Re: PotM Re: A Typology of Scientism

Burkhard <b.schafer@xxxxxxxx> wrote:

On 15 Aug, 10:56, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
Burkhard <b.scha...@xxxxxxxx> wrote:
On 15 Aug, 08:49, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
Burkhard <b.scha...@xxxxxxxx> wrote:
snex wrote:
On Aug 14, 2:51 pm, Bob Casanova <nos...@xxxxxxxx> wrote:
On Thu, 13 Aug 2009 15:01:46 -0700 (PDT), the following
appeared in talk.origins, posted by snex <x...@xxxxxxxxxxx>:

On Aug 13, 4:51 pm, Bob Casanova <nos...@xxxxxxxx> wrote:
On Wed, 12 Aug 2009 15:23:36 -0700 (PDT), the following
appeared in talk.origins, posted by snex <x...@xxxxxxxxxxx>:
On Aug 11, 3:17 pm, Bob Casanova <nos...@xxxxxxxx> wrote:
<snip>
If circles are part of the world...
they arent. show me a circle. not a drawing of a circle. an
actual >>> circle. >> Ah, a Platonist! Why didn't you say so? I
would have ignored >> you from the beginning. > platonists claim
that there *are* "real" circles out there somewhere, Not
exactly, but I wouldn't expect you to know what they actually
believe (assuming any exist today).

yes, clown, thats exactly what the claim.

Well, I would not have put it quite like that. "out there"
denotates a place, and while abstract objects like numbers exist,
they are not spatiotemporally located. That is pretty much the
view of Goedel, Cantor, Dedekind etc.

There are some exceptions to this. Penelope Maddy for instance
used to claim that sets at least have spatiotemporal properties -
they are wherever the objects that are members of the set are. So
rather th eoposite from "out there", more "all around us".

Only real sets, surely? (composed of spatiotemporal objects)
Abstract sets are just as ideal
as all other mathematical objects,

Jan

Well, both. Sets of concrete objects are still abstract objects. For
her (old view, she changed this in the late 90's) when you perceive
three objects on a table, both the physical objects and the set of
these objects (an abstract entity) causally interacts with you. Sets
that have physical objects as members are then the bridge element
between purely physical and purely abstract objects.

Sounds like Russell rehashed.

That way, she
tried to explain how highly abstract mathematical thinking can
nonetheless be rooted in the activity of counting, incorporating
insights from cognitive psychology of how we develop a sense for
numbers, and also account for the appeal to intuition mathematicians
make when discussing which axioms to add to ZF

Against this view:
there are easily visualised sets, like the Cantor set,
(all reals not having a 1 in their ternary expansion)
that nevertheless (being uncountable)
cannot have anything to do with sets of real objects.

Jan

Sure, that;s why it is only a bridge. Not all sets are spatio-
temporal, but we learn from them first, our intuitions get shaped, and
then we move on to those sets that can be visualised but are not sets
of eal objects, and finally to those that can't even be that.

More heuristic and didactic than foundational.

What you
would expect, and what she tired to show (as I said, she gave up this
view later) are so to speak nested hierarchies that link ways in which
mathematicians actually reason to this "generative" account of types
of sets.

The giving up seems understandable.
Moreover, (no need to tell you of course)
this view is completely a-historical.

Historically sets were introduced by high calibre mathematicians,
working at the highest levels of abstraction,
in their attemps to make sense of the real numbers.
The notion didn't descend to the kindergarten
until much later, with attemps to rewrite math education.

Jan

.

Relevant Pages

  • Re: PotM Re: A Typology of Scientism
    ... appeared in talk.origins, posted by snex: ... not a drawing of a circle. ... and also account for the appeal to intuition mathematicians ... (all reals not having a 1 in their ternary expansion) ...
    (talk.origins)
  • Re: PotM Re: A Typology of Scientism
    ... appeared in talk.origins, posted by snex: ... to generations of mathematicians and physicists... ... Engineers and scientists deal with finite precision, ... Squaring a real world circle is no problem at all, ...
    (talk.origins)
  • Re: PotM Re: A Typology of Scientism
    ... appeared in talk.origins, posted by snex: ... not a drawing of a circle. ... that have physical objects as members are then the bridge element ... and also account for the appeal to intuition mathematicians ...
    (talk.origins)
  • Re: PotM Re: A Typology of Scientism
    ... appeared in talk.origins, posted by snex: ... not a drawing of a circle. ... and also account for the appeal to intuition mathematicians ... (all reals not having a 1 in their ternary expansion) ...
    (talk.origins)
  • Re: Platonism
    ... I said that they'd retreat to ZFC when pressed. ... To most mathematicians, there is something very ... The set of reals is not hard to construct in ZFC, ... that provide intuition, and better intuition is that which avoids ...
    (comp.theory)
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