Beggars do not envy millionaires, though of course they will envy other beggars who are more successful.

To avoid the various foolish opinions to which mankind are prone, no superhuman genius is required. A few simple rules will keep you, not from all error, but from silly error.

Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".

I wish to propose for the reader's favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true.

I suggest to young professors that their first work should be written in a jargon only to be understood by the erudite few. With that behind them, they can ever after say what they have to say in a language 'understand of the people.'

What else is there to make life tolerable? We stand on the shore of an ocean, crying to the night and to emptiness. Sometimes a voice of one drowning, and in a moment the silence returns. The world seems to me quite dreadful, the unhappiness of many people is very great, and I often wonder how they all endure it. It is usually the central thing around which their lives are built, and I suppose if they did not live most of their lives in the things of the moment, they would not be able to go on.

Collective wisdom, alas, is no adequate substitute for the intelligence of individuals. Individuals who opposed received opinions have been the source of all progress, both moral and intellectual. They have been unpopular, as was natural.