Why Do We Need Definitions?

Note: This post has been automatically imported from my old blog. Formatting may be incorrect.

The topic of definitions has always been an aspect of epistemology that eludes me a bit. I kind of see the value when trying to communicate a concept to others: If someone tells me that a memristor is a resistor whose resistance depends on the history of the current through the device, then I can get a general sense of what the referents of the concept are like, even without knowing anything about any particular one. But Rand thought that definitions are essential for cognition, not just communication, and that the formation of a concept isn't really complete until you have a definition. I would say though that for the vast majority of the concepts I use, I don't really have a good concise definition and would have to spend some significant time coming up with one. So, what am I missing? Why are definitions so important? What kinds of real-life situations are improved by having a proper definition for your concepts?