# Intuitionism and rejection of standard logic postulates

Intuitionism refuses the Cantor hypothesis about continuum as a hypothesis meainingless from the intuitionistic point of view Also, 'the tertium non datur' principle: $$A\vee\neg{A}$$ is rejected 'a priori' in the sense that we can only prove the validity of $A$ or $\neg{A}$. My question is: given the rejection of these principles, in particular the second, is it still possible to keep the validity of the mathematical analysis within the intuitionism? Or maybe, accepting the intuitionistic approach, you need to develop a new kind of analysis, because, for example, it's impossible to use the 'reductio ad absurdum' to prove a theorem? Thanks

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Today at least, Weyl's predicativism is often taken to be "predicativism given the natural numbers". That is, we begin with the assumption that the set of natural numbers exists, but we proceed predicatively beyond that point, avoiding quantifiers over $P(N)$ but allowing arbitrary quantification over $N$. –  Carl Mummert Feb 29 '12 at 13:56