I want to define something which I'll call object X. I have to come up with a sentence, but how can I tell that the sentence will be right? I can't compare my attempt with the definition of X of course, because there is no definition of X - the definition of X is the very thing I'm trying to find out. It seems I have to know what X is in order to find out what X is - paradox?

I'm not convinced that there's really a paradox here. Let's consider various cases.

1) You want to coin a new term, perhaps "snurp" which you define as the sound a half-empty balloon makes when cut with scissors. No paradox here. You wanted a word to refer to this sound. You coined a word and assigned it that meaning. You know what a snurp is because you decided what a snurp is. That's what makes the sentence right.

2) You're in a contest in which you get points if you can recite the standard definition of a term correctly. The quizmaster asks what the definition of "bachelor" is. You reply "an unmarried male of marriageable age." You defined it correctly. You had to know what a bachelor is to give the correct definition, but again, no mystery. That amounts simply to knowing a certain convention about a certain word. No paradox. The sentence summing up the definition is made right by social facts about accepted conventions.

3) You're a lexicographer, and you are trying to give a definition of some word that's entered the language recently. Maybe the word is "furgle." (I'm making this up.) You have to know what a furgle is to give the definition. But no paradox. What this really means is that you need to know a bunch of empirically ascertainable facts about how people actually use the word "furgle." Lexicographers have various ways of gathering that sort of information. If you do your job right, you'll give a correct account of what people use the word to mean. Still no paradox. Your sentence about what "furgle" means is true because it accurately reflects how people happen to use the word, and you found that out by assembling evidence.

4) The sense of "define" that's at issue isn't about words, but about things. There's an object or kind of object (maybe a kind of animal) whose "nature" you're trying to specify. The question of how you should characterize it is quite possibly a scientific question---a biological one, let's suppose. You investigate the creatures you're trying to characterize. You discover that they have thus-and-such genetic characteristics, such-and-so phenotypical characteristics, this kind of behavior... You came to this knowledge gradually, in the way that scientists typically do. Your sentence is true because it accurately describes what you've discovered about these kinds of creatures: it gets things right. You had to know this before you could actually spell out the "definition," but there's no mystery about how you came by this knowledge.

Now of course, to investigate Xs, I have to be able to recognize them. In that sense, I have to know what Xs are. But that doesn't mean I have to be able to state their scientific nature, let alone know it before I investigate. Children can recognize cats; they can't tell you much about their biology. There's typically much more to what Xs are "really" like than it takes to recognize Xs.

5) We aren't really talking about words, nor about objects as usually understood. We're trying to come up with a philosophical analysis. For example, perhaps we're trying to "define" free will in a philosophically illuminating way. This isn't a matter of stipulation, there's no "standard definition," and simply investigating how people use the phrase won't settle the question of what the best philosophical theory of free will is.

That's the typical situation in philosophy. But it doesn't mean that we have to "know" exactly what free will is at the outset. If that were so, it wouldn't account for something that every working philosopher is familiar with. As an analysis proceeds, philosophers find themselves changing what they think. Things that they might have thought to be essential come to appear not to be; things that seemed not so important come to matter.

Suppose, for example, that a philosopher starts by thinking that if Newtonian-style determinism is true, this would be incompatible with free will because it would mean that given the history of the world before someone's "decision," there would be no genuine alternatives. But she also thinks that there are clear examples of people making free decisions. This might lead her to conclude that determinism is false, since it's incompatible with the apparent fact that people sometimes do display free will. But at that point our philosopher will push harder. Which is clearer? That determinism is false? Or that these decisions really should count as free? Settling questions about how the universe actually works by armchair philosophical reflection seems like a shaky enterprise. But simply saying that we're never free conflicts pretty sharply with our usual view of ourselves.

What the philosopher will find is that there are competing considerations with varying degrees of importance, and there are apparent truths with varying degrees of plausibility. The philosophical analysis will be an attempt to find the best overall way of reconciling all of this---deciding what's more central to how we think about freedom, our our selves, or our knowledge of the world, and what's less so; deciding which parts of our superficial views about freedom seem sound on reflection and which parts don't. A philosophical analysis of a deep concept isn't just a discovery and isn't just a stipulation; in an important sense, it's a creation. And it's a creation whose final details aren't forced on us by a set of axioms or definitions in the way that a mathematical theorem might seem to be.* So once again, there's no paradox. When we set forth on a project of philosophical analysis, as any philosopher will tell you, we don't start out already knowing the answer. We assemble it gradually by arguments, tweaks, reconsiderations, and flashes of what we hope is insight.

So I don't think there's a genuine paradox here. In the first case, what you "know" is how you've decide to use a word. In the second and third, what you know are facts about linguistic conventions and behavior---things you can find out by gathering evidence. In the fourth case, word meaning isn't at stake; the nature of things is. But we know how to find out things about things. And in the philosophical case, reflection on how philosophical analysis actually proceeds makes it hard to believe that we must or even could start the process of analysis already knowing what the analysis should be.

That's a bit long-winded, I realize. But I hope it helps.

-----
* I'd hasten to add that there's a great deal of creativity in mathematics as well. But that's another whole topic.

Read another response by Allen Stairs
Read another response about Language