Brouwer’s analysis of logic led him to an intuitionistic logic which rejects the law of excluded middle and the law of double negation. These laws are not valid in intuitionistic type theory. Thus it does not contain classical (Peano) arithmetic but only intuitionistic (Heyting) arithmetic. (It is another matter that Peano arithmetic can be interpreted in Heyting arithmetic by the double negation interpretation, see the entry on  intuitionistic logic.)