I do not understand the basis of one of Russell's claims at the end of the chapter 'Similarity of Relations' in his Introduction to Mathematical Philosophy. I have taken an excerpt and emboldened the parts that I do not follow.
[...] it is often said that space and time are subjective, but they have objective counterparts; or that phenomena are subjective, but are caused by things in themselves, [...]. Where such hypotheses are made, it is generally supposed that we can know very little about the objective counterparts. In actual fact, however, if the hypotheses as stated were correct, the objective counterparts would form a world having the same structure as the phenomenal world, and allowing us to infer from phenomena the truth of all propositions that can be stated in abstract terms and are known to be true of phenomena. [...] In short, every proposition having a communicable significance must be true of both worlds or of neither.
I don't understand how Russell can say that the objective world will necessarily have the same 'structure' as the subjective world.