Re: Opinions on mathematics.

In article
<BLOCKSPAMfishfry-F49691.22540810122006@xxxxxxxxxxxxxxx
om>,
fishfry <BLOCKSPAMfishfry@xxxxxxxxxxxxxxxx> wrote:

In article <jack-872DE5.20595710122006@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Michael Press <jack@xxxxxxxx> wrote:

In article
<BLOCKSPAMfishfry-934B15.19505210122006@xxxxxxxxxxxxxxx
om>,
fishfry <BLOCKSPAMfishfry@xxxxxxxxxxxxxxxx> wrote:

In article <jack-9BB5C5.19391010122006@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Michael Press <jack@xxxxxxxx> wrote:

In article
<BLOCKSPAMfishfry-1B105C.19230410122006@xxxxxxxxxxxxxxx
om>,
fishfry <BLOCKSPAMfishfry@xxxxxxxxxxxxxxxx> wrote:

In article <jack-0A4BC5.16490010122006@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Michael Press <jack@xxxxxxxx> wrote:

Folks have talked about the how mathematics is
practiced and the nature of mathematical objects. It is
difficult to address these matters without saying
'mathematical objects' and expecting to be understood.
It looks like we are stuck with the notion of
mathematical objects.

From time to time someone tells me that mathematics is
not science. I disagree with this assertion. The reason
is that a mathematical object is a structure that we
construct in our mind with the aid of writings and
diagrams. When doing mathematics we are mapping our
minds, and changing our minds. This is my outlook in a
nutshell. Mathematics is a science. Our minds are real.

Unicorns are a construction of our minds. By your logic, are unicorns
real?

Somebody writes a story about a unicorn. At the end the
unicorn dies. Some people who read the story will feel
sad.

So in your opinion, a unicorn has the same reality as the Golden Gate
Bridge or any other physical object?

No. Observe that I did not bring in unicorns.

I answered to illustrate my drift, that we take
seriously our mental constructions.

Yes, we do. Do we take the mental construction of unicorns seriously in
the same way as we take the mental construction of the natural numbers?

Depends who we ask.

If not, then what's the crucial distinction we're trying to make?

I am not trying do draw a distinction. I examine the
notion mathematical object, since it just won't go
away.

Because some people would say that the natural numbers exist as an
object of mathematical interest; whereas unicorns do not actually exist,
even though some people enjoy them.

The notion of unicorns are not a mathematical object. I
am very surprised to discover the notion in a math
forum.

I think that mathematical objects are mind
constructions developed from observation, abstraction
from observation, mappings of mental processes, and
striving for explication that leads to forming new
mental paths.

--
Michael Press
.

Relevant Pages

  • Re: Opinions on mathematics.
    ... 'mathematical objects' and expecting to be understood. ... minds, and changing our minds. ... Unicorns are a construction of our minds. ... the same way as we take the mental construction of the natural numbers? ...
    (sci.math)
  • Re: Opinions on mathematics.
    ... Michael Press wrote: ... 'mathematical objects' and expecting to be understood. ... minds, and changing our minds. ... Unicorns are a construction of our minds. ...
    (sci.math)
  • Re: Opinions on mathematics.
    ... Michael Press wrote: ... 'mathematical objects' and expecting to be understood. ... minds, and changing our minds. ... Unicorns are a construction of our minds. ...
    (sci.math)
  • Re: Opinions on mathematics.
    ... Michael Press wrote: ... 'mathematical objects' and expecting to be understood. ... minds, and changing our minds. ... Somebody writes a story about a unicorn. ...
    (sci.math)
  • Re: Opinions on mathematics.
    ... Michael Press wrote: ... 'mathematical objects' and expecting to be understood. ... minds, and changing our minds. ... Unicorns are a construction of our minds. ...
    (sci.math)