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## My Philosophical Development, 1959, by Bertrand Russell

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### W uw[̐wIʁv n.13

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### Chapter 8 Principia Mathematica: Mathematical Aspects, n.13

The whole theory of ancestral relations is very important not only in connection with numbers. For this reason we developed the theory before introducing the definition of number.

I come now to what I call erelation-arithmetic' which occupied the second half of the second volume of Principia. From the mathematical point of view this was my most important contribution to the work. What I called erelation-numbers' were numbers of an entirely new sort of which ordinal numbers were a very specialized example. I found that all the formal laws which are true of ordinal numbers are true of this far more general kind. I found, also, that relation-numbers are essential to the understanding of structure. eStructure' is one of those phrases, like eand so on' or eseries', which are familiarly employed in spite of the fact that no precise significance is attached to them. By means of relation-arithmetic the concept estructure' can be precisely defined.
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