Re: Cantor's definition of set

On Nov 2, 1:44 pm, John Jones <jonescard...@xxxxxxx> wrote:

1) Sequence needs redefining because
2) the notion of sequence carries with it 'order', and
3) order cannot be defined mathematically.
4) Order cannot be defined mathematically because order is not
presented by objects, mathematical or otherwise.
5) So we must keep everything that sequence already has, except
order.
6) Sequence displays repetition.
7) Acts of repetition are indistinguishable as there is nothing to
determine one applicative act (via a function for example) from
another.
8) Sequence is therefore not repetition.
9) The outcome's of a repetition may be distinguishable.
10) Thus, a function that 'adds one' displays different integers with
each application.
11) So a function that does not produce new elements will, with each
application, be indistinguishable both in its applications and in its
outcomes.
12) That is, a function may produce a distinguishable sequence and a
function may produce an indistinguishable sequence.
13) A sequence is independent of function.
14) There are no sequences of numbers.
15) Sequence is a list.

That's quite profound. And I'd like to follow up on it:

1) Identity needs redefining because
2) the notion of identity carries with it 'existence', and
3) existence cannot be defined mathematically.
4) Identity cannot be defined mathematically because identity is not
presented by concepts, mathematical or otherwise.
5) So we must keep everything that identity already has, except
concepts.
6) Existence displays order.
7) Acts of ordering are indistinguishable as there is nothing to
determine one applicative act (via a relation for example) from
another.
8) Identity is therefore not order.
9) The outcome's of an instantiation may be undistinguishable.
10) Thus, an expression that 'subtracts zero' displays no different
numerals with
each application.
11) So an ordering that does not produce previous classes will, with
each
instantiation, be distinguishable both in its expression and in its
expectations.
12) That is, an instantiation may produce a distinguishable ordering
and an ordering may produce an indistinguishable instantiation.
13) An instantiation is independent of classification.
14) There are no classifications of equivalences.
15) Therefore, ordering is a comfortable chair with down pillows.

MoeBlee





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