Having considered the (informal) logical fallacies bandied about during the recent general election campaign, and in political discourse generally, we now come to the rather more nuanced matter of Brexit and the EU Referendum of 2016. Do the various claims made about the 2016 vote stand up to (logical) scrutiny?

We commonly encounter three main types of proposition:

1. Because not everyone voted (or because the margin was narrow) it is not the case that the British people really voted to leave the EU.

2. We voted to cut immigration/to leave the Single Market/etc.

3. Staying in the Single Market would mean we haven’t left the EU

Additionally, there is much disagreement and confusion about the precise meaning of:

4. Hard/Soft/Full/Pragmatic/Open (etc.) Brexit

Evaluating the claims of (1) is a matter of political or constitutional judgement, though pace Professor Anthony Grayling, it seems straightforwardly the case that this plebiscite was at least valid in the same way that other British democratic votes are. First, a constituency MP may win his or her seat by a single vote and on a minority of the total votes cast. Second, voting is not compulsory in the UK and we therefore regard non-voters as those who choose not to vote, for whatever reason, not prevented from doing so. The legislation which led to the EU Referendum could have set determined things otherwise, either by setting a minimum level of turn-out or a minimum percentage majority.

On the other hand, the margin of victory (for Leave) was narrow, and politicians (with an eye to future elections) might reasonably want to take account of that fact. Indeed the narrow margin of victory was acknowledged by a number of prominent Leavers, such as Daniel Hannan:


There are many ways that one might question the validity, strength or fairness of the referendum result. Professor Grayling, as I have already mentioned, has tried a number of avenues, but as Pete North has already criticised them with characteristic verve, I shall not consider them here. Instead, I shall move on to (2), (3) and (4).

How Hard is Your Brexit?

To take the last (4) first, how can we be clear what is meant when an adjective like hard, soft, or open (among others) is used to modify Brexit? We shall return to this question, because first we must settle what Brexit means, but for now let us note that one of our problems is that we are dealing with recent coinages. Brexit itself is the major element, and the OED tells is that it was coined in 2012 by Peter Wilding (the founder and director of the British Influence think tank, and a ‘Remainer’, by the way). Around the same time, The Economist came up with the alternative Brixit, but that, to my mind, rather more elegant coinage failed to enter the lexicon.

However, just because Mr Wilding coined the term, that does not mean that he retains ownership of its definition. Words are conventional signs and for them to function as such there must be a measure of agreement about that to which they refer, or what they signify, if you want to get Suassurean about it. A dictionary can help, but a dictionary definitions are current or historical survey examples of how a word is used.

Even a word’s etymology can be the refuge of the pedant and yield uncertain results. If you are over 40, you may recall your English teacher chastising you for using the word nice (to mean pleasant) and pointing out that nice actually means fine or subtle. It would have been more accurate to say that it used to mean that, but a look at the etymology shows its origin to be the Latin nescius, meaning ignorant, which is usually neither fine nor subtle. Other words can often have both common and specialist meanings. The word chronic means recurring or persistent over time when used in a medical context. When applied to anything else it can also mean serious, poor quality or even acute (its precise antonym). Also, many words have very specific meanings when they are new, but develop more general meanings as they become more widely used. Many people, for example, hoover using with a Dyson® vacuum cleaner, or play with flying discs that are not genuine Wham-O Frisbees®. Another example would be internet which is used by most people to mean what geeks would call the web (that portion of the internet accessible with a web browser).

And since we’re talking about logic here, there are plenty of examples from philosophy. The most common, and the most annoying is, “begs the question…” which people (understandably) use to mean “Such-and-such leads (begs) us to ask the question…” What it actually refers to is a (fallacious) argument which takes one of its premises for granted:

“I know that the events in Dan Brown’s The Da Vinci Code actually happened because it says so at the beginning of the book.”

The ‘proof’ is merely a restatement of the premise. Another example of specialist/non-specialist usage which concerns us more is referring to something as a valid argument. People use this to mean that a particular argument or statement is good or convincing, but in the area of formal logic its meaning is very particular. It simply means any argument where the conclusion follows ineluctably from the premises. Thus:


A. All Prime Ministers live at 10 Downing Street

B. Theresa May lives at 10 Downing Street

.˙. Theresa May is Prime Minister


C. All monkeys are elephants.

D. All elephants are amphibians.

 .˙. All monkeys are amphibians.

The conclusion of syllogism (i) is true, and so are its premises (A and B), but the argument is invalid. The conclusion of syllogism (ii) is false, and so are its premises (C and D), and yet the argument is valid. An argument is valid if the truth of the premises guarantees the truth of the conclusion. Premise B could have been “Philip May lives at 10 Downing Street”, and the conclusion “Philip May is Prime Minister” would be false. Premises C and D are untrue, and yet if they were true, then the conclusion would necessarily be true. However, most people would say that (i) is a valid argument whereas (ii) is invalid. As we have seen, (ii) is actually valid, but because its premises are obviously untrue, it is unsound. Far more dangerous is the invalid argument that at first glance seems valid (and even sound). But, again, we shall come back to this.

Now, back to hard and soft Brexit…

Brexita portmanteau of Britain (or British) and exit fairly clearly refers to the process or completion of Britain (the UK) leaving membership of the European Union. People differ over whether Brexit is something that has already begun and of which we are in the midst, or whether it describes some future status of the UK having left. The way it is used suggests that it is a noun, rather than a verb (few talk of Brexiting, though it also functions as an adjective in phrases like ‘Brexit Britain’) which means that Soft Brexit and Hard Brexit are noun phrases. Noun phrases function like words, in effect, and we must consider the whole phrase as a single unit, with its own accepted definition.

