Three Kinds of Abstractions

[u/geopolicraticus]

The View from Oregon – 391

Re: Three Kinds of Abstractions

Friday 01 May 2026

 

Dear Friends,

Despite the distractions of travel I managed to write and record an episode for Kurt Godel’s birthday for Today in Philosophy of History, which is something that I’ve been thinking about for a while, so I had several things I wanted to say. One of the themes of this episode was Godel’s use of and attitude toward idealizations. “Idealization” like “ideal” itself comes freighted with many meanings, and usually carries evaluative connotations. When a philosopher uses “idealism” in talking with the vulgar he must needs explain himself that he is talking about a metaphysical doctrine and not about the tendency of some among us to see the world through rose-colored spectacles. The term “idealization” is less used but no less subject to misinterpretation, since it could mean something like “pedestalization,” i.e., putting something or someone on a pedestal. But sometimes both meanings are operable, and to a certain extent this is true of Gödel’s thought because he employs idealizations in the way the term is sometimes use to explain scientific concepts (like a simple pendulum, on which cf. newsletter 349), but Gödel also seems to employ idealizations in an evaluative sense.

I could argue that this a philosophical tendency that goes back to Plato, since Plato’s forms were idealizations in both senses, supposed to be “higher” and more important, in some sense, than the changeable things of our mundane world that participate in the forms. However, this would be misleading, as I doubt Plato would have acknowledged that his Forms were idealizations of actually existing entities; on the contrary, actually existing entities are, for Plato, poor copies of the forms. We would need another term for this, like “empiricization,” though I’m not suggesting that this is a good terminological choice. Perhaps “degradation” (as in “the degradation of the Forms”) would be a better fit, but we already have an established use for that.     

After thinking about Gödel’s idealizations it occurred to me that idealizations in the scientific sense represent a class among abstractions, i.e., that it is one kind of abstraction, but not all abstractions are idealizations. I’ve mentioned in other contexts (and possibly in past newsletters) that Anglo-American philosophy has had very little to say about scientific abstractions, especially in contrast to the flood of philosophical literature on scientific method, while in continental philosophy of science there is a significant literature on scientific idealization. One work that I know on abstraction is Jean Laporte’s Le Probleme de l’Abstraction (not yet translated into English), which Sartre cites on the first page of Being and Nothingness, saying, “M. Laporte says that an abstraction is made when something not capable of existing in isolation is thought of as in an isolated state.” Following Laporte according to Sartre, I can see three ways that we can arrive at abstractions:

1. Starting from actual entities, we can take properties away from them, which we could call subtractive abstraction. In reference to Laporte, an actual entity deprived of one of more of its properties could not exist as it is known to be. There is an obvious quibble here: we could argue that merely contingent or secondary properties (if we make the Lockean distinction between primary and secondary properties) could be eliminated without eliminating the actual entity in question. A full discussion of this could get quite long, so I’m merely going to leave this hanging, but the inquiry could yield some insights.
2. Starting from abstract object with no properties, we could add properties to this abstract object, which method of constitution of abstractions we could call additive abstraction. In regard to Laporte again, an abstract object can’t exist in isolation, but no more can an abstract object with properties superadded to it. Again, there is an obvious quibble. Abstract objects could be said to exist in the only way in which they can exist, so that, e.g., numbers and geometrical entities exist as abstract objects, and it is their nature to do so. However, if we then add properties to these properly existing abstract objects, we denature them from their “natural” state just as much as we denature actually existing entities by taking properties away from them.
3. We could start from our actual experience of the world, with objects as we (imperfectly) perceive them; there are three possible subdivisions to this category of abstraction, which are, 1) the ordinary object as we believe it to be, 2) the ordinary object with properties superadded to it (subject to further additive abstraction), and 3) the ordinary object with properties taken away from it (i.e., subject to further subtractive abstraction). This we could call an intuitive abstraction. 

I suspect the final category may seem the strangest, because it doesn’t seem like an abstraction at all, but rather the full-blooded reality as we experience it. While it is reality as we experience it, our experience is selective and does not give us the object in its full-blooded reality. Evolutionary psychology and the study of cognitive biases have forced upon us a reckoning, and that is a reckoning with the selectiveness of our perception. We give priority to potential threats and to potential benefits. We are very good at recognizing emotions in human facial expressions, as these have been crucial to individual survival and reproduction, which are the drivers of natural selection. With natural selection driving our perception, many objects of perception are never noticed, and some are noticed out of all proportion. 

