Even if your argument is valid for unique things, it's not valid for universals. And your view of internal relations has to apply to both. On your view, not just things but terms are what they are because of the way they are related to things. And there's no reason to think that an abstract characteristic is so connected with other things that none of its relations to those things could be different without that characteristic itself being different. Many believe that to say fully what something is, you have to know everything about how it's related to other things.
But notice they don't demand this for universals. Having red hair may occur in many people with different temperaments, histories, and states of health. Therefore, having red hair is related to all those characteristics as well as all others. If having red hair was not having red hair unless it was related this way, then no one could know what having red hair was without first knowing all its relations to the mental and bodily traits of those who had red hair.
We do not know all these relations. But we do know what red-headedness is. We have knowledge which on this theory would be impossible. Hence the theory is wrong.
Yet this argument does not prove what it tries to prove. It proves that we can have some knowledge of red-headedness without knowing all the relations of redheadedness. What it ought to prove is that we can know red-headedness fully and as it really is without such knowledge.
And there's a big difference between these two statements. It would be absurd for the theory of internal relations require that we deny that we can have knowledge of red-headness without knowing all the relations of redheadedness. Because it's obvious that we do attach some meaning to red-headedness even though we do not know all its relations. No defense of internal relations has ever denied that, because it would imply that every bit of knowledge we have is illusion, since nothing ever comes before us whose relations we know exhaustively.
The fact that all knowledge is a matter of degree does not imply knowledge nihilism. We can and do have some knowledge without an exhaustive grasp of relations. When we use the term 'red-headedness', we use it with a meaning and we have some knowledge of the attribute it names, even though we don't know all the relations of that attribute.
But is that equivalent to saying that the red-headedness now explicitly in our thinking is all there is to that attribute as it exists in the nature of things?
Well that's what is implied in the criticism, because unless the criticism means that we can know the real nature of an attribute without knowing its relations, it is saying nothing we disagree with. But to assume that what is now presented in idea gives the whole nature of what is referred to us begs the question and adopts a position we've already shown is false. An idea always points beyond itself. It always means more than it is. It always refers to more than it includes within the circle of its explicit content. That's what makes it an idea. This difference comes under the head of immanent and transcendent meaning (See 1.2.18).
That there is such a difference is undeniable. It's the difference exemplified (though of course not perfectly, since transcendent meaning can never be captured completely) by the interval between what presents itself to the schoolboy when he thinks of Napoleon's loss of Waterloo and what presents itself to the historian. Both refer to the same thing, but by general admission the historian's explicit grasp is nearer to the fact than the school-boy's (188.8.131.52 - 184.108.40.206).
What makes the the second grasp better than the first? It's the fuller grasp of context, that is, of the antecedents, methods, and bearings of the engagement. The schoolboy must understand these things to be able to understand the defeat as it really was, and as he apprehends the context more fully, his thought immediately remolds itself internally and approximates to the external fact.
Similarly of the more trivial thought we have used to illustrate. For everyday interaction on the level of common sense, the ordinary notion of it suffices. Therefore, does our notion at this level exhaust the nature of the object? There is no more reason for thinking that than there is for thinking that our ideas of anything else on this level are truly adequate to their objects.
As little as might be the point of reflecting on it ordinarily, it's still a fact that red-headedness is an integral part of an organism, and is so bound up, for example, with the structure of hair fibers and this in turn with all kinds of constitutional factors determining racial and individual differences that our common notion of it supplies scarcely more than a sign-post to its real or ultimate nature., that is, to what is as embedded in its own context.
As we grasp those further relations, our explicit thought o fthe attribute is modified while our reference remains the same. We see that we are advancing toward the character as it really is.
In such a series of ideas, our reference is the following: In such a series of ideas, our reference is the same throughout. Our comprehension of what we refer to changes throughout. The changes in comprehension arise from grasping our original content in a fuller context of relevant relations. Our Comprehension at the end of the series is a closer approach to the real character than our comprehension at the beginning. Further advance must be assumed to lie along the same line. And no limit can be set beforehand to the context that complete comprehension would demand. This is what can be verified as fact in any process of improving knowledge.