In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 11 Jun., 21:32, Virgil <virg...@nowhere.com> wrote: > > > > The idea that the infinite union of finite segments1 > > > 1,2 > > > 1,2,3 > > > ... > > > results in an infinite segment is false. > > > > The idea that an INFINITE union of finite "segments", no two of which > > are identical, must result in a finite segment is not even false. It is > > ridiculous. > > Nearly correct. Absolutely correct is this statement: > The idea of an INFINITE union of finite "segments", no two of which > are identical, is ridiculous.
Not outside of WM's deceitful world of MathUnealism. > > > > > At least not until WM, or someone, comes up with an axiom system in > > which those properties WM posttulates are less self-contradictory than > > they are at present. > > There is no axiom system required.
An axiom system need be no more than a list of the truths that one holds to be self evident. If WM holds nothing to be self evident, then why is he arguing?
> We accept the hierarchy of types;
Which "hierarchy of types" would that be? Google has over 5 million hits on that subject.
> but we assume only one category of primary objects, the numbers; and > one basic binary relation between numbers, namely "x is followed by > y." All other relations of the various types are explicitly > constructed, the quantifiers (Ex) and (Ax) being applied only to > numbers and not to arguments of higher type. No axioms are postulated.
If you accept some hierarchy of types, a category of primary objects , etc. You are proposing a set of axioms.
But if the above are not axioms, then we shall ignore them.