Rand’s philosophy misrepresents the position of the other side.
Defining the words “intensional” and “extensional” Hayakawa, Language in Thought and Action says: “The intensional is the map, the extensional is the territory…. The map is not the territory. The word is not the thing… “ (pg. 19 and 20). Some things only have a definition and no concrete extensional existence, such as… “the mathematical point which has a position but occupies no space and the mathematical circle which is a closed figure in which all points are equidistant from the center… Actual points occupy some space and actual circles are never exactly circular…” (pg 122)
Compared to Rand/Piekoff, Objectivist Epistemology: “By extension of a concept, the theory’s advocates mean the concretes subsumed under that concept.”
When Rand says “concretes subsumed” she means the concrete things observed in the real world which inspired the concept in the first place (pg 21). However, since mathematical points and circles have no concrete extension, concretes cannot be “subsumed” and cannot be the extensional meaning intended by the theories advocates. Therefore, she misrepresents the other side.
And then she says, “by the intension of a concept, they mean those characteristics of the concretes which are stated in the concepts definition…” (pg. 141) However, since geometric points and circles have no concrete characteristics in their definitions, that cannot be the intensional meaning intended by the theories advocates. Again, she misrepresents the other side.
The nature of the misrepresentation is that her premise of concretes is assumed to be a premise the other side shares when it does not.
Ayn Rand, Introduction to Objectivist Epistemology, Mentor Book, New American Library, 1979 Ch. 2, The Analytic/Synthetic Dichotomy by Leonard Piekoff.
S I Hayakawa, Language in Thought and Action, Harvest edition, Harcourt Brace & Co, 1992