"The trouble is that concepts, without which we do not connect one thing with another, are apt to become a network which confines minds. We need to be at once like someone who has seen much and forgotten nothing, and also like one who is seeing everything for the first time. It is, I believe, extremely difficult to breed lions. But there was at one time at the Dublin Zoo a keeper who bred many lion cubs without losing one. Asked the secret of his success, Mr. Flood replied, "Understanding lions." Asked in what consists the understanding of lions, he replied, "Every lion is different." It is not to be thought that Mr. Flood, in seeking to understand an individual lion, did not bring to bear his great experience with lions. Only he remained free to see each lion for itself" (John Wisdom, "Paradox & Discovery," Eponymous volume, 137-8).
We can recognize many things we can't define. Meno knows virtue. Any acquired perceptual ability that gives us 'direct perception' of physical objects or sensory qualities, or perhaps even abstract ideas, gives us the ability to immediately recognize those things. Often these are what we might call 'higher-order properties'--i.e. they aren't simple; they are more like 'virtue' than like 'red.' But 'red' and 'virtue' are in the same boat when it comes to definitions.
Can we say how we recognize the things we recognize? Sometimes, yes; and this will be like saying how we do actions we've learned to do by heart. Saying how we recognize what we recognize immediately will be like saying how we do something we never have to think about the method for doing. Some of these features we will have forgotten, if we ever had to think through them at all. Whether we can bring them into our awareness will vary: there's not much I can say about how I recognize red things, since my visual data processing just isn't available to me; but I can say something about virtue, lions, fear, or kinds of philosophical skepticism.
How we recognize things is important. Knowing how we recognize things often tells us what they are (or tells us what they are relative to our current conceptual scheme). I don't only mean how we actually do recognize things, but both how we do and how we could. It's important that someone knows how to tell an elm from a beech, and that he or she could tell me; there are more recognizable features of the elm than I currently know how to recognize.
A concept, like 'elm,' denotes a collection of recognizable features of the world. (This is a variant on "possible experience.") The concept may be cobbled, and less straightforward than a natural kind, but that doesn't make the situations that prompt its application unrecognizable, or even non-delineable. Philosophers, so far as they are concerned with conceptual analysis, should be concerned with the actual application of the concepts with which they are concerned (if these concepts aren't neologisms). But it's crucial to not take the particular words people use as rigid guides to what exists.
The reason for this is that the words are not enough. One also needs the circumstances--and not just the social circumstances, not simply what words the speaker was responding to, but the features of the world she was responding to in thinking, say, "look, that's probably an elm." And the features of the world to which she responds may include features of her own mental life: "that was an interesting thought," "there's that strange feeling again." None of these are metaphysically problematic, I claim, in that what makes a tree look elmy, or one's thought seem interesting, could not be closer to first-person experience, and farther from the view-from-nowhere.
That "every lion is different" does not mean that we can't recognize lions. It only means that we can't easily sum up what it means to "understand" lions so as to breed them successfully as Mr. Flood did. Maybe we can't recognize the features he recognized in them, whatever those were: 'lion-breeding-conducive' features, we could call them. We can all recognize lions.