> I know there are some fancy arguments around stretching limits of language, but none of them seemed all that sensible to me.Did you read Robert Kegan "The Evolving Self"? It was pretty popular at HN some time ago. Robert Kegan stretching limits of language and he's got a reason: he introduces some notions like "culture of embeddedness" that you just can't define in a way like dictionaries do, one cannot simply get to a point. Kegan uses another approach, he gives his reader an experience that makes her to understand "culture of embeddedness".
Philosophy by definition deals with uncategorised (or poorly categorised) aspects of our world, with aspects that have no good language to talk about them. Anything that was categorised to a point when there is an accepted language to talk about it is not a philosophy, it is a science or something. Philosophy makes first attempts to categorise and when philosophers found a way then a new branch of science emerges.
When you try to talk about uncategorised things, you just can't talk about it. For example, lets assume that there are no widely accepted categorisation of colors, but you've developed one including names for colors like "blue", "red", "magenta" and so on. How you could communicate your ideas to others? The only way I know is to point to different examples of blue and say "blue", point to red and say "red". You need to lead your audience through experiences of blue/red/magenta while they train their neurons to classify them and only then you can refer to their experiences with words "blue", "red", "magenta" to convey the idea that they always appear in a rainbow in the same sequence. While you keep pointing at different colors saying their names, your audience will probably think, that it takes too long for you to get to a point.
I didn't read GEB, so I cannot say how this reason to "stretch limits of language" relates to it, but you've sad that you know no good reason for such stretching, and I hope that now you know at least one reason for it.