The fundamental difference between a physical set and a symposition is that the latter explicitly considers and addresses repetition. The underlying premise is that an entity cannot be apprehended adequately by itself; it must be compared to other entities. The problem eliciting that premise is that sem-linking is ultimately an arbitrary act: why select these few primitives or symponents for sem-linking rather than those? Whereas physical proximity provides a useful criterion for non-arbitrariness, it is insufficient to remove it entirely, and in some cases, the criterion is downright counter to sense—a bee is part of its hive, not part of the flower it’s visiting. Other criteria may be attempted, like being fastened together, or being a living being, but what happens in all of these attempts is that there are symponents that we believe should be symposed,¹ and the commonalities shared among many different examples of the belief become the criteria. I believe the most apt approach concentrates not on the development of any specific criteria, but on shared commonality itself: on repetition.

Repetition implies a multiplicity of singles. Thus we can define the individual symposition: a single, specific symposition in the World with a hierarchy of symponents all the way down to the physical primitives. The Moon is an individual symposition. Antarctica is an individual symposition. The room I wrote this sentence in is an individual symposition. In English writing, an individual symposition is often capitalized or preceded by the word “the,” and it could also just be called an individual. We can also define the populational symposition or the population: a symposition whose many symponents are similar individuals.

This definition of population suffers from the fact that the similar individuals need not be in any spatial relationships with each other whatsoever, flouting the notion of “pose” needed for symposition, in this case the symposition of individuals into a population. However, if we allow ourselves the population of populations of individuals, we can compare it to regular populations. The symponents of the population of power strips all bear a similarity pertaining to having certain symponents with certain poses. The symponents of the population of populations of individuals all bear a similarity pertaining to having symponents that are similar. Thus what is similar among the symponents of the population of populations of individuals is similarity itself and not some configuration of symponents and poses. What repeats from one population to the next is repetition. Though the original definition of “pose” is violated to accommodate the definition of “population,” the violation is justified by an additional reckoning of repetition, which is the very point of symposing in the first place.

It is trivial that the partonomy of a population has one more level at the top than the partonomy of any of the individuals in it. Consider the possibility of a symposition that, like the population, accounts for multiplicity, but that, like the individual, does not have an extra level. Such a symposition could be crafted by taking an average of sorts of all the individuals in a population. It would distill the similarities that repeat, so we can call it a distilled symposition, or a distillation. Unlike an individual and population, however, a distillation is not present in a specific place or places in the World upon a specific subset of the Dust; it is rather the ghost of repeated similarity. Thus the distillation and the individual are alike in that they have a similar partonomy, at least at the top; the individual and population are alike in that they both are grounded on the Dust; and the distillation and population are alike in that they both consider multiplicity. When necessary for clarity, I’ll identify the three with subscripts: {}_i, {}_p, and {}_d.

Let’s compare hydrogen and helium. {hydrogen}_i and {helium}_i would refer to some specific atom of hydrogen and some specific atom of helium floating somewhere; both would have an exact number of primitives, but neither would ever be referred to since we basically never care about individual atoms. {hydrogen}_p and {helium}_p would refer to all hydrogen atoms and all helium atoms in the Universe; since the former is so much more abundant than the latter, {hydrogen}_p has more mass than {helium}_p. {hydrogen}_d and {helium}_d would refer to the abstract notions of the hydrogen and helium atoms; neither would have an exact number of primitives, instead incorporating the isotopic abundances and ionization profiles throughout the Universe of both; finally, since the former has both fewer quarks and fewer electrons than the latter, {hydrogen}_d has less mass than {helium}_d.

A distillation reckons and incorporates the abundances of the different individuals in the distilled population. Consider the population of shirts. Some shirts have sleeves, some don’t, some have long sleeves or frilly sleeves. Some shirts have necks, most don’t. Some shirts have pockets. Many shirts have buttons or zippers. {shirt}_d must account for all of these varieties of symponents. {shirt}_d has at least one symponent that can be any of multiple sympositions or none—the zipper/row of buttons for instance. Such flexible symponents exhibit modularity. Modularity is implicit in the original definition of a distillation, but I include it to highlight the fact that sympositional variation can be more than just quantitative (like in the number of symponents as in isotopy) but also qualitative; the symponent need not always come from one given population. If the number of populations that the symponent can be drawn from is large, the modularity is high, and if the number of options is small, the modularity is low.

Footnotes

1. Mereological nihilists and universalists have analyzed themselves into a corner where they deny this. The denial appears to me to be the most precarious contention of analytic philosophy. See Every Thing Must Go: Metaphysics Naturalized by James Ladyman and Don Ross.