Re: Cantor's definition of set

John Jones <jonescardiff@xxxxxxx> writes:

On Nov 1, 11:15?am, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Oct 31, 3:01 pm, John Jones <jonescard...@xxxxxxx> wrote:





On Oct 31, 9:52?pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Oct 31, 1:38 pm, John Jones <jonescard...@xxxxxxx> wrote:

While we, ourselves, are able to distinguish between left and right
and before and after, mathematics is not able to distinguish these.
That is, mathematics has no axiom that can lay down order, sequence,
left and right, before and after.

The question of what mathematics "is able to do" shouldn't require
treating mathematics as if it is some agent itself of action.
Mathematics is a field of study; it's not a thing that itself goes
around "laying down" order or anything else.

So, in that field of study that is mathematics, we've shown you, for
example, ordered pairs in set theory. And that's just for starters. To
study mathematics is to study virtuosic explications of all kinds of
orderings and their attributes.

MoeBlee

I am trying to point out the difference between
1) 'order' that is required to read mathematics and
2) 'order' that is formulated by mathematics.
The two are not the same. My claim is that 2) is not possible.

Your set example displayed 1) and not 2).

No, the examples are of (2) (but not formulated BY mathematics as if
mathematics itself is some agent of action, but rather formulated IN
mathematics as mathematics is a field of study). Then, to read them
requires knowing left from right in order to read them from left to
right.

MoeBlee- Hide quoted text -

- Show quoted text -

Those examples you gave didn't show 'mathematical order', even though
we might need 'reading order' to look at them and understand them.
Those examples showed mappings and associations, and didn't really
tackle order.

so, go to it and use your own imagination ...


--
Alan Smaill
.

Relevant Pages

  • Re: Cantors definition of set
    ... That is, mathematics has no axiom that can lay down order, sequence, ... treating mathematics as if it is some agent itself of action. ...
    (sci.logic)
  • Re: Cantors definition of set
    ... That is, mathematics has no axiom that can lay down order, sequence, ... treating mathematics as if it is some agent itself of action. ... ordered pairs in set theory. ...
    (sci.logic)
  • Re: Cantors definition of set
    ... That is, mathematics has no axiom that can lay down order, sequence, ...
    (sci.logic)
  • Re: Cantors definition of set
    ... That is, mathematics has no axiom that can lay down order, sequence, ... ordered pairs in set theory. ...
    (sci.logic)
  • Re: Choice sequences, intuition, etc
    ... specifying a different method of constructing the sequence, ... Regarding Bishop, ... axiom systems for mathematics that are weaker. ... Somehow the distinction in meaning between an implication ...
    (sci.logic)
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