Reification of Zero

The reification of the zero is the error of treating "nothing" as though it were a kind of something — a special existent with a nature and effects of its own, rather than the absence of any existent. The term is Objectivist, and the fallacy it names is a failure to observe that concepts of absence are formed by reference to what is absent.

The error

"Nothing" is not the name of an entity. It is a relational concept: it means the absence of the things one was looking for, and it has no meaning apart from them. There is nothing in the refrigerator, nothing in the mail, nothing in the room — each is intelligible only against the specification of what would have been there.

Reification takes the word and treats it as designating an item in reality. Once that step is taken, "nothing" acquires properties: it can be a state the universe might have been in, a force that acts, a realm that surrounds existence, or a thing consciousness can be aware of. Each of these attributes an identity to what is defined as the absence of any identity. See Existence, Identity and Axioms.

Objectivism's position follows from the axiom that existence exists. Existence is the widest concept there is, and a concept that wide has no contrast class — there is no "outside" of everything for a nothing to occupy. Non-existence is not an alternative state of affairs but the absence of one. See Primacy of Existence.

Where it shows up

"Why is there something rather than nothing?" The question presents "nothing" as a coherent alternative that requires existence to be explained against it. On the Objectivist view the alternative is not a possibility that failed to obtain; it is not a possibility.
Nothingness as a force or a realm. Treating the void as a thing that surrounds, precedes or threatens existence, rather than as a term for regions where a given kind of matter is absent.
Creation ex nihilo. A creation out of nothing takes nothing as the material acted upon. See Causality, Law of Causality and Religion.
Zero as an entity. In mathematics zero is a legitimate concept of method — a placeholder and a measurement of absence. The error is treating it as naming a quantity that exists in the way that three apples exist. See Measurement.
Death as a state one will experience. Anticipating non-existence as a condition one will be in, rather than as the cessation of the entity that could be in conditions. See Life and Consciousness.

Its relation to the other conceptual fallacies

Reifying the zero is a specific instance of losing the referents of a concept. Concepts of absence — nothing, void, zero, non-existence — are formed at one remove: they identify what is not there, which means they depend entirely on the concepts of what would be. Detach them from that base and the word remains while its content is gone. See Floating Abstraction and Concept formation.

It also tends to become a stolen concept, because arguments built on a reified nothing generally use existence, identity and causality to reason about a thing defined by the absence of all three.

Common misunderstandings

That Objectivism denies that "nothing" is a valid concept. It is valid, and useful. What is invalid is treating it as naming an existent rather than an absence.
That it rules out talking about empty space or a vacuum. A vacuum is a region without matter of a given kind, which is a fact about a real region. That is not nothing; it is something with specified contents.
That it settles cosmology. The claim is about the concept, not about physics. What the universe contains and how it behaves are questions for science; what "nothing" can coherently designate is a question prior to them.
That zero is being rejected in mathematics. Objectivism treats mathematical concepts as concepts of method, and zero as a legitimate one. The fallacy is metaphysical: giving the measurement an existence of its own.

Discussion

References

Rand, Ayn. Introduction to Objectivist Epistemology. 2nd edition, Meridian, 1990 — concepts of method, and of absence.
Rand, Ayn. Atlas Shrugged — Galt's speech, on existence and the attempt to posit its opposite.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 1.