History is for human self-knowledge…the only clue to what man can do is what man has done. The value of history, then, is that it teaches us what man… - R. G. Collingwood

When a student is in statu pupillari with respect to any subject whatever, he has to believe that things are settled because the textbooks and his teachers regard them as settled. When he emerges from that state and goes on studying the subject for himself he finds that nothing is settled. The dogmatism which is an invariable mark of immaturity drops away from him. He looks at so-called facts with a new eye. He says to himself: 'My teacher and textbooks told me that such and such was true; but is it true? What reasons had they for thinking it true, and were these reasons adequate?

Lastly, what is history for? This is perhaps a harder question than the others; a man who answers it will have to reflect rather more widely than a man who answers the three we have answered already. He must reflect not only on historical thinking but on other things as well, because to say that something is 'for' something implies a distinction between A and B, where A is good for something and B is that for which something is good. But I will suggest an answer, and express the opinion that no historian would reject it, although the further questions to which it gives rise are numerous and difficult.

We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking.