  With this view in place, Brouwer sets out to reconstruct Cantorian set theory. When an attempt (in a draft of the dissertation) at making constructive sense out of Cantor’s second number class (the class of all denumerably infinite ordinals) and higher classes of even greater ordinals fails, he realises that this cannot be done and rejects the higher number classes, leaving only all finite ordinals and an unfinished or open-ended collection of denumerably infinite ordinals. Thus, as a consequence of his philosophical views, he consciously puts aside part of generally accepted mathematics. Soon he would do the same with a principle of logic, the principle of the excluded middle (PEM), but in the dissertation he still thinks of it as correct but useless, interpreting \(p \vee \neg p\) as \(\neg p \rightarrow \neg p\).