A step back: an excluded middle?

The discussions above due to Peano and Dedekind freely used the classical logic. Further development of set theory in works of Cantor, Zermelo, Koenig, von Neumann and others (see in further sections) also assumed that the laws of logic - though not properly formalized as yet (because the need to formalize logic followed only after the attempts to formalize mathematics) - are clear and obvious. Let us stop at an important dissenting voice: we will read a translation of an address by L. E. J. Brouwer from 1923 in which he attacks the law of the excluded middle. At the beginning of the 20th century, Brouwer stood for intuitionism while Hilbert (which we'll met later) stood for formalism. The first-order predicate logic which is predominant today is based on Hilbert's work.

Read an answer the following in prepartion for November 1:

• Read the address On the significance of the principle of excluded middle in mathematics, especially in function theory (1923).
• Can give an example of a mathematical statement whose validity Brouwer question?