Good point about Plato, I remember him making this point quite explicit in several places.

But yes, arguments without good definitions are often futile, especially when somebody refuses to define their terms. There was a discussion in the Artist's forum a week or so ago where somebody was asking 'is this really art?' of a certain shabby picture and expected the answer to be determined. I pointed out that if they don't provide a definition for art then the entire discussion is an absolute circus and if you do provide a definition then the question is trivial, but their position seemed to be that the word 'art' had some kind of objective meaning and wasn't created by humans, which is of course bunk.

Another good example in my experience is whether or not 1 is a prime number. Arguing about mathematics more than any other subject is utterly ridiculous because if you define your terms properly then there is absolutely no room for ambiguity. A prime is commonly defined as "a number that only divides by itself and 1". People would then say nonsense things like "1 isn't prime in this definition because itself and 1 aren't two separate numbers", but of course this is required nowhere in the above definition. If you want primes to include 1, use that definition. If you don't, use a different definition, such as "a number that only divides by itself and 1, and is not 1". There is no point at all in arguing. The only reason we commonly use the latter definition and not the former is because it turns out to be neater and more useful; the key point that primality is not something which descended from the heavens for us to fathom out, but rather was a concept created by humans for its utilitarian value.