# Re: Prime Numbers

```On 9/26/2012 2:53 PM, Jason Resch wrote:
```
```

```
On Wed, Sep 26, 2012 at 2:33 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:
```
On 9/26/2012 12:11 PM, Jason Resch wrote:

On Sep 26, 2012, at 12:29 PM, meekerdb <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb
<meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is

Propositions can be self contradictory, but how can

Brent

Brent, it was roger, not I, who wrote the above.  But
in any
case I interpreted his statement to mean if some
theoretical
object is found to have contradictory properties, then
it does
not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a
doesn't exist, e.g. the largest prime number. But then of
course the
proof of contradiction is relative to the axioms and rules
of inference.

Well there is always some theory we have to assume, some model
we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is
the
existence proof.  You can't even define an object without using
some
agreed upon theory.

Sure you can.  You point and say, "That!"  That's how you learned
the
meaning of words, by abstracting from a lot of instances of your
mother
pointing and saying, "That."

Brent

There is still an implicitly assumed model that the two people are
operating
under (if they agree on what is meant by the chair they see).

Or they may use different models and define the chair differently.  For
example,
a solipist believes the chair is only his idea, a physicalist thinks it
is a
collection of primitive matter, a computationalist a dream of numbers.

Then while they might all agree on the existence of something, that
thing is
different for each person because they are defining it under different
models.

But if they are different then what sense does it make to say there is a
contradiction in *the* model and hence something doesn't exist.

```
It means a certain object (which is defined in a model) does not exist in that model. A model in one object is not the same as another object in a different model, even if they might have the same name, symbol, or appearance. "2 in a finite field", is a different thing from "2 in the natural numbers". The "chair in the solipist model" is different from the "chair in the materialist model". A chair made out of primitively real matter is non-existent in the solipist model. I don't see how you can escape having to work within a model when you make assertions, like X exists, or Y does not exist.
```
I don't try to escape that.

```
```What is X or Y outside of the model from which they are defined and exist
within?
```
```
```
The whole point of having a model is that X and Y refer to something outside the model. The model is a model *of* reality, not reality itself. So when you prove "X and ~X" in the model you may have proved X doesn't exist or you may have shown your model doesn't correspond to reality.
```
Brent

```
```
Jason

That's why it makes no sense to talk about a contradiction disproving the
existence
of something you can define ostensively.  It is only in the Platonia of
statements
that you can derive contradictions from axioms and rules of inference.  If
you can
point to the thing whose non-existence is proven, then it just means you've
error in translating between reality and Platonia.

Brent

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