The trouble with these arguments to the non-linguist person-in-the -street is what do you do about border areas. Bagpuss above takes the line that Scots and English are different languages,for example. OK'let's accept that, but what does that mean in say Gretna and Rockcliffe( two villages close to each other each side of the Scottish English border). To the untutored person having a pint in Gretna and then popping across for the other half in Rockcliffe, it is commonsense that the people in the two pubs are speaking the same language.
   So, if Scots and English are different languages, what language is being spoken in the pubs concerned? Border Sconglish? And if this a real third language, what are they speaking in Carlisle 5 miles further into England, or Ecclefechan ditto Scotland. And so on and so on.
To me this is no problem, I think English and Scots are the same language with different names . But if you think they are different languages you have to be able to answer these questions satisfactorily.