[FOM] FOM] FOM: The Principle of Excluded Middle

Giuseppina RONZITTI Giuseppina.Ronzitti at univ-nancy2.fr
Mon Oct 17 20:06:11 EDT 2005

A small remark and a question.

in his paper "Begründung der Mengenlhere unabhängig vom logischen Satz vom
ausgeschlossenen Dritten. Erster Teil: Allgemeine Mengenlehere" (1918)
[Foundation of set theory independent of the logical law of excluded middle],
Brouwer (consistently, I would say), does not attack the 'classical principle'
but simply uses some other methods of reasoning, such as the continuity
principle. The two 'principles' are of course incompatible, that is to say they
cannot be both 'principles' of the same theory ... so why (this is my question)
when discussing the validity of the classical principle of excluded middle, the
continuity principle (almost) never enters the scene ?

best regards,

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