On 24 Feb., 21:04, William Hughes <wpihug...@gmail.com> wrote: > On Feb 24, 8:32 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 24 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote: > > > > So, when WM says that a natural number m does not > > > exist, he may mean that you can prove it exists > > > but you cannot find it. > > > > Suppose that P is a predicate such that > > > for every natural number m, P(m) is true. > > > Example: Every line of the list L > > > 1 > > 1, 2 > > 1, 2, 3 > > ... > > > contains all its predecessors. > > > > Let x be a natural number such that > > > P(x) is false. According to WM you cannot > > > prove that x does not exist. (WM > > > rejects the obvious proof by contradiction: > > > > Assume a natural number, x, such that P(x) > > > is false exists. > > > call it k > > > Then P(k) is both true and false. > > > Contradiction, Thus the original assumption > > > is false and no natural number, x, such > > > that P(x) is false exists) > > > > We will say that x is an unfindable natural > > > number. > > > > It is interesting to note that WM agrees with > > > the usual results if you insert the term findable. > > > > E.g. > > > > There is no findable last element of the potentially > > > infinite set |N. > > > > There is no findable index to a line of L that > > > contains d. > > > > There is no ball with a findable index in the vase. > > > > etc. > > > > It does not really matter if nonfindable natural > > > numbers exist or not. They have no effect. > > > > I suggest we give WM a teddy bear marked unfindable. > > > I suggest, William keeps abd comforts it until he can find the first > > line of L that is not capable of containing everthing that its > > predecessors contain. > > Every line of L is capable of containing everything that > its predecessors contain.
And why then do you believe, or at least claim, that something that is completely in the list must be distributed over more than one line?
> In WM's world, just because you can't > find something does not mean it does not exists.