"flipper" wrote in message
...
On Mon, 13 Mar 2006 23:09:13 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
. ..
On Mon, 13 Mar 2006 02:14:18 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
m...
On Mon, 13 Mar 2006 00:12:55 GMT, "Rich Wilson"
wrote:


"flipper" wrote in message
news:n114125cjsid15km22ea3sml22u6u4p6vj@4ax. com...
Which, btw, is exactly the same situation as those who don't think i
exists.

It doesn't. But then, "numbers" don't exist in any meaningful sense.

If you go back and look at the context that's been removed you'll see
that I said it's as 'real' as the 'real' numbers are. The point is
it's 'reality' is conceptually no different regardless of what common
conceptualization, or lack thereof, you now wish to obscure the
matter with.

I wasn't disputing your argument! Yes, i is as real as any other number.

You can
have, say, five apples, but you can't just have five. It's just an
idea.

Ideas 'exist'. They must since you apparently have one

I have an idea of, say, a machine that turns lard into banknotes. That
doesn't mean it exists. Equally, I have an idea of the number "five".
The
idea exists, the number doesn't necessarily exist.


The difference is 'numbers' are part of a conceptual (mathematical)
system that is defined, consistent , well regulated, transportable,
and testable. That's enough for the conceptual world but for the 'hard
core realist' numbers, and the mathematical system, also apply to the
'real world' in useful ways. You may claim that '5' doesn't 'exist'
but it does, in fact, correlate to 5 'real world' apples. It's simply
the 'real world' conceptualized so that '5' works equally well with
horses, bails of hay, neutrinos, or any other 'real world' thing, as
well as it does for apples. Further, we'd find it impossible to
understand or explain the quantify of apples without it.

OK, but it's still just an abstract thought. Agreed?

I think the problem here is that "the number 5 exists" doesn't actually
mean
anything. It's not made of matter or energy so it can't exist in the same
way that the apple can. There's no way you can directly experience "5"
with
any of your senses. If "5" exists I'd like you to put one in the mail and
send it to me, on its own, without any apples or any other item that you
might want to apply the idea of "5" to.

You're using a self fulfilling argument by first defining 'exist'
specifically to exclude what you will then argue doesn't 'exist'
because you first defined it away.

I'm not, I'm trying to find a definition of "exist" that could actually give
any meaning to the statement "numbers exist".

5 'exists' as a member of a mathematical system

....and *only* as a member of a mathematical system...

that meets the
mathematical criteria for 'existence'

Which are what exactly? Your definition of mathematical "existence" seems to
be what I'd call validity.

and it is in that same context
that the matter of whether the square root of -1 'exists' was being
discussed..

Your parochial definition of 'exist' seems intuitive on the surface
but, to turn a phrase, "an idea can change the world."

Not without people to think it.

However, that's
hard to stomach for something that doesn't exist

I don't have a problem with that.

and I submit that
your narrow definition leads to more mysticism, with non existence
changing the world, than accepting a broader view of it.

What I'm trying to say is that "existence" has no meaning when applied to
numbers.

On the other hand, you may claim to have the 'idea' of a money lard
machine but it isn't well defined, much less testable, even in the
conceptual sense, not to mention it contradicts reality as we
currently understand it.

OK, OK, I'll come up with a more sensible idea next time. But proving an
idea makes sense doesn't prove its existence.

Or, put another way, we accept the reality of things we can, by some
means, verify even if we can't 'see' them, like electrons and protons.

Stand in front of a source of beta radiation for long enough and you'd be
able verify the existence of electrons.

Well, at least the observed results will, hopefully, be consistent
with present day theory.

I'm mean they'd have a direct effect on your body that you could experience
with your senses.

One the other hand, '5' is consistent with present day mathematical
theory too.

We can devise tests that 'confirm' their existence and, similarly, we
can confirm the 'existence' of 5 by it's adherence to mathematical
principles and useful, even necessary, applicability to the 'real
world'.

Go ahead, prove it. I think all you're going to show is that it's a useful
idea.

Which I contend exists, in the broader view.

Meaning what exactly? How do you differentiate between an idea that exists
and one that doesn't?

One the other hand, if we flip the coin over we could argue that
there's no such thing as 'reality' since everything we pretend to
'know' about it is simply our mind's own conceptualization.

I see where you're going with that but there's still a distinction between
abstract concepts such as numbers and non-abstract concepts such as
apples.

If you're willing to accept subsets of concepts why not subsets of
existence?

I'm not sure what you mean by that.

As far as I can tell, some people have a notion of some kind of "ether" of
mathematical laws and rules that had to exist before any matter could exist
in the universe. That's what I'm trying to argue against.