| | Nate,
Actually, upon rereading it, there is something about the way you summarize my position that isn't quite right: when you say that "open-ended" refers to something about the number of referents. Open ended really doesn't have to do with the number of referents of the concept-- it has to do with the fact that if another existent comes along, you can recognize (if necessary) that it needs to be subsumed under the concept or not. Without this, concepts would be useless to humans, since they would only refer to a static collection of referents.
That is how I understood you.
I'll take your suggestion from earlier in your post and ask what what you mean by the "objective" and "subjective" sense of a concept? Remember that if you don't know exactly which referents are subsumed under a concept, you really don't have one yet (c.f. the kindergartener example).
The kindergartner in your example has a concept attached to the word "red" - just not the one you want him to have.
Your latter statement sounds a lot like the claim that if I can't define a tree in words, I have no coherent concept of a tree. I obviously disagree, but I am not sure if that is your claim. Testing sufficient understanding of a concept is done in different ways, but I have no respect for the view that makes it mostly a matter of words. There are many good reasons to respect words and languages, including their role in communication and transmitting culture, but the idea that possession of knowledge is strictly embodied by being able to express it in words is not one.
The objective sense depends upon some ideal view of knowledge (usually scientific). It is usually bound up with absolute judgments of truth and falsehood in the widest context, but is practically surrogated by some standard.
The subjective sense of a concept is how an individual defines a concept - it might agree with the objective view, but it might not. And within the context in which the individual defined the concept, the individual that possesses the concept has usually found it sufficient.
Well, if you do have a concept, you know exactly to what in reality that the concept refers. Therefore, you should be able to, in a given context, to propose a statement that fundamentally distinguishes the referents you're interested in from the rest of them. This statement is a definition, and your definition is correct if it refers to the same things that the concept does. Yes, this is fine, as long as it is not being used to make thought subservient to language and its practical limitations are accepted. Those practical limitations would lead me to a weaker (and inevitably more verbosely expressed) view:
1) If you have a concept, you have a good idea of what an instance of it (or a referent ) would look like if you came across it in introspective thought or perception.
2) To communicate your ideas, or maybe to record (and clarify) the nature of and changes in your thoughts as you continue your inquiry, you define it in a statement so that you can distinguish it from i) other concepts with other referents, ii) from other concepts with the some similar referents but which do not capture the sense in which you want to use this concept.
3) This statement, correctly understood, should enable you to identify what you are discussing with others and to use it to make judgments which you and others can appreciate.
4) This statement is a definition, and if it communicates your ideas to others, or clarifies your ideas, it is serving its function adequately.
5) To the degree that the definition, after enabling easy identification of the referents and understanding of your ideas, makes a judgment about the nature of its referents and that judgment is true, the definition is correct. To the degree that it fulfils both in the functions in the widest context, it is objective.
Note that a referent can be other ideas or thoughts.
The only way that you could meaningfully talk about Martians would be as objects of imagination (since, as you rightly point out, all of the evidence that we have suggests that there are no sentient creatures inhabiting Mars.) Hence, you could say something like "Martians do not exist," but you couldn't say "Martians have green skin," since there are no referents to the concept.
If it is currently the only way if I intend to speak of Martians as existents in the external world, what bearing does that have on my claim? If human beings build a civilization on Mars, wouldn't there be Martians? The distinction between imagination and reality is the standard by which judgments attached to them. The way we conceptually refer to them is the same.
I can say that "Martians have green skin", but once again, it is the meaning in the mind that is important. It could be a judgment about the external world, or my imagination, or some popular work of fiction(Tim Burton's Mars Attacks). Yes, my current use is imaginative or hypothetical. I have advanced no argument for it, have adduced no evidence for it and I know of the cultural status of Martians. I would be more careful making such statements about God around Christians even though I regard gods essentially the same way.
If all you're worried about is that people don't play semantics when they're trying to argue a point, I agree with you. To be fair, however, a dead man isn't a man-- it's a pile of decomposing organic chemicals that was a man. Whether such points are relevant would depend upon the argument (for instance, the distinction between a man and a dead man would be useful if, say, the government tried to give corpses rights by arguing that they are men).
I agree with what you written, and it only enforces my point that meaning is what matters first and foremost.
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