Ayn Rand started with a _notion_ that concepts were a kind of unit ("Two square feet are units; two stones are two units"). She developed her _notion_ into a _theory_.

That's often how theories start: as notions.

Don't be so hypersensitive. It's immature of you.

If Rand is wrong in her _notion_ about concepts, any _theory_ built on that _notion_ will be wrong, too.

Don't worry. That she's wrong in her epistemology in no way detracts from the heroism of Galt, Dagny, Rearden, or D'Anconia.

And what does topology have to do with any of this? Concepts obviously include mathematical ideas such as "number", "function", "continuous", "discontinuous", "discrete", "complete", "closed", "open", etc., but they are not mathematical in nature themselves. "Units" are concepts, but "concepts" are not units.

Ayn Rand did not have a "notion about concepts" she had a _theory of concepts_. I was tempted to give that one-line zinger a thumbs down. However, I agree that as I read Rand's references to mathematics and measurement in ITOE, I kept thinking of topology as a counter-example. It bears some discussion. Here in The Gulch under Books, if you scroll back four weeks or a bit more, you will find opportunities to discuss ITOE chapter by chapter. Not many people are up to it, apparently, but there it is.

Rand had a rigidly narrow idea of mathematics (measurement), making her notion about concepts incorrect.