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Bad nasty Sorites disrupts infant nap time

2010-07-15

Here’s a bit of an old one that I had lurking around. I was going to post it weeks ago, but as the Hansard source it is discussing is already over a decade old, I figure a few more days in the freezer wouldn’t do it any harm.

For today’s Parliamentary logic lesson, we’re going back to the 11th of March, 1998, for a debate on class size limits in schools. The debate reminds me that an upper limit on school class sizes was one of New Labour’s 1997 manifesto commitments.

This is not a particularly controversial topic: everyone really agrees that it is a preferable situation to have fewer children in classes – it really is not justifiable to have, say, 40 students in a class. One of the key selling points for independent schools, prep schools and also of some universities later in the educational cycle is the one-to-one and small group attention. Dealing with 15 students rather than 40 means that during an hour, one can have more personal attention to each person’s work and learning, and one has less disciplinary problems.

Any kind of policy needs to fit in with government’s “choice” agenda: the very idea of choice has become an ideological commitment for government. You need to have a choice of hospitals, a choice of schools, a choice of surgeons, a choice of this, that and the other. It sure is nice to have a choice of dentists. I would like it more if my previous NHS dentist could communicate with patients better and wasn’t a rampant misogynist, but, you know, choice!

Stephen Dorrell brought up the issue of faith schools and choice: if one is supposed to have choice between going to a Catholic school or a Church of England school or a Jewish school or whatever, the imposition of a class size limit may make it so that your child cannot go to the religious school of your choice. The same is true of specialist schools, which have been blossoming across the country. In my area, we now have specialist secondary schools doing technology, arts and sport. Across the country, there are also specialist secondary schools for languages, humanities, mathematics, business, music and so on. How has your choice been increased, then, if you have a kid who is really good at music but can’t get into the specialist music school because he would put the school above the size limit? That’s a problem.

Or, as Stephen Dorrell put it:

The hon. Gentleman shakes his head, but I shall willingly give way to him if he can explain how a limit on class size and a refusal to accept a 31st child into a class, although that may reflect the parents’ preference, enhances parental preference. How does it enhance parental preference to deny parents the opportunity to put their child into the 31st place, if that is their choice and if the head teacher believes that it is consistent with the educational interests both of the 31st child and of the other 30? How does the removal of that opportunity enhance parental choice?

Here we have a budding Sorites fallacy living in the wild, in an evolutionarily undemanding environment – the House of Commons. A Sorites fallacy is intriguing. To understand the fallacy, you must understand the paradox it is based on. To understand that, ask yourself a question: what is a heap of sand? If I put a grain of sand on the table in front of you, you would agree that is not a heap. If I add another grain of sand next to it, that doesn’t make it a heap. Now, I can keep on adding grains of sand, and at some point it becomes a heap. But at whatever point I add that grain of sand and you declare it a heap, I can take one grain of sand away and it doesn’t suddenly stop being a heap. There is a real vagueness we have about grains of sand, crowds of people, herds of cows, swarms of bees, expressions like “quite a lot” and, indeed, class sizes.

Where does the fallacy come in? If you argue from the vagueness of the heap to the non-existence or over-existence of the heap, you have committed a Sorites fallacy. So, if you say that because we can’t actually say at which point the heap comes into existence, there is no heap, that’s obviously wrong. Or if you go the other way and say that because you can’t say at what point the heap comes into existence, then any grain of sand sitting alone is a heap, that’s an erroneous conclusion too. Any conclusion from the existence of the Sorites paradox other than “gee, there’s either a philosophical puzzle or just vague langauge in play” leads you to the wrong conclusion. In fact, it is self-defeating, because if you deny the heap, then the Sorites paradox doesn’t arise, which means you don’t have your grounds for dismissing it.

How does this apply to the infant class size discussion? Simple. Everyone agrees that there is a point at which the class is too big. But it isn’t an absolute limit: if the limit were 30, then the odd case of there being 31 pupils in the class is not a major concern. And maybe 32 is okay. But if 32 is okay, why not 33? And if that is okay, why not 34? If 34, why not 35? Feel free to carry this logic on for as long as you like. But then you get to your endpoint – 40, say – and then you say “hold on, there really is a big difference between having 40 in the class and 30? Damn you, logic, how did you get me to this point?”

The problem here seems to be that the law ought to have an absolute upper bound, but also have some other way of ensuring that the class numbers are kept towards the preferred upper bound. So, you’d say the absolute upper bound is 35, but the preferred upper bound is 30. You’d then average out the school or the LEA’s adherence to this rule, and if, on average, they kept their schools at the preferred upper bound rather than the absolute upper bound more often than not, they’d get a financial reward for doing so. There are clear analogies here: if you are going 71 miles per hour in a 70 miles per hour limit (a motorway, say), you will not get punished in the same way that someone going 75 miles per hour in a 30 miles per hour limit will. This involves both discretion (from the police, the CPS and judiciary) and some clear set rules over things like statutory penalty notices.

Of course, when you have a big cloud of politics over the proceedings, you cannot necessarily tell the intent of the government. Perhaps 30 is supposed to be the absolute upper limit, and that the government really want schools to try and cut class sizes down to 25, with the ability to go up to 30 at a push.

The problem here is that you can’t have vague legislation: however you slice it up, with whatever incentives, flexible options and the like, you still need to have some point at which you say “too much is too much”. Hence Bob Blizzard’s later remark:

In setting, in effect, a class size limit of 35, would not the hon. Lady, by her own argument, then face the problem of the 36th child—if that is deemed to be a problem?

Now, to try and give weight to this Sorites-backed argument, Stephen Dorrell constructs a hypothetical:

Surely to goodness, when deciding about class size against the background of the different skills and experience of individual teachers, a head ought to take that into account. It is nonsense to say that it is always better to be in a class of 29, even if the teacher is young and recently qualified and has had some difficulty in qualifying, than to be in a class of 31 taught by a very experienced, highly qualified and successful infant school teacher.

The fallacy here is far more clear: if you don’t compare like with like, you can come to silly conclusions. Hence the need for our politicians to take a spoonful of ceteris paribus with their morning tea.

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