# Re: Numbers in the Platonic Realm

```On 10/30/2012 11:22 AM, Stephen P. King wrote:
```
```On 10/30/2012 2:00 PM, Quentin Anciaux wrote:
```

```

2012/10/30 Stephen P. King <stephe...@charter.net
<mailto:stephe...@charter.net>>

On 10/30/2012 1:43 PM, Quentin Anciaux wrote:
```
```

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:

```
```        On 10/30/2012 4:30 AM, Bruno Marchal wrote:
```
```        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.
```
```
Truth applies to proposition, or sentences representing them for some
machine/numbers. If not, comp does not even makes sense.
```
```
So your are agreeing?  "Two" has no truth value, but "Two equals one
plus
one." does.
```
```
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

```
```    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?
```
```
I agree with that. But you're talking about the tokens "17 is prime" not the concept that 17 is prime. Could not a person who grew up alone on an island realize that 17 has no divisors, and he could even invent a private language in which he could write down Peano's axioms.
```
Brent

```
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?".
```

--
Onward!

Stephen
--
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