Re: (OT) Re: Object identity

On 5 Jul 2006 17:16:07 -0700, David Barrett-Lennard wrote:

Dmitry A. Kazakov wrote:
On 5 Jul 2006 08:47:20 -0700, David Barrett-Lennard wrote:

Dmitry A. Kazakov wrote:
On 5 Jul 2006 05:39:21 -0700, David Barrett-Lennard wrote:

Dmitry A. Kazakov wrote:
On 4 Jul 2006 19:10:28 -0700, David Barrett-Lennard wrote:

For me the word Platonism refers specifically to belief in the
independent existance of things like integers, and has nothing to do
with absolute truth.

Existence independent on what?

Our universe or multiverse or physical reality or whatever you want to
call it. I don't believe mathematics exists because of physical
reality. I believe it's more likely to be the other way around.
Physics is a branch of mathematics!

But you have no mathematics. There is a many formal systems floating
around. Where do numbers exist?

For me it is obvious that numbers exist. Can you imagine that numbers
don't exist?

Huh, there are tribes which have only numbers 1, 2 and "many."

I was asking you personally!

Yes, I do. Numbers do not exist, in material sense. They don't have taste,
color, mass, spin, charge etc.

On the other side do hyper-inaccessible cardinals exist?

That's a good question. I'm not sure if I can dodge it! It seems to
me that some mathematical things like the integers are obviously
self-consistent,

Integers aren't consistent or not. Consistency is a property of a formal
system. You should specifically talk about:

1. A consistent formal system with entities resembling what *you* consider
integers.
2. Whether any system having them is necessarily consistent
3. Whether any consistent system necessarily has them

even though no formal system can prove itself to be
self consistent. I regard that as a limitation of language or
mathematics itself.

This was the reason why I asked you to present the language of Truth. You
answered that there is no one. That means what it means. You cannot prove
your thesis, in fact, you can't even formulate it! So in WHAT sense it is
true?

I use the rule : if it's self consistent then it exists. That's my
definition of "exists".

And if it exists then? Do inconsistent things exist?

I give you an example: is MS-Windows consistent? Or, let's take German
taxation system. Is it? (:-))

BTW, you can take any inconsistent system and wrap it into a consistent
one. It is trivial, you replace each statement P of the original system
with <P is X> in the new system. For example:

"All Cretans are liars" ---> <"All Cretans are liars" is contradictory>

However this is where I blame formalism rather than
platonism.

Sure, because the latter is inconsistent with the former. I choose
formalism.

You must be very careful about "obvious" things. Consider a lamp. Let you
turn it on at 11:30. Then you turn it off at 11:45, on then at 11:52:30,
and so on. In a platonic Universe such lamp definitely exists. Now, will it
be on at 12:01?

I just see incompleteness as being orthogonal to inconsistency.

Egh? You do mean that in a larger super platonic system you'd be able to
answer this question? Why didn't you started with that system? Platonic
philosophy is too naive to elude such attacks.

Show me a proof that they don't.

Show me the language in which you could formulate such theorem. See the
discussion above about the language of absolute Truth.

How often
do you assume numbers exist in your daily life?

I think the answer could be: never.

You dodge the question!

So you don't mind spending a lot of your time thinking and reasoning
about numbers (like all that time as a child learning your
multiplication tables), and yet believing they don't exist?

Sure I don't. Precisely I don't believe in a system where this question
could be asked.

Even if you create an isomorphism between a
system A and a system B, there must be a third system C where that
isomorphism would exist and could be formulated.

An isomorphism is just a relabelling.

Whatever it be. You have to present the language C.

Why?

Because "there is an isomorphism" must be a proposition in C. This way C
was defined. If the proposition is true and C is consistent, then according
to your own definition C exists.

But we know there is no universal truth.

1. How are you going to conciliate this statement with a universal
existence of numbers?

2. Observe that the sentence is the liar paradox.

I treat universal existence of numbers as a *postulate* that I cannot
prove.

Why didn't you say it before? If you said: "There exists a postulate that
numbers exist," I wouldn't object!

What I mean is that if we believe
computers can be self-aware, then that gives us some confidence in the
proposal that our own awareness is computable as well.

OK, that's a tautology, provided "computer can" <=> Turing-complete.

In the space of all Turing machines, computing resources doesn't
present any limitations.

Do you seriously believe that solving equations of theoretical physics is
Turing complete?

No idea. There is no proof either way.

Hmm, I wouldn't be so sure. But I admit it is out of my competence.

1. You don't know if intelligence is computable. Brains can be built of
incomputable elements.

2. You don't know if intelligence is material (a part of the Universe), and
again what is material, in which sense etc.

1. => You can create AI if you change the platform
2. => You cannot create it at all.

The suggestion was premised on a demonstration that computers one day
exhibit awareness.

And? Why "intelligence-completeness" must be equivalent to
"Universe-completeness"?

I don't say "must be".

If there is no connection between them, then you cannot come to your
conclusion. Questions whether we can cognize the Universe, whether it can
us, whether machines can both and themselves are all fictitious, as long as
no any term here was properly defined...

--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
.

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