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.