The combination of possibly with can't and couldn't seems to me on the increase. Or perhaps I just notice it more since I've been living in France. For in French there is no direct equivalent of possibly. You have probablement (= probably), but there is no French word *possiblement. What, then, is going on when you find in English, to take a recent example, ‘For all the malfunctions of the past few years, it's assumed the structure of British society can't possibly be refashioned’ (standfirst to an article by Marina Hyde, The Guardian, 7 July 2012)?

Wondering whether I was right to think it had become popular only comparatively recently, I did a computer search of the e-book versions of three novels written 80 years ago or more that have plenty of dialogue in them, Dickens's Great Expectations, Sinclair Lewis's Babbitt, and Agatha Christie's The Secret Adversary. Although there were many examples of can't and couldn't, there were none of can't possibly or couldn't possibly. Of course, this tiny investigation doesn't prove anything, but I think I wouldn't be surprised now if some exhaustive research suggested more convincingly that those authors neither used those constructions in their own voice nor imagined their characters using them. To test more modern usage, you just need to type ‘can't possibly’ into Google. You get 60 million results. I checked the first twenty pages and all but one of the examples were from recent times. The odd one out was from Scott Fitzgerald: ‘There can't possibly be a summer love.’

Going back to the Guardian example above, if we adopt a logical approach, which is usually inadvisable when discussing language, the result looks bizarre. For, if ‘It can't be refashioned’ means ‘It is impossible to refashion it,’ then ‘It can't possibly be refashioned’ looks as if it means ‘It is impossible possibly to refashion it,’ which doesn't seem to have any sense. It seems, then, that possibly in this example is just an intensifier. For, if something can't be done, it adds nothing to say it can't be done within the limits of what can be done. We can get some support for this conclusion if we consider French again, where can't possibly is often translated by using some intensifier, such as absolument (= absolutely). So ‘I can't possibly stay here’ is translated as ‘Je ne peux absolument pas rester ici’ (= I absolutely can't stay here).

Are there uses of this construction where the possibly indicates something other than intensity? I would say there were. Whereas the reply ‘I couldn't say’, for example, might easily be a simple admission of ignorance, I think it less likely that ‘I couldn't possibly say’ could be taken so straightforwardly. Indeed, in some contexts you would be more inclined to infer the opposite: that the person was far from ignorant, but had an interest in not revealing the truth. For an ironic use, some of you may remember the BBC television drama of the 1990s, House of Cards, in which the scheming politician Francis Urquhart had the catch-phrase, spoken directly to the viewer, ‘You might very well think that; I couldn't possibly comment.’ The implication was, of course, ‘Yes, you are right to think so.’ We might also include the tentatively polite use in requests, as in ‘You couldn't possibly bring a spare set of golf clubs at the weekend?’

Maybe, then, we should think of this construction as being of two types: one where the possibly is just an intensifier, in many cases irritating for its superfluousness, and the other where it conveys something more or different, providing an insight into the attitude of the speaker or writer.