# Re: Numbers in the Platonic Realm

```On 10/30/2012 2:27 PM, Quentin Anciaux wrote:
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2012/10/30 Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>>
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On 10/30/2012 2:00 PM, Quentin Anciaux wrote:
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2012/10/30 Stephen P. King <stephe...@charter.net
<mailto:stephe...@charter.net>>

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:
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2012/10/30 Stephen P. King <stephe...@charter.net
<mailto:stephe...@charter.net>>

On 10/30/2012 12:51 PM, Bruno Marchal wrote:
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On 30 Oct 2012, at 17:04, meekerdb wrote:

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```            On 10/30/2012 4:30 AM, Bruno Marchal wrote:
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```            My argument is that concepts of truth and
provability of theorems apply only to the concepts
of numbers and their constructions, not to numbers
themselves.
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```
Truth applies to proposition, or sentences
representing them for some machine/numbers. If not,
comp does not even makes sense.
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So your are agreeing? "Two" has no truth value, but
"Two equals one plus one." does.
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Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using
this to assert that the truth of, say  "Two equals one
plus one." depend on some numbers or subject having to
discover it, or prove it.

Bruno

http://iridia.ulb.ac.be/~marchal/
<http://iridia.ulb.ac.be/%7Emarchal/>

```
```            Dear Bruno,

My point is that a number is not a capable of being
an ontological primitive *and* having some particular
set of values and meanings. A statement, such as 2 = 1+1
or two equals one plus one, are said truthfully to have
the same meaning because there are multiple and
separable entities that can have the agreement on the
truth value. In the absence of the ability to judge a
statement independently of any particular entity capable
of "understanding" the statement, there is no meaning to
the concept that the statement is true or false. To
insist that a statement has a meaning and is true (or
false) in an ontological condition where no entities
capable of judging the meaning, begs the question of
meaningfulness!
You are taking for granted some things that your
arguments disallow.

Hmm... but that's what arithmetical realism is all about...
If you deny meaning to '17 is prime' absent an entity which
gives to it its meaning... then you're simply negating
arithmetical realism and with it computationalism (ie:
consciousness is emulable qua computatio).

Quentin

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```        Hi Quentin,

Well, therefore I must reject arithmetical realism as
"unreal" by definition! Individual entities are incapable of
"giving meaning" to things, be they puppies or prime numbers.
It requires an *agreement between many entities* to have
meaningfulness. I claim that it takes at least three entities...

If objects that are proposed to be "real" are not
observable by anyone then they don't exist! Where am I going
off the rails? I think that the problem here is that the
distinction between "not observable by any particular entity"
and "not observable by any entity" are being confused. I am
reminded of Einstein's silly quip about the Moon still
existing even if he was not looking at it. The poor old
fellow neglected to notice that he was not the only entity
that was capable of being affected by the presence or
non-presence of the Moon!

You might have seen my definition of Reality. Do you
recall it?

So in your view, no humans (no consciouness) implies... 17 is
prime or not is not meaningful ? Only consciousness gives meaning
to thing... yet it seems absurd that truth value would disappear
without consciousness.

Quentin
```
```
Unless multiple entities can agree that the sequence of
symbols "17 is prime" is an indicator of some particular
mathematical object and one of its particular properties, then how
does "17 is prime" come to mean anything at all? Can you stop
subconsciously assuming an invisible observer whose sole job is to
observe everything from infinity? It seems that you cannot if what
I am writing is mysterious to you!
How is it not absurd that meaningfulness exists in the absence
of anyone that can apprehend it? Please note that I am not
considering the absence of any one entity; I am considering the
absence of all possible entities in the degenerativeness or
vanishing of meaningfulness. I am asking "Why is it OK to think
that meaningfulness exists in the absence of any means to
determine it?".

```
Well what you're explaining just feels like the egg and the chicken... meaning is an internal view, if computationalism is true, observer and meaning arise through computation... computation would be ontologically real and primitive.
```
Quentin
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```
Dear Quentin,

```
It is exactly wrong, IMHO, to think of this as a 'chicken or egg" case. There is no "cause and effect" relation within ontological arguments, there are only atemporal logical arguments. I am not assuming that there are ontological primitives that have particular properties where as you and Bruno seem to find them indispensable. Just read B. Russell's stuff on neutral monism, he was much better at writing than me. He convinced me, maybe he can convince you.
```
--
Onward!

Stephen

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