Re: PotM Re: A Typology of Scientism

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. 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.

.

Relevant Pages

  • 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. ... 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: ... 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: ... not a drawing of a circle. ... Sets of concrete objects are still abstract objects. ... that have physical objects as members are then the bridge element ...
    (talk.origins)
  • Re: PotM Re: A Typology of Scientism
    ... appeared in talk.origins, posted by snex: ... not a drawing of a circle. ... Sets of concrete objects are still abstract objects. ... that have physical objects as members are then the bridge element ...
    (talk.origins)
Loading