it be important? What does it matter to me?" What is interesting is how we use mathematical propositions.
 This is how calculation is done, in such circumstances a calculation is treated as absolutely reliable, as certainly correct.
 Upon "I know that there is my hand" there may follow the question "How do you know?" and the answer to that presupposes that this can be known in that way. So, instead of "I know that here is my hand", one might say "Here is my hand", and then add how one knows.
 "I know where I am feeling pain", "I know that I feel it here" is as wrong as "I know that I am in pain". But "I know where you touched my arm" is right.
 One can say "He believes it, but it isn't so", but not "He knows it, but it isn't so". Does this stem from the difference between the mental states of belief and knowledge? No. - One may for example call "mental state" what is expressed by tone of voice in speaking, by gestures etc. It would thus be possible to speak of a mental state of conviction, and that may be the same whether it is knowledge or false belief. To think that different states must correspond to the words "believe" and "know" would be as if one believed that different people had to correspond to the word "I" and the name "Ludwig", because the concepts are different.
If Moore says he knows the earth existed etc., most of us will grant him that it has existed all that time, and also believe him when he says he is convinced of it. But has he also got the right ground for this conviction? For if not, then after all he doesn't know (Russell).
However, we can ask: May someone have telling grounds for believing that the earth has only existed for a short time, say since his own birth? - Suppose he had always been told that, - would he have any good reason to doubt it? Men have believed that they could make the rain; why should not a king be brought up in the belief that the world began with him? And if Moore and this king were to meet and discuss, could Moore really prove his belief to be the right one? I do not say that Moore could not convert the king to his view, but it would be a conversion of a special kind;