Intuitionist definitions, developing from the philosophy of mathematician L. E. J. Brouwer, identify mathematics with certain mental phenomena. An example of an intuitionist definition is "Mathematics is the mental activity which consists in carrying out constructs one after the other." A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions. In particular, while other philosophies of mathematics allow objects that can be proved to exist even though they cannot be constructed, intuitionism allows only mathematical objects that one can actually construct. Intuitionists also reject the law of excluded middle (i.e., formula_1). While this stance does force them to reject one common version of proof by contradiction as a viable proof method, namely the inference of formula_2 from formula_3, they are still able to infer formula_4 from formula_5. For them, formula_6 is a strictly weaker statement than formula_7.