FOOD for THOUGHT PROGRAMME - Blog 5: Critical Moment

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This week, I would like to focus on the following strand of the Food for Thought programme:

The purpose of this strand is to get pupils thinking more explicitly about the construction and deconstruction of logical arguments. Forgive a potted history-of-philosophy lesson here, but I think it’s useful if we all work with the same terminology. So to summarise:

Arguably the whole basis of (Western) logical thought is the ‘syllogism’. In simple terms, a syllogism is a three-part logical argument in which two premises are combined to arrive at a conclusion.

So long as the premises of the syllogism are true and the syllogism is correctly structured, the conclusion will be true.

An example of a valid syllogism is:

All mammals are animals. [PREMISE] 

All elephants are mammals.  [PREMISE] 

Therefore, all elephants are animals. [CONCLUSION] 

An example of an invalid syllogism is:

Some trees are tall things.   [PREMISE] 

Some tall things are buildings.  [PREMISE] 

Therefore, some trees are buildings. [CONCLUSION] 

In both cases, both premises are in themselves true statements and in both the premises have been combined to form the conclusion; but in the first one, that process of combining the premises is logically valid, so the conclusion is true, but not so in the second.

Of course, the process can be extended into multi-stage arguments as well, with intermediate conclusions which then in turn become one of the premises of the next stage of argument.

Just because the conclusion is true, it doesn’t necessarily mean the syllogism is valid; nor does it necessarily mean the premises were true. E.g.

Some chocolates come in tins.

All biscuits come in tins.

Therefore some biscuits are chocolate-flavoured.

In this instance, one of the premises is true; one of the premises is false; the argument is invalid; but the conclusion happens to be true.

Therefore it is important to separate in our minds the truth-value of a statement from the validity of the argument by which we may have reached it.

We all do this on a frequent basis. I’m sure we have all at some point said in a meeting, ‘Well, I agree with you but for not for those reasons, actually.’ Maths teachers frequently come across pupils with the ‘right’ answer but the wrong working!

So the challenge is to encourage our children to think more explicitly about the logical arguments they are constructing. This year, I have been discussing with my teaching colleagues some ideas about how we could do this kind of thing in lessons.

But we can also have some critical fun with our children at home. Most of us will have heard of, and probably read (or watched!), the Alice stories by Lewis Carroll (real name, Charles Lutwidge Dodgson – fun fact to follow on him at the end!).

Most people don’t know that Dodgson was actually an Oxford mathematician, and apparently a very dreary lecturer at that. There was a famous story, which Dodgson denied, that Queen Victoria, having admired Alice in Wonderland, expressed the desire to be sent Dodgson’s next book; and received in due course ‘An Elementary Treatise on Determinants’.

Despite the apocryphalness of the story, Dodgson’s literary efforts were very influenced by his mathematical background, especially his love of logic and its ability to be twisted into illogicality and nonsense. He invented a game for children called The Game of Logic (which you can still buy in book form, or even access for free online) to teach syllogistic reasoning.

One term coined in Dodgson’s writings that has caught on is ‘sillygism’. A ‘sillygism’ produces a ‘delusion’, rather than a conclusion. Here are a couple:

No cat has eight tails.

A cat has one more tail than no cat.

Therefore, a cat has nine tails.

I am a nobody.

Nobody’s perfect.

Therefore, I am perfect.

Although Dodgson made up the (very silly!) term ‘sillygism’, the idea of a ‘sillygism’ has been around for a very long time: in the Middle Ages, scholars compiled and analysed whole catalogues of ‘sillygisms’ (only they called them sophismata). One of my personal favourites is a whole catalogue of sillygisms proving that ‘you are an ass’, by a chap called William Heytesbury. I don’t know if he and his friends ever traded off such syllogistic insults, in a sort of logical rap-battle, but I like to think they might have. Here’s one example:

You are the owner of an ass.

An owner is something.

Therefore you are something of an ass.

Why not have some fun at home coming up with the silliest sillygism you can think of? Do email me any particularly good ones, so I can share them with the Food for Thought Team.

Now for that promised fun fact. Charles Lutwidge Dodgson loved messing around with words, and names were no exception. He chose the pen name Lewis Carroll as an inversion of his first two names (Lutwidge became Lewis; Carolus is the Latin form of Charles, which is why we call the reign of Charles I the Caroline era). But Dodgson also had a stammer. So often when he met people, he ended up introducing himself as ‘Do-Do-Dodgson’, and gained ‘Dodo’ as a nickname. So the Dodo in Wonderland is, in a way, Lewis Carroll himself…

Have a fantastic Half Term!

DPB