On 01 May 2013, at 22:09, John Mikes wrote:
Bruno asked why I have problems how to figure out 'numbers'.
In his texts (as I remember and I have no quotes at hand) the
"world" can be construed from a large enough amount of numbers in
simple arithmetical ways (addition-subtraction). Also: numbers do
not mean quantities.
If his older post with pegs (II=two, IIII=four etc.) is OK, the
'words' two and four DO mean quantities. If not, as 'numbers' they
are meaningless combinations of letters (sounds?) we could call the
series any way, as well as e.g.:
tylba, chuggon, rpais, etc. for 1,2,3 - or take them from any other
language (eins,zwei,drei, - egy, kettő, három) as they developed in
diverse domains/lifestyles. The 'numbers' would be like "Ding an
Sich" (German) however used as qualifiers for quantities if so
applied (see Bruno's 'pegs' above).
The terms we are using are not important. All we need is some
agreement on some theory.
Most things we need for the natural numbers can be derived from the
following axioms (written in english):
any number added to zero gives the number we started with (= x + 0 = x)
0 is not the successor of any natural number
if two numbers are different, then they have different successors
a number x added to a successor of a number y gives a successor of the
sum of x and y.
Are you OK with this?
In science we know that we cannot define what we are talking about,
but we can agree on some principles about them.
More reasonably sounds the idea of my wife, Maria, who assigns the
primitive development of quantities originally to proportions:
"larger (amount)" - "smaller (amount)" evolving in some thousand
centuries into the process of 'counting' the included units.
That's very good, but we can also develop general statement. We would
not have discover the universal number (the computers) without
agreeing on those principles.
I published on this list my thought for developing the Roman
numbering signs. I started with 2 - a PAIR of hands etc. (not with
one, which means only the existence) and branching into 5 (as
fingers, as in pentaton music) already as 'many'.
OK.
I still have no idea what description could fit 'number' in Bruno's
usage (I did not study number - theory - to keep my common sense
(agnostic?) thinking free).
See above.
Bruno
John Mikes
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