Everyone has a vague understanding of what 'space' is. You don't always need to give a formal definition for everything. I imagine few people can give a formal dictionary definition for the word 'the' but any native English speaker has a good grasp of how it is used. For instance, if you're a native English speaker you almost intrinsically know there's something wrong with the sentence 'Monday is first day of week'. In fact, I almost read it in a foreign accent since it's something you'd expect of a non-native English speaker. It's quite hard to give a formal definition of such things as 'space' and 'time', yet everyone has a notion of them. You can give formal definitions involving mathematical terminology, in how space-time is viewed in general relativity, but I'd imagine you would not accept them. In GR there is a very clear and distinct difference between an explosion of material in space and the explosion of space containing material. The form, assuming no back reaction, has a time independent metric. The latter does not. The former has time varying positions of the dtuff which makes up the matter, the former doesn't need to, they are stationary in a comoving frame. The FRW metric can model an 'exploding space-time' without needing to make reference to any actual matter. So your claim James's statements are mute without a formal definition is mute itself.