Originally Posted by peptic pete:
“"At the end of the Lent Term, Alys and I went back to Femhurst, where I set to work to write out the logical deduction of mathematics which afterwards became Principia Mathematica. I thought the work was nearly finished, but in the month of May I had an intellectual set-back almost as severe as the emotional set-back which I had had in February. Cantor had a proof that there is no greatest number, and it seemed to me that the number of all the things in the world ought to be the greatest possible. Accordingly, I examined his proof with some minuteness, and endeavoured to apply it to the class of all the things there are. This led me to consider those classes which are not members of themselves, and to ask whether the class of such classes is or is not a member of itself. I found that either answer implies its contradictory. At first I supposed that I should be able to overcome the contradiction quite easily, and that probably there was some trivial error in the reasoning. Gradually, however, it became clear that this was not the case. Burali-Forti had already discovered a similar contradiction, and it turned out on logical analysis that there was an affinity with the ancient Greek contradiction about Epimenides the Cretan, who said that all Cretans are liars. A contradiction essentially similar to that of Epimenides can be created by giving a person a piece of paper on which is written: 'The statement on the other side of this paper is false.' The person turns the paper over, and finds on the other side: 'The statement on the other side of this paper is true.' It seemed unworthy of a grown man to spend his time on such trivialities, but what was I to do? There was something wrong, since such contradictions were unavoidable on ordinary premises. Trivial or not, the matter was a challenge. Throughout the latter half of 1901 I supposed the solution would be easy, but by the end of that time I had concluded that it was a big job. I therefore decided to finish The Principles of Mathematics, leaving the solution in abeyance. In the autumn Alys and I went back to Cambridge, as I had been invited to give two terms' lectures on mathematical logic. These lectures contained the outline of Principia Mathematica, but without any method of dealing with the contradictions."”
this doesn't ring true......