How could Ceres have remained a planet?

I do wonder, however, if it is true that people were thinking along those lines then. Again: perhaps they were, and in that case I'd love to learn about it. But as far as I understand it, they were mostly concerned about the small size and relatively great number of what we came to call the asteroids. As I read it, the small size raised few objections initially, hence 'planet', but once it became clear there were a lot of them, objections began to be raised -- hence early voices already arguing against these bodies being 'planets'. But I also speculate that if there had only been, say, four asteroids and no more, they'd have retained the name 'planet', and few people would have cared that they basically shared the same orbit. What I'm trying to say is: concepts like "clearing the neighbourhood" or "dominant body" did become important later on, and for the very good reasons you mentioned-- and when they did, their relevance was implicitly seen in the 1851 decision, with which such concepts fit perfectly. But I suspect that in 1851, they weren't actually a deciding factor at all.
The small size of asteroids actually raised objections from quite early on. As early as 1802, William Herschel suggested that they be called asteroids because they were too small to be planets.
But from what I can find out from sources (mostly summaries rather than works published in the 1850s, those being hard to find nowadays) the presence of multiple bodies in a similar orbital zone also played a part, and particularly the prospect of many more bodies in that zone. So clearing the zone appears to be almost inevitable at that point.

If I am right, however, about the state of such things in 1851, and we accept such a POD as possible (although I do not even consider it very likely-- just not ASB or anything), then you'd get a scenario where concepts like "clearing the neighbourhood" or "dominant body" never become a part of the definition of 'planet'. Not even implied. In fact, the opposite happens: certain objects that basically share one orbit (namely Ceres, Pallas, Vesta and Hygiea) are all called planets in that scenario! In this specific scenario, it is still possible that - after the discovery of increasing numbers of trans-Neptunian objects - 'planet' is redefined pretty much as it is in OTL. But given the circumstances, just going with "has achieved hydrostatic equilibrium" is also possible (unlike in OTL). That would keep Ceres as a planet (as well as Pluto). And yes, that would mean... dozens of potential small trans-Neptunian planets. Pretty unacceptable in OTL, but who knows? Perhaps acceptable in the ATL. (After all, I doubt they'd force kids to learn all those names in school. ;) They'd just call them "the trans-Neptunian planets". Maybe mention Pluto by name.)
The problem is that in the 1850s, there's no way to draw a line. It's not clear in the 1850s which bodies are in hydrostatic equilibrium and which aren't; telescopes aren't yet that powerful to do so reliably. So there will be a case of asteroid after asteroid being discovered and no-one being sure where to classify them. They're not even sure if Ceres is or isn't, and no real chance for the smaller ones. So the pressure will be along the lines of "all these things share the same orbital zone; whatever they are, they aren't planets".
 
The essential difficulty with defining planets is that there are two quite different ways of categorizing “things that aren’t stars” in a given solar system, which may be referred to as the “dynamical” and the “planetological” approaches. The dynamical approach is concerned with how things move, while the planetological approach is focused on what things are; that is, the dynamical approach asks, “How does this body affect other bodies, and how is it affected by them in turn?” whereas the planetological approach asks, “What is this body made out of, what is its internal structure, what processes made it the way it is?”

This immediately leads to quite different approaches to classification. The dynamical approach is, naturally, interested in grouping together objects that share similar dynamics: objects that orbit other objects (that aren’t stars), objects that are more influenced that influencer, and objects which are more influencer than influenced. Hence the language of moon, minor planet (and dwarf planet, and comet), and planet, which maps quite distinctly to this way of looking at the universe, especially with the recent definition of the last term to explicitly use dynamical criteria. By contrast, the planetological approach groups together objects that share similar internal characteristics, sizes, and other body-specific properties, as with “super-Earths” or “hot Jupiters” in exoplanetary research. In this case, a useful dividing line between planet and not-planet might be something like "is this body in hydrostatic equilibrium", since bodies which are in equilibrium tend to be internally differentiated and therefore have quite different geologies than bodies which are not in equilibrium, but in truth the focus would be on classifying planets rather than distinguishing them from non-planets.

Both of these systems are, in their way, quite useful, and in a perfectly rational world both would be incorporated into any classification system. Unfortunately, the world is not perfectly rational, and there was a key factor that meant that the dynamical approach was almost inevitably going to be dominant: it had been around a lot longer. And by a lot I mean “since people started looking up at the night sky”; the very language of “stars” versus “planets” encodes a distinction between fixed, unmoving lights (stars) and wandering, moving ones (planets, of course). It was practically inevitable that people would wonder why the planets moved across the sky whereas the stars stayed still, and practically inevitable that they would start theorizing. Practically inevitable, too, that when science as such gradually began to emerge as something distinct from philosophy that its methods would be turned on understanding this movement, and that the very foundation of astronomy as a science would be laid on dynamics.

By contrast, the planetological approach is very recent, and inevitably so; its key tool, given the limitations of even telescopically-aided observations, is the space probe, so it would not have made sense before the past fifty years to even think about classifying bodies in the solar system according to their unknowable internal structures or geological properties. Even, as Jared notes, basic features like "is this body in hydrostatic equilibrium" were unknowable for marginal bodies until quite recently. The result was inevitably that the culture of astronomy became dominated, on a subconscious level, by dynamical considerations and a dynamical scheme of looking at things, and that there is no sufficiently large body of planetologically interested people around to counterbalance this feeling. I expect this to change in the future, provided people continue traveling into space and continue to observe exoplanets (for which, as I noted, planetological considerations tend to overwhelm dynamical considerations in classification, largely because we can only practically see “planetary” bodies…), which may cause another change in how these bodies are defined. Or perhaps not; people may just shift to using other words and leave "planet" as an antiquated relic of an earlier age.

But the upshot is that I can see no plausible method of having Ceres remain a planet, and just barely a potentially plausible way for Pluto, mostly involving more space activity early on that tips the balance towards planetological concerns. That’s a very narrow window, though, because you need that shift to happen before exoplanets or TNOs become a significant concern, which is likely to happen relatively soon (within a few decades) after space flight becomes practical, and hence before that shift is actually likely to take place!
 
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