§182

Eager not to spare other people the trouble of thinking, Wittgenstein presents us with some exercises in §182 with the intention of getting us to think about, "[t]he grammar of 'to fit', 'to be able' and 'to understand'."

"Exercises: (1) When is a cylinder C said to fit into a hollow cylinder H? Only as long as C is inside H? (2) Sometimes one says that: C has ceased to fit in H at such-and-such a time. What criteria are used in such a case for it having happened at that time? (3) What does one regard as criteria for a body's having changed its weight at a particular time, if it was not on the balance at that time? (4) Yesterday I knew the poem by heart; today I no longer know it. In what kind of case does it make sense to ask, 'When did I stop knowing it by heart?' (5) Someone asks me, 'Can you lift this weight?' I answer 'yes'. Now he says, 'do it!' - and I can't. In what kind of circumstances would one accept the excuse 'when I answered 'yes' I could do it, only now I can't'?"

(1) We don't only say that a cylinder fits a hollow cylinder when it is inside it. If the two cylinders were very heavy and we didn't want to have to put one inside the other to check that it fits we might measure each of them. This would tell us that one fits inside the other.
(2) It could be that C was heated and expanded between t1 and t2 and H did not expand. If C fitted H very tightly we might say that it ceased to fit as soon as it expanded. - We'd need some way of determining that C had expanded and that H (or the hollow area within H) hadn't expanded to the same extent.
It could be that H was hit with a hammer at 12o'clock and that the shape of it was distorted in such a way that C would no longer go inside H. You could then say that C ceased to fit H at 12o'clock (this might be clearly visible - it could be that H was completed flattened by the blow).
(3) You could see the effect that the body has on other bodies at various times - e.g. that a boat sinks when the body (whatever it is) is placed on it at t2 but hadn't sunk at t1 when the body was placed on it.
You could perhaps see that something has grown significantly and be quite sure that it had grown heavier.
- There are various criteria by which you might determine that a body has changed weight at a particular time.
(4) It may be that you can recall knowing a poem by heart at school but then remember being asked to recite it at some later date and not being able to. You might then say that 'I stopped knowing the poem by heart at some point between when I was at school and the occasion when I was asked to recite it.'
Hacker: "Primarily when one can associate the loss of ability with a temporally identifiable cause (a blow on the head, a sudden shock, etc.)
(5) You could imagine a case where someone is presented with a fairly light weight and asked whether they can lift it. The person is an experienced body-builder and knows the kind of weight they're able to lift. In that case they could quite reasonably say that they are able to lift the weight. But you could then imagine that someone punches them hard in the back (having asked them if they were able to lift the weight).


I found this passage confusing. What kind of philosophical problems does Wittgenstein have in mind when he says that reflecting on cases like these could help us to resolve them? - Presumably, since he has been discussing understanding he thinks that this could help us to resolve philosophical confusions regarding understanding. Do these exercises help us to appreciate that understanding is akin to an ability? Is the intention to help us to recognise the variety of criteria by which we determine whether someone has correctly said that they understand/or are able to go on? - One parallel you could draw is between the cases of B observing A and annoucning that he can go on and the weightlifter saying that they are able to lift the weight (in each case someone is saying that they are able to do something and in each case they might turn out not to be able to do the thing they said they could).

Where does something fitting something else come into all of this? - The last time I remember Wittgenstein talking about fitting was when he was talking about the mistake of thinking that 'true' fits 'proposition' and that the meanings of words fit together in a proposition.