Symbolic evidence in arithmetics

I will first remind how Husserl's view on the roles of symbols in arithmetics evolved from 1891 to 1901. Starting from a Kroneckerian point of view according to which only natural numbers, conceived as abstract pluralities, and basic operations of gathering or dividing such pluralities, were genuine objects of intuitive knowledge, Husserl came to see symbolic characterization of numbers within manifolds and formal proofs on the metalogic properties of such manifolds as another way to provide arithmetical knowledge. I will then say a few words on the kind of knoweledge that can be gained from epistemological projects contemporary to Husserl's works such as Peano's axiomatization of arithmetics, Frege and Russell's logicization of arithmetics or Hilbert's attempt to prove the consistency of elementary arithmetics "from the inside".