Following my meditation on the implied reader of the if-then statements proposed in Dorothy Law’s poem Children Learn What They Live, I recognized that the doubt I encountered as a child, peering into the gap between the apparently interlocked puzzle pieces reached to the heart of inference itself.
Only much later I found my kindred spirit while reading Wittgenstein’s Philosophical Investigations. A child – I imagine, in his scenario – wedges apart the logic holding together a simple rule, revealing that for any given rule, you need a further rule that tells you how to follow the given rule. Even if I use neither words nor mathematical symbols and simply point with my finger you need a rule to interpret the gesture.
If you have ever found room for an misinterpretation divergent interpretations where you thought there was none, if you have ever *almost* been tempted to say that s/he has understood wrong, when someone failed to follow your instructions, you may wish to consider the case Wittgenstein presents in §143 of a person B whom you have instructed to write the series of natural numbers. But what if:
he copies the series 0, 1, 2, 3, 4, 5, …. like this: 1, 0, 3, 2, 5, 4, ….. Here we shall almost be tempted to say that he has understood wrong.
Giving further examples in §185, Wittgenstein asks us to consider this:
Such a case would present similarities with one in which a person naturally reacted to the gesture of pointing with the hand by looking in the direction of the line from finger-tip to wrist, not from wrist to finger-tip.