When I first read Ludwig Wittgenstein’s Philosophical Investigations,
I was a student struggling to make sense of it. Now as I read it on the
70th anniversary of its posthumous publication, I am a teacher
struggling to make sense of it. In my job, I teach adults who speak
English – or at least have a good grasp of it as a spoken language –
how to read and write. And not how to read and write ‘professionally’,
but rather how to connect sounds to shapes on a page and vice versa,
how to spell the language’s most common words, and how to write a
complete sentence.
There is a member of my class who, although he can say and use the
words we study, and has a good grasp of consonants, will not include
vowels when he spells. I will ask him to spell the word ‘went’, for
example, and he will spell out ‘wnt’. If I correct him once, this
currently makes no difference – the next time, he will spell without
vowels just the same. As you may imagine, I can find this very
frustrating.
Wittgenstein writes of a similar case in one of the central sections of
the Investigations. He describes teaching a pupil the series 0, n, 2n, 3n,
etc, where n = 2. Only, when the pupil gets to 1000, he writes 1000,
1004, 1008, 1012:
We say to him: ‘Look what you’re doing!’ – He doesn’t understand.
We say: ‘You should have added two: look how you began the series!’
– He answers: ‘Yes, isn’t it right? I thought that was how I had to do
it.’
– from §185 of Wittgenstein’s Philosophical Investigations (4th ed,
2009)
Wittgenstein then compares this to a case of someone who does not
react naturally to a gesture of pointing: someone who looks in the
direction from fingertip to wrist instead of following the line beyond
the fingertip. We might also think of a cat, staring blankly at a
pointing finger. He goes on to suggest that the rules we take for
granted as governing all manner of human activity, from mathematics
to the grammar of propositions, cannot be explicated by the Platonic
tradition of reference to ineffable objects, nor by a subjective
‘interpretation’ at the moment of each instantiation of the rule. Rather,
they in a sense rely on shared agreement in natural inclination, or in
common practices. Our understandings are just what we do. They are
our form of life. (This is, it strikes me, a very teacherly attitude. Every
teacher knows that it is no use just having a learner say they
understand: we have to watch them do it.)