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Author: John JonesJohn Jones Date: Sep 17, 2008 14:25
We talk of the set of all the natural numbers, and numbers going on for
ever, even though these notions don't look arithmetical. Numbers, the
ones we work with, are always generated by addition, multiplication, and
other funcions.
Numbers don't barn-dance. All contemporary theories of number, like
finitism and ultra-finitism, suggest otherwise. But numbers don't do
collections, or orderings, or listings ... numbers don't arrange,
period. We may fool ourselves into thinking that 'numbers' do these
things when we aren't looking or calculating, in some Platonic realm
perhaps.
For example, we say that 2 'follows' 1. But 2 never follows 1. Whoever
heard of a number coming 'after' another number, except in the context
of being a teaching expedient? What sort of function allows a number to
usher in a 'next' number and sit by its side?
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Author: bigfletch8bigfletch8 Date: Sep 17, 2008 17:10
On Sep 18, 7:25Â am, John Jones aol.com> wrote:> We talk of the set of all the natural numbers, and numbers going on for
> ever, even though these notions don't look arithmetical. Numbers, the
> ones we work with, are always generated by addition, multiplication, and
> other funcions.
>
> Numbers don't barn-dance. All contemporary theories of number, like
> finitism and ultra-finitism, suggest otherwise. But numbers don't do
> collections, or orderings, or listings ... numbers don't arrange,
> period. We may fool ourselves into thinking that 'numbers' do these
> things when we aren't looking or calculating, in some Platonic realm
> perhaps.
>
> For example, we say that 2 'follows' 1. But 2 never follows 1. Whoever
> heard of a number coming 'after' another number, except in the context
> of being a teaching expedient? What sort of function allows a number to
> usher in a 'next' number and sit by its side?
>
> Numbers don't do lists, amorphous collections, sequences... look what
> happens if we think they do. Take the 'sequence' of 'natural numbers'. ...
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Author: ImmortalistImmortalist Date: Sep 17, 2008 21:40
On Sep 17, 2:25 pm, John Jones aol.com> wrote:> We talk of the set of all the natural numbers, and numbers going on for
> ever, even though these notions don't look arithmetical. Numbers, the
> ones we work with, are always generated by addition, multiplication, and
> other funcions.
>
> Numbers don't barn-dance. All contemporary theories of number, like
> finitism and ultra-finitism, suggest otherwise. But numbers don't do
> collections, or orderings, or listings ... numbers don't arrange,
> period. We may fool ourselves into thinking that 'numbers' do these
> things when we aren't looking or calculating, in some Platonic realm
> perhaps.
>
> For example, we say that 2 'follows' 1. But 2 never follows 1. Whoever
> heard of a number coming 'after' another number, except in the...
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Author: ZerkonXZerkonX Date: Sep 18, 2008 08:56
On Wed, 17 Sep 2008 22:25:51 +0100, John Jones wrote:
> My point? My point is that we have generated myths about 'numbers';
> myths whose sources are found among school rote teaching methods. These
> methods worked only if we believed in the idea that numbers are
> independent, individual entities independent of the functions that
> create them. So, numbers possibly could, we believed then (and now),
> order themselves.
Let's try and trace this.
Two guys are going to trade (the beginning and traditional function of
numbers, I believe). Each has a table. One guy puts up three apples on
his, the other two oranges on his. They agree. The trade is made.
There is no need for numbers here (nor name for that matter). To them,
there were not 3 apples and 2 oranges but rather only some apples and
some oranges by concept or name, the amount being self-evident with sight.
Later, they are away from their tables but want to trade. They both have
agents or workers who actually look over and handle the apples and
oranges. They now need a way to describe, in abstraction, an amount. The
actual act of trading or physical exchange is being abstracted through
their workers.
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