Page "Absolute Infinite" Paragraph 3

The idea that the collection of all ordinal numbers cannot logically exist seems paradoxical to many.

This is related to Cesare Burali-Forti's " paradox " that there can be no greatest ordinal number.

All of these problems can be traced back to the idea that, for every property that can be logically defined, there exists a set of all objects that have that property.

However, as in Cantor's argument ( above ), this idea leads to difficulties.