In article <email@example.com>, firstname.lastname@example.org wrote:
> 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.
Everything we attempt to define ultimately has no formal definition
> > You can see best that it is rubbish by "proving" something and "proving" > exactly the opposite (using other axioms).
Why is there any problem with different assumptions leading to different, even possible exactly opposite conclusions?
Anyone who is incapable of realizing that one's conclusions derive from one's assumptions, and different assumption tend to lead to different conclusions, knows nothing about mathematics or logic and had no common sense.
Anyone who, like WM, prides himself on such a willful amalgam of ignorance and stupidity, should be forever prohibited from teaching anyone anything. That he has not been is evidence of corruption at Hochschule Augsburg, University of Applied Sciences --