Take the noun-phrases white paint, oil paint, exterior paint, finger paint and paint brush. In the first, white describes a quality of the paint, in this case its colour. Oil does a similar job, inasmuch as it describes what kind of paint it is, viz. one with a linseed oil base (rather than an oil coloured paint). Exterior paint tells us what a paint is primarily used for, yet finger paint is not for painting fingers, but paint deigned to be applied with fingers. In paint brush, the syntax alerts us to the fact that paint is here the adjectival portion of the noun phrase and modifies brush, rather than brush modifying paint as in the other examples.

Thus, when it comes to hard and soft Brexit, we cannot simply rely on a knowledge of the ordinary meaning of those adjectives to tell us what the noun phrases hard Brexit and soft Brexit mean. The adjective soft often appears in noun phrases along with words like butter or clay, where it means (physically) malleable; glow, breeze, focus and whisper where it means pleasing or subtle; option, words, Left or southerner, where it means lenient, compassionate or weak; drugs or porn where it means less powerful or less explicit; prices where is denotes falling or weak value; water where it means low in mineral salts; and so forth. In some of these cases (e.g. soft butter, soft Left, soft water) the antonym is formed by using hard, but this is not so in every case. We do not (commonly) talk of a hard breeze (but rather a stiff breeze) or hard focus (but rather sharp focus). All these are examples of what Aristotle (in the Metaphysics) labelled the Pros Hen Ambiguity; where a particular word operates in a related but subtly distinct sense.

The meaning of soft (or hard) in a given noun phrase does not function in an identical way, although its meanings are related. The extent to which soft/hard have positive or negative connotations rather depends on one’s point of view. Plenty of people would say that Peace Studies is a soft subject (easy and insubstantial) in a way that is intended to be derogatory, although lecturers in Peace Studies would no doubt disagree. Being hard headed is usually regarded as a good thing (logical and clear-minded) whereas to say that someone is hard hearted is normally regarded as an insult (cruel or unfeeling).

Some uses are more ambiguous, and wether one regards the use of soft/hard and positive or negative will depend on one’s point of view. Soft power, for example will be regarded as a good thing by those who regard diplomatic and cultural influence as geopolitically important. It will be regarded negatively by those who feel that coercion, cash and combat are the only kinds of power that these foreigners understand. Hard and soft Brexit seem to fall into that ambiguous category. Indeed, Paul Staines has recently suggested that they may now be obsolete as useful terms.

Most (though by no means all) Leavers will tend to regard hard Brexit as preferable to soft Brexit, and vice versa. Because the use of these noun phrases usually expresses a value judgement, exactly what, precisely, is being signified in either sense is far from straight-forward. However, the following figure might be a reasonable picture of how the terms are used.

Screen Shot 2017-06-20 at 19.44.04

The far left hand side of the figure — retaining all of our current links to the EU — cannot be regarded as any kind of Brexit, as it would mean no change. This is the 100% Remain extreme. The far right hand side of the figure represents the severing of all ties, not only with the EU but with any body related to the EU, possibly up to and including withdrawing from agencies like Eurocontrol and perhaps even the Council of Europe. This is the 100% Leave extreme.

Other options, such as Single Market participation, UK/EU Free Trade Agreements, ‘crashing out’ and relying on ‘WTO Rules’, or thousands of other details, can all be plotted somewhere between these two extremes. Many of them would also be somewhere on the blue ‘Brexit continuum’ (and thus within the Soft/Hard range). Where, precisely, they will be placed (between 100% Remain and 100% Leave, between softer and harder) largely depends upon an individual’s own understanding of what Brexit means. In the view of many, for example, any kind of Single Market membership would not even make it onto the blue ‘Brexit continuum’.

What seems clear is that neither Soft Brexit nor Hard Brexit have a precise meaning given the enormous number of possible Brexit outcomes. A term is said to be used univocally when its meaning is precise. For example, the word animal has a precise meaning when used in a literal/technical sense, whether it refers to a cockroach or a human being. A word used equivocally may have a different meaning in different contexts. A nut may refer to an edible seed or a hexagonal head of a threaded bolt. Most words are used analogously (though not necessarily metaphorically). Thus when I say that I love my wife and I love my dog I use the word love correctly and meaningfully in both cases. Yet it is clear (I hope) that I do not love both in the same way and to the same extent. I love each in a way which is intelligible and appropriate to each. I do not throw sticks for my wife to fetch, neither do I take my dog out for romantic meals.

Soft and hard are also used analogously (and relatively). We know what is being described when someone talks of butter being hard or soft. We do not suppose that hard butter will be hard in the way that marble is hard, or that soft butter will be soft in the way that candy floss is soft. The softness and hardness of butter are relative to one another. Refrigerated butter is softer than frozen butter, but harder than room temperature butter. Thus, Brexit is soft(er) in comparison to some harder’ Brexit, or hard(er) in comparison to some ‘softer’ Brexit. Nigel Farage’s soft Brexit may even be harder than Nick Clegg’s hard Brexit.

We can understand adjectives like soft and hard when used with respect to butter because we understand what butter is. Whether we can understand them when used with respect to Brexit all depends upon whether we understand what Brexit is, and is not. But that is a matter for the next post…