I used to make a distinction between the phenomenalist intension and extension, on one hand, and the physicalist intension and extension, on the other hand:

1. The “phenomenalist intension” of a set distinguishes between the possible-to-imagine sensory complexes belonging to the set and the possible-to-imagine sensory complexes not belonging to the set. For example, the phenomenalist intension of the word “fish” is such that anything possible-to-imagine is taken as possible input, and it tells you, as its output, yes or no: It tells you whether any given possible-to-imagine sensory complex is, or is not, a “fish.”
2. The “phenomenalist extension” of a set generates, one by one, all of the possible-to-imagine sensory complexes belonging to the set and none of the possible-to-imagine sensory complexes not belonging to the set. For example, the phenomenalist extension of the word “fish” would generate 🐟, 🐡, etc., endlessly—for there are, presumably, an infinite number of possible-to-imagine sensory complexes belonging to that set.
3. The “physicalist intension” of a set distinguishes between the physically existing beings belonging to the set and the physically existing beings not belonging to the set. For example, the physicalist intension of the phrase “university professor” tells you whether any given person, actually existing physically (whether in the past, present, or future), is, or is not, a “university professor.”
4. The “physicalist extension” of a set is all of the physically existing beings (again, whether in the past, present, or future) belonging to the set. For example, Hayek was a university professor but Hume wasn’t.

Originally, I thought that I was just naturally falling into a phenomenalist perspective, which is the more fundamental perspective, and the mainstream was just naturally falling into the physicalist perspective—obviously the mainstream doesn’t use definitions #1 and #2. But I now understand why the mainstream defines the terms “intension” and “extension” as they do: The work that my system does elsewhere, the mainstream does here. The word “Hemingway,” as a set, has a different intension, but the same extension, as the phrase “the author of The Sun Also Rises.” Those two words/phrases, then, can be freely interchanged in a proposition without there being any way that the truth value will change: If “Hemingway committed suicide at age 61” is true, then “the author of The Sun Also Rises committed suicide at age 61″ is also true—well, assuming that Hemingway is indeed the author of that book.

Interestingly, though, interchangeability can be lost: While—as I wrote above—”Hemingway committed suicide at age 61″ implies “the author of The Sun Also Rises committed suicide at age 61,” adding the subjectivity of a phrase like “John knows” causes the interchangeability to be lost: “John knows that Hemingway committed suicide at age 61″ doesn’t imply “John knows that the author of The Sun Also Rises committed suicide at age 61.” Why? Because John may not know that Hemingway is the author of The Sun Also Rises.