FOM: "Relativistic" mathematics?
kanovei at wminf2.math.uni-wuppertal.de
Fri Oct 16 11:26:02 EDT 1998
> I need more details to understand
>what do you mean by "human knowledge of counting".
It is just the human knowledge of counting. At some
basic (for educated people but not professional
mathematicians) level it includes the following observations.
(1) any collection A of objects has a measure called the
number of its elements, #A: which can be easy to grasp (the number
of fingers on your hand) or difficult (the number of trees in
the tajga etc.)
(2) to any collection we can add one more object, thus
giving "+1" to the number of the elements.
(3) if A and B are two (disjoint) collections then
#(A \cup B)= #(B\cup A), --> commutativity.
I could continue but this makes it pretty clear how I
understand the "human knowledge of counting".
Then a professional comes and gives this knowledge
professional treatment, that is, writes Peano axioms.
What is "feasible number" ? I don't know (mathematically).
> eponentiation, Ackerman function, Friedman
>functions m(k), n(k), etc.? I do not know what is this
"etc" means just that to any number x you have x+1
(in the classical setup of mathematics, but of course
philosophically this leads to known controversies).
>Even the "set"(?)
>of feasible numbers each of which seems to be a very
>concrete "thing" seems to me very umbiguous, nothing to
>say about the whole story on "all" imaginary infeasible numbers
No contest, if umbiguous is ambiguous, my pocket dictionary
is too small.
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