I am glad you have not let this conversation drop, and I have been following it with some interest. If you don't mind, I would like to make a couple of comments, but do not want to change the course of the discussion.
I think there is some confusion about the definition of a word and the meaning of the concept the word represents. On that issue, I think Ayn Rand made one of her most important contributions to epistemology. A word does not mean its definition. The definition serves only to isolate the concept the word designates from all others, and what a concept means is whatever is identified by it, its units or referents. On that issue, however, I do not think Rand was so clear, and made some mistakes.
Now, about feet and dogs.
Of the two concepts, dog is the simpler. A dog is an entity, a foot is an abstract, arbitrary, "unit" of measure of length, a quality, not an entity. Only entities have metaphysical existence. Events, qualities, and relationships exist only as actions of entities (events), attributes of entities (qualities) and relationships between entities. (I am referring only to concepts of the physical, not concepts of concepts or the psychological, though, by analogy, the same rules apply if "entities" is changed to "existents.")
We have all seen dogs, but no one has ever seen a foot. The concept foot is a very complex and abstract one. Like all, "units of measurement," it is arbitrary, that is to say, it is not discovered, it is invented or chosen. While length is a real attribute of physical entities and relationships between them, it does not exist independently of those entities. Something can have length and things can be a certain "distance" from each other, but "length" and "distance" do not exist on their own.
All units of measure, when actually used, have some level of imprecision. Counting is always absolute (there are five dogs or six dogs, but never five and three eighths dogs), measurement is always relative and approximate (nothing can be known to be exactly three feet). Measurement can be made as accurate as we like [within limits], but is never absolute.
This is where Ayn Rand's distinction between definition and meaning are so important. The definition of a unit of measure is never wrong, because it is chosen. Once an attribute of existents that can be measured has been identified, any useful unit may be "defined" as a unit of measure. The definition is always exact, because it is by means of the definition the meaning of the concept for a unit of measure is selected. The meaning is still not the definition, however, but the actual unit of measure.
The definition of a concept that identifies existents (entities, for example) is determined by the meaning of the concept. The opposite of the definition of units of measure.
Suppose a child learns the word "dog" for the family dog. When the child says the word dog, it means "the dog" (which is the only one it sees). On seeing the neighbors dog, if it is similar enough to the family's own dog, the child will probably say "dog" when seeing it. The child does not mean, "family dog," but simply, "one of those things that looks like that." It may not know it has only ever seen one dog, and it makes no difference, because what the child means by dog is "whatever looks like that," whether it is different dogs or the same dog on different occasions.
If the child's father is a veterinarian, his definition of dog may be quite sophisticated. The child's definition exists only ostensively, that is, "that" when pointing to a dog. What they both mean by dog (an actual dog) is exactly the same thing. The father's definition is more sophisticated because it is made in the context of much wider scope of knowledge and requires more detail to differentiate the word from others and integrate it within the hierarchy of that knowledge. The child's ostensive definition is sufficient to isolate the word within the very limited scope of the child's knowledge.
The meaning of words is not determined by their definition (except in that way that units of measure are). The meaning of words is determined by whatever concepts they designate identify; that is, the existents (including other concepts), their qualities, actions, or relationships that are the concepts units or referents. The idea of an "endless regress of definitions," gets the nature of concepts backwards. We do not start with the abstract concepts and work backward to concretes. First we have simple concepts, like dog. Then we notice there are differences in dogs. One of those differences we notice is one dog fits in the chair the other one does not. The concept we form for that observation is "length" or "size."
There are very long chains of reason that lead to our most profound abstract concepts, like A is A, but they are all derived, if they are correct, by a process of abstraction and integration from concepts originally defined like the child's dog. There is no endless regress. Working backwards, the chain always ends on the solid ground of observed facts. If it doesn't, the concept is false.
(Edited by Reginald Firehammer on 6/18, 9:16am)