Tal Bachman wrote:
You are a mathematician...so, I hope I am right in saying that "quantity" as a concept would be meaningless unless we contemplated finitude, or if you prefer, exclusion. That is, if we deny that any parcel of anything can be discrete or bounded or exclude something else, then we can have no "parcel of anything", for all would merely all melt together - it would be entirely unquantifiable, and therefore, we could hardly understand it, if at all.
I am not sure what you are getting at here. Are you just insisting that words must have precise meanings?
by the way, Ordinary mathematicians might not even feel that what you are saying here is clear. Finite and discrete are not the same thing for example. I also don't know how I am to take "melt together" Does that have precise meaning? (we both know one can quantify both ice cubes by number and water by volume ;)
I think words and concepts are like that. For any proposition to be intelligible to us, it must have content; and it can only have content, if it has bounds - dividers (however provisional perhaps for purposes of inquiry) between it and other conceptual parcels, as it were. If, for example, the (just-invented) word "mig" can refer to absolutely anything, then what would this statement mean to us?:
I would say the the boundaries between our concepts are often not perfect but only need the kind of precision appropriate to the task.
Consider three examples.
1. That is a mountain! Is the meaning clear? How about "That is a mountain in the same familiar sense that skiers understand"
Now is the following true?
M1. If you remove one molecule from a mountain it is still a mountain.
If so, shouldn't I be able to proceed iteratively and conclude that when only one molecule is left I still have a mountain?
"When canaries mate with other canaries, baby canaries are often conceived". This obviously tells us something.
Yes, in its usual context it tells a lot but you remind me of another point:
Consider:
P1: The parent of any naturally conceived chicken is a chicken.
Therefore
C: every naturally born ancestor of a chicken was a chicken (contra evolution)
You might think the problem is that C1 is wrong.
But suppose I argue that C1 is wrong because some mutation means that there was a first chicken. But this isn't right either.
The problem is that the word chicken isn't up to the task. It is not well defined when we view species over long periods of time.
So which ancestor of joe the chicken was not really a chicken? Dennett would use the phrase "there is no fact of the matter".
I can talk about the first double digit prime but not the first chicken.
How about the words cup, bowl and saucer?

An infinity of possible meanings led to the impossibility of intelligibility;
I catch your drift but,....,well I can't quite perfectly agree with that either. If the infinite meanings clump together like the continuum of points near the center of a 2D bell curve in meaning space (as it were) with small standard deviation then the variance in meaning may have no untoward practical implications for our domain of discourse. It may go unnoticed (until a philosopher shows up and makes his demands).
So, in order to understand anything about the world, we maintain many hundreds of thousands, I am sure, of conceptual, lexical, etc., boundaries. It might be argued that the boundaries are not inherent in nature, but are only the result of our own projections born of psychological necessity. But if so, it is no matter - without them, the world would be unintelligible to us...it becomes less intelligible the more we depart from a kind of ideal state (though that must always be in dispute) of meaning- or boundary-granting.
Lexical boundaries have to clear be enough to serve our purposes. That's why we are so very troubled when we can't
quite get it to happen as in deciding how to define knowledge for purposes of philosophical discussion.
For example, if the words knowledge, theory, hypothesis, conjecture, and guess, were all to be granted something like synonymity, I think this would be a blow to our ability to comprehend the world, not a boon to it.
I grant that we should use words as precisely as is necessary for the task and in philosophy and science that usually means as precisely as possible (which still might not be perfect).
Will that work for you?
Perhaps you do not need to be so socratic with so many rhetorical questions. Perhaps you can just say what you are getting at directly.