On Monday, 17 June 2013 00:36:03 UTC+2, Virgil wrote: > In article <email@example.com>, firstname.lastname@example.org wrote: > On Sunday, 16 June 2013 21:16:06 UTC+2, Virgil wrote: > > Since WM apparently claims to be able to define everything, what words will > > he use in his very first definition, before he has defined any words? > > The definitions are based upon the knowledge already acquired in school. In other words, all formal definitions are ultimately based on things which are not formally defined at all. --
Of course. "Formal" is a very subjective word that could be attached to any kind of arguing, by sketches as well as by dancing or singing or speaking.
Today it is mainly used for the formalism of FOPL+ZFC, but it is based on that thinking that has been acquired during life and that is informal. And the important things like set or definition or truth has no formal definition. Therefore this matheological branch is as useless as the rest.
You can see best that it is rubbish by "proving" something and "proving" exactly the opposite (using other axioms). A real proof is nozt the "formal" of some nonsense from some assumed nonsense, but includes above all to use the correct premises sometimes called axioms. But this word has been perverted and besmirched by matheology such that one feels some disgusting taste when using the word axiom.