What does the “atomism” in “logical atomism” mean?

On r/askphilosophysomeone asked about the meaning of the “atomism” in Russell’s “logical atomism”:

Today I started reading Bertrand Russell’s “Logical Atomism,” as I’m trying to prepare for reading the Tractatus in the near future. I feel that I have a basic understanding of Russell’s general arguments, and I certainly understand why he chose a title with the word “logic.” As for “atomism”, this is a term I’ve previously only heard in the context of John Dalton and Democritus. Russell’s only explanation of the title that I’ve seen is that “atomism” refers to his belief in multiple perceivable realities as opposed to a single “true” Reality. What is this notion of “atomism” that he’s referring to here? How did it happen to be named in the same way as Dalton and Democritus’ extremely scientific notions? What does atomic theory have to do with perceptions of reality? Are there any other notable members of this atomist school of thought besides Russell? Thanks everyone. -u/officialbobbydunbar

I like this question because it is an easier and different question from “What is logical atomism?” Russell address the “atomism” in his logical atomism explicitly:

The reason that I call my doctrine logical atomism is because the atoms that I wish to arrive at as the sort of last residue in analysis are logical atoms and not physical atoms. Some of them will be what I call “particulars”—such things as little patches of colour or sounds, momentary things—and some of them will be predicates or relations and so on. The point is that the atom I wish to arrive at is the atom of logical analysis, not the atom of physical analysis. –Lecture I, page 3 here

So Russell does not want to merely arrive at physically indivisible entities. They should be logical atoms. What does this mean? Russell tells us in the 1911 essay “Analytic Realism” (the essay wherein he first coins the phrase “logical atomism”):

This philosophy…claims that the existence of the complex depends on the existence of the simple, and not vice-versa, and that the constituent of a complex, taken as a constituent, is absolutely identical with itself as it is when we consider its relations. This philosophy is therefore an atomic philosophy. –Collected Papers Vol. 6, page 133

So what Russell wants from the atoms, whatever they are, is that they are logically separable entities: one logical atom exists and has whatever properties it has independently of the any other atom.

Russell’s view on what the logical atoms in fact are changes over time. In 1924, for example, he says that the world consists of events rather than facts (see “Logical Atomism,” page 148 here) without sense-data as constituents, which is a rejection of most of his 1918 view of particulars. But he never wavers in his view that whatever is a logical atom should be what it is independently of all other atoms, even if it comes into causal relationships with other atoms as a contingent matter of fact.

This is a crucial tenet of logical atomism: in Russell’s view, it underwrites our practice of deploying terms in symbolic logic, even if we realize later that such symbols really designate entities that are logically complex, is underwritten by a claim about the structure of the world: it is structured so that a given entity, if it is a logical atom, is logically independent of all others. This is what underwrites his claim (on pages 143-145 here) that we can know properties of one logical atom without thereby needing to consider the logical properties of other logical atoms. This claim about the structure of the world is part and parcel of his denial of the doctrine of internal relations (which he describes on pages 140-141 here), a doctrine that he attributes to idealists like Bradley.

It is useful to compare Russell’s account of logical atomism with Bradley’s overall view: Bradley held that all entities are necessarily related to one another, so that talk of any one entity was a misleading abstraction from the only genuine entity, the entire cosmos (see Appearance and Reality, Chapters 1-3, e.g., page 23 here). Russell emphatically rejects this view, holding that there are no such necessary relations between things, and that talk of a single entity (logical atoms) is perfectly scientifically and philosophically acceptable. This, and chiefly this, is the underlying purpose of the atomism in his logical atomism.

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