Lichtenberg says that very few people have ever seen pure white. So do most people use the word wrong, then? And how did he learn the correct use? — He constructed an ideal use from the ordinary one. And that is not to say a better one, but one that has been refined along certain lines and in the process something has been taken to extremes.
In this image, exactly the same shade is used for A and B
We have to distinguish between a white surface and a white illuminant. When Lichtenberg said that few people had ever seen pure white, he was probably thinking of the mixture of colors in light, in other words, of white illuminants.
There are various ways in which an illuminant might count as "pure white". It might have exactly the right mix of red, green and blue wavelengths to stimulate each of the eye receptors by just the right amount. Or it might have a very smooth spectrum profile, like black body radiation (such as that from incandescent bulbs, which have recently been "banned" in the EU, effectively putting an end to "pure white light" in familiar places).
There are also various ways in which a reflective surface might be pure white.
There are still further ways in which a surface might be represented as being white in a painting or photograph, as discussed in remarks 1–3.
In the case of reflective surfaces, "being pure white" is very much a matter of context — in other words, it is a matter of how much the other reflective surfaces in the entire scene absorb and reflect light. The eye takes account of this by means of opponent cells, which I will explain shortly.