Why does Wittgenstein have a problem with logical statements saying nothing ? (5.5303) . How would Wittgenstein want us to interpret f(a,a) ?
He also mentions axiom of infinity from which Russell argued for the existence of an infinite number from the definition of cardinal number. He defined 0 as number of propositions that are true and false or the number of elements in an empty set. Then the set containing only 0 has 1 element. Hence the number 1 exists and other natural numbers can be easily proven to exist. Does avoiding the use of equality symbol prevent us from equating objects that are not identical or especially in case of Aleph numbers, say equating the set of odd numbers with the set of even numbers since they have the same cardinality. For example in case of 1=p and 1=q , we conclude p=q but p and q are not identical. Which may cause problems according to wittgenstein as he writes
" Roughly speaking: to say of two things that they are identical is nonsense… "
I am really confused here and l am quite sure that l am getting this wrong completely or missing the key issue beforehand. It would be great to see some clarification regarding the points shown in the picture. I am quite happy to change my mind if l see some interpretations that are polar opposite of what l have understood.