Invalid Concept

An invalid concept is a word that does not designate a legitimate concept — one whose alleged units share no common defining characteristic, or which was formed by a process that violates the requirements of concept formation. Objectivism holds that a term can be fluent, familiar and widely used and still name nothing, and that identifying such terms is part of philosophical hygiene rather than of vocabulary policing.

What makes a concept valid

A concept is formed by isolating two or more concretes that share an attribute and omitting the particular measurements of that attribute. Its meaning is the units it subsumes. See Measurement omission and Introduction to Objectivist Epistemology.

Validity therefore has requirements a word can fail:

There must be units. The concept must subsume existents — actual or possible things of a definite nature.
The units must share a defining characteristic. Not a loose resemblance or a cultural association, but an attribute they genuinely have in common. See Rule of Fundamentality.
The grouping must serve cognition. Concepts exist to condense knowledge, so a grouping that obscures more than it identifies fails the purpose that makes concepts necessary. See Unit-economy.
It must be reducible. A valid concept can be traced down the hierarchy to the perceptually given. A word that cannot is a floating abstraction at best.

Anti-concepts

The most consequential category is what Rand called the anti-concept: an unnecessary term coined to replace and obliterate a legitimate one. Its function is not to identify anything but to make something previously identifiable hard to think about.

An anti-concept typically works by package-dealing — grouping the thing to be discredited with something genuinely objectionable, so that the valid concept has no clean word left. Rand's own examples included "extremism", which fuses consistency in an idea with the use of force, and "the public interest", which fuses the sum of individual interests with a collective entity that could have interests opposed to all of them.

The test is Rand's: ask what the term adds that existing concepts do not already cover. If the answer is nothing, and its effect is to make a previously usable distinction unsayable, the term is an anti-concept. See Definitions and Objectivity.

Concepts of the supernatural

Objectivism holds that terms purporting to name supernatural entities — God, angels, ghosts and the like — are invalid concepts, and the argument is not that no such thing has been observed but that the terms are constructed by negating the axioms:

An entity outside existence is a contradiction, since existence is the widest concept there is and has no outside.
An entity with no identity — infinite, undefinable, beyond the categories that apply to everything else — has had removed from it the very thing that would make it something rather than nothing.
A consciousness prior to and creating existence inverts the relationship between awareness and its object. See Primacy of Consciousness.

The claim is thus that these terms do not designate something whose existence is in doubt; they fail to designate. Objectivism treats assertions built on them as arbitrary — to be dismissed rather than refuted. See Faith, Mysticism and Religion.

Common misunderstandings

That fictional or hypothetical terms are invalid. "Unicorn" is a perfectly good concept: it designates an imagined animal of definite characteristics, and one can say what would count as one. The concept is valid; the claim that unicorns exist is false. Invalidity is a different charge from falsity.
That a concept is invalid because it is disputed. Disagreement about a term's referents is normal and is settled by examining them. The charge here is that there are none to examine.
That calling a term invalid ends the discussion. It has to be shown — by exhibiting the alleged units and their absent common characteristic, not asserted.
That every vague word is an anti-concept. Vagueness is common and usually harmless. An anti-concept is defined by its displacing function: it exists where a clear concept used to be.

Discussion

References

Rand, Ayn. Introduction to Objectivist Epistemology. 2nd edition, Meridian, 1990.
Rand, Ayn. "'Extremism,' or the Art of Smearing", Capitalism: The Unknown Ideal.
Rand, Ayn. "Credibility and Polarization", The Ayn Rand Letter, 1971 — where the term "anti-concept" is introduced.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapters 1 and 3.