What is a Number

Our goal is to build an artifact that can think. A more concreat question is: what is i the head of our thinker. I particiular what does it think of nombers.. This essay revisits the discussion of over a century about the nature of the natural numbers numbers and proposes a new vision of what is actually i the head of an artifact that can think about numbers.

The computable ancestral

  (FORALL obj
    (IMPLIES 
      (AND (HOST-NATNUM? obj) (NOT (EQUAL obj Host-Natnum-Zero)))
      (RXIST (h [host-natnum]) (HOST-NATNUM-PRED h obl)) ) )

If (NATUM-REP? obj) (ATTACHED n obj) (E

  (deflam pred*-aux (n l)
    (IF (EQUAL n 0) 
      (list-cons l 0)
      (list-cons (pred*-aux (pred n) l) n) ) )

Theorem:

1) 

  (pred* n m)

  (forall (n [umeral])
    (EQUAL (least-ancestral n) 0) )
The Skolem view of iductio

  (forall (n [numeral]) 
    (IMPLIES
      (AND
        (A (a-mak-umeral 0)))
        (forall (m [nueral]) (IMPLIES AND (less-than m n) (A m)) (A (succ m)))
      (A n) ) )


  (IMPLIES (LIST? l) (
Bibliography