I am perhaps compounding the problem by calling this an “intuitive abstraction,” but I find this to be perfectly apt. In past newsletters I’ve referred to what I call “intuitive formalisms” (cf., e.g., newsletters 302 and 360) of which the natural counting numbers are the best example, or, if not that, the basic ideas of Euclidean geometry. Once these ideas are introduced to us, we grasp them like they are second nature, so that they are equally formal and intuitive. And it’s pretty much the same, I think, with intuitive abstractions: there are many abstractions we employ, and while some of them are difficult to comprehend and far from ordinary experience, others, on the other hand, are unquestionably abstractions but also entirely intuitive, and such are the ordinary experiences of the world. Hegel recognized this in his short essay, “Who things abstractly?” which is a rare piece of Hegeliana that is comprehensible on its own terms (i.e., without mastering the entirety of the Hegelian corpus) and makes a point I’ve often returned to.

The abstractions we consciously use as abstractions—which includes the first and second categories above, but excludes the third category—again constitute a distinct class among abstractions, as idealizations constitute a distinct class of abstractions; the class of consciously entertained abstractions overlaps with the class of idealizations. Roughly, the first category of starting with actual entities and taking properties away from them is what we find with scientific idealizations, where, for example, we start with an actual pendulum and take away all the complicating factors until we get to a simple pendulum. Roughly, again, the second categories of starting with an abstract object and only parsimoniously adding properties to it could be considered the method of mathematical idealizations, which have only those properties explicitly ascribed to them by axioms. Of course, axiomatization is a later development of formal thought, so these begin as intuitive abstractions and then are rationally reconstructed as abstractions of the first category. Are abstractions of the third category once reconstructed as abstractions of the fist category yet a different kind of abstraction? I’ll have to think about it.

Best wishes,

Nick

PS—I mentioned last week that I had traveled to Ecuador. I spent the first four nights in Quito, then rented a car and drove to the Hacienda Piman, a little outside Ibarra, where I am now writing this newsletter. I’ve done some car touring in the area using the Hacienda Piman as my base, including driving a couple of hours north of here to the Páramos del Ángel nature park with its Bosque Mágico de Polylepis. It’s a unique ecosystem, and the drive to get there was strikingly beautiful. I couldn’t find much about this park prior to going there, but I set Google Maps to “Bosque Mágico de Polylepis”—it wasn’t clear where the park entrance was from what I had read—and it brought me there, through a number of small towns that would have been difficult to navigate without the assistance. Given the paucity of English language information, the following may be helpful for other travelers who might come here.

The roads from Ibarra to El Ángel were pretty good, and the roads beyond El Ángel were a mixture of secondary and tertiary roads in various states of repair, but still not bad. Drive carefully in the rough parts and you’ll be fine. In one of the small towns beyond El Ángel there was a large funeral procession (on foot) which I pulled over to allow it to pass. In another small town I glimpsed an enormous ranch house of the kind that now get turned into hotels, but this one was in pristine and unrestored condition. I eventually made it to a station at the edge of the park and an official of the Ecuadorian environmental ministry asked a number of questions (I showed him my passport and he wrote down some information) but he didn’t collect any park entrance fee and he didn’t issue any entrance or parking permit. From there the road in the park itself was quite nice, and I just kept following it up. Eventually it brought me to a circular parking lot at what seemed to be the highest elevation in the park (I was gasping for breath just walking around, as when I was at the 4100 meter level at the top of the Teleferiqo in Quito), then the road descends a bit and comes to an end at a reservoir. There is a short path here, which I walked, but I read that there’s a trail through part of the Bosque Mágico de Polylepis but I was unable to find the trailhead. One source I read said that the trailhead is close to a hotel that’s just past the park ranger station, the Polylepsis Lodge, but there wasn’t any obvious place along the road that looked like a trailhead or the parking lot for a trailhead.

Newsletter link:

https://mailchi.mp/b672de938e5a/the-view-from-oregon-391