No deal is better than a bad deal

My friend Michelle reminded me that Theresa May said this back in January, and has kept on saying it since then. Most people have been non-pedantic enough to let it go by without comment (after all, there's enough politics happening for us to talk about) but she, I and Chris Maslanka in the Guardian all noticed that it was ambiguous.

Negation, as I've mentioned in previous posts, is usually ambiguous because it takes scope over different bits of the sentence it's in. Here's Chris Maslanka's explanation of the two meanings:

Incidentally, there's a long bit in Alice Through The Looking Glass (or the other one) where a messenger pouts that 'nobody walks faster than I do' and the king says 'he can't, or he'd be here already'. Lewis Carroll was keen on logic and semantics jokes.

After some back and forth with my colleague (& friend) Christina, we think we've translated the two meanings into what looks like gibberish to non-linguists, but is actually a formal representation of the meaning. The notation explains how the bits of the sentence interact to give two different meanings from the same set of words in the same order. I've translated them underneath into increasingly more idiomatic English.

The meaning Theresa means, presumably, is this:

∀x∀y.[NO.DEAL(x) & BAD.DEAL(y) -> x > y]

(Roughly,

"For all x and for all y, if x is no deal and y is a bad deal, then x is better than y"
or "If x is no deal and y is a bad deal, then x is better than y"
or "Having no deal at all is better than having a bad deal".)

Whereas the meaning that's much more salient to me, and which made the sentence seem quite bizarre, is this one:

 ~∃x.[DEAL(x) & ∃y.[BAD.DEAL(y) & x > y] ]

(Roughly,

"There is no x such that x is a deal and there is some y such that y is a bad deal and x is better than y"
or "There is no deal which is better than a bad deal"
or "A bad deal is the best deal".)

Incidentally, I'm pretty sure that this particular type of negation scope ambiguity is regional - it seems less obvious to US speakers (see this post and the comments). But that's a purely anecdotal observation so do let me know if you have anecdata to add to that.

Can you not?

I've written before about negation and the difference in meaning when it takes different scope. The other day, a friend in the pub said this, directed at a football 'pundit' on telly:

You're 60, can you not wear a suit and trainers? 

By this, he meant

Because you're 60 [and should know better/are too old], please don't wear a suit and trainers. 

It can have another meaning, though, and one that I think is much more accessible, or perhaps only available, in certain dialects:

You're 60, so is it impossible for you to wear a suit and trainers?

For me, both those readings work fine for the sentence and the intonation is pretty much the same in each case. The difference is once again a matter of how 'high' the negation is in the sentence:

Is it the case that
you can
[not wear a suit and trainers]?

vs

Is it not the case that
you can
[wear a suit and trainers]?

For more on this, a very easy to read article (old now, but still good) is Bob Ladd's 1981 paper.

The location of 'not'

I overheard an interesting conversation on the train this weekend. One man was telling his friend about 'the most racist moment ever on live television'. It went approximately like this (and I don't know what TV programme it was - he'd seen it on the internet):

On a television programme, some people had to choose who to give the money to out of a couple of women, a black man, and someone else of some ethnic minority (the speaker thought 'maybe Hawaiian'). Someone on this programme apparently said of the black man,

'I don't think he should get the money because he's black'. 

He apparently followed up with some justification about it giving ethnic minorities a bad name, 'always playing the victim'.

This is not great however you spin it, but there are actually (at least) two interpretations, and one is way worse than the other. It has to do with what's called the 'scope' of the negation. In other words, what is it that's negated here?

One meaning is something like this: 'I think that this man should not get the money, and the reason I think that is because he is black and I'm against black people being given money'. On this interpretation, the speaker simply doesn't want the black man to get the money.

The other is something like 'I don't think that this man should get the money simply by virtue of his being black, because racial discrimination is a bad thing even if it's positive discrimination'. On this interpretation, the speaker may decide that the black man should get the money for some other reason, but doesn't think his race should be the criterion for making the decision.

We can see what's going on if I write out those paraphrases using some formal phrasing 'it is the case that', which means something like 'the following is true', and put each part of the sentence on a new line:

It is the case that
I think that
he should not get it because he is black

It is not the case that
I think that
he should get it because he is black

You can see that the not, which I emboldened in the examples above, is in a different place in each one.

In the first one, the negation is part of the 'lowest' level of embedding and only negates the 'getting the money' situation: he should not get the money because he is black. The higher levels tell us that the speaker does indeed believe this (negated) proposition.

In the second one, the negation is 'higher up' - it negates the whole situation of the speaker thinking something. The lowest level is the proposition that he should get the money because he is black, and the not tells us that speaker does not believe this.

Maybe it's hard to follow this if you just read it through, but if you think about the two paraphrases you'll probably find you have these same two interpretations. I leave you with a joke that requires a similar scope-of-negation ambiguity:

A newly-wed couple are leaving for their honeymoon. The man says to the woman, 'Would you have married me if my father hadn't left me a fortune?', to which she replies, 'Darling, I'd have married you no matter who had left you a fortune'.