempted to say that you can’t even meaningfully interact with an abstraction that lacks a proper translation scheme. You can solve a math problem by shuffling symbols, that’s something you can do. But in philosophy you have all these intractable problems, and it looks to me like one of the main reasons for their intractability is that you can’t “get at them” the way you can “get at” math. You have no tether, no way of concretely interacting with the objects and ideas under consideration, so they just kind of aimlessly float around.
3) So anyway, I’d like a name for these tethers, these abstraction-leashes. And I think a good one is “concretization schemes”. A concretization scheme is a method for translating between the elements and conclusions of your abstraction on the one hand, and the concrete elements of your immediate experience (things you can see and do, etc.) on the other hand.
The concretization scheme in mathematics is mathematical formalism. The concretization scheme in physics is measurement. Actually there’s a quote, which I think I saw in Spivak’s Physics for Mathematicians, that’s something like “In mathematics we introduce new primitives by providing axioms for their behavior. In physics we introduce new primitives by defining a process for measuring them.” That’s exactly what I’m talking about. That’s laying down a concretization scheme.
In general, measurement and experiment are the concretization schemes for the sciences, but I think it’s important to distinguish this concretizing role (whose primary function is, in some sense, to give the abstraction meaning) from the epistemic role of experiment (whose primary function is to check whether a theory is predictive). But these things are maybe somewhat inextricable, since giving meaning to an abstraction often means giving truth conditions, and giving truth conditions is often inextricable from having a specific way to check truth conditions. So I think it’s fair to say that truth-checking procedures are often a fundamental part of concretizing, of reining in abstractions, but they don’t in principle have to be.
Here are some more diverse examples. I think the concretizing scheme in language learning is speaking, reading, listening and so on. You turn abstract grammatical concepts into something specific you can do with people, and thereby get (implicit and explicit) feedback and can appropriately modify the abstractions in your head, etc. The concretization scheme for these same abstractions (grammar) in linguistics is a bit different—it should be measurement and experiment—because linguistics is aiming to be a science. So the same abstractions can have different schemes for different ends. A lot of good philosophy has a concretization scheme burried in it somewhere, like a lot of philosophy of science is concretized in actually performing various different scientific methodologies. And so on.
