# Re: Fictionalism!

```
On 10 Jun 2013, at 22:06, Stephen Paul King wrote:```
```
```
```So numbers do not exist?
```
```
Why?

```
In most elementary (first order) theory of arithmetic, you can prove the following:
```
Ex(x = 0)
Ex(x = s(0))
Ex(x = s(s(0)))
etc.

Bruno

```
```

```
On Mon, Jun 10, 2013 at 1:52 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
```
On 10 Jun 2013, at 18:25, meekerdb wrote:

On 6/10/2013 12:19 AM, Telmo Menezes wrote:
```
On Sun, Jun 9, 2013 at 2:40 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
```On 09 Jun 2013, at 11:20, Telmo Menezes wrote:

```
On Sun, Jun 9, 2013 at 9:23 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
```
On 08 Jun 2013, at 17:55, meekerdb wrote:

On 6/8/2013 1:02 AM, Bruno Marchal wrote:

On 08 Jun 2013, at 05:15, meekerdb wrote:

On 6/7/2013 4:00 PM, Stephen Paul King wrote:

Yes, if there was a text of this it would be nice... I found this:
http://plato.stanford.edu/entries/fictionalism-mathematics/

```
A fictionalist account holds that some things are fictional, i.e. don't
```exist even though their complete description is self-consistent.
Everythingists apparently reject this idea.  Platonists seem to equate
'true' with 'exists'.  If you believe 17 is prime you must believe 17
exists.  I think this is wrong.  If you believe that a flying pink
elephant
is pink, must you believe a flying pink elephant exists?

Flying pink elephants are pink and not pink. That's why flying pink
elephant
can't exist.

A pink elephant is pink by construction.

```
Exact. But the flying pink elephant are also not pink. By logic. Or show
```me
a flying pink elephant living on this planet which isn't not pink.

Bruno, how are flying pink elephants any different from things that I
remember but am not experiencing this very moment?

I add explanation. Here you describe two 1p events. They are similar,
```
although I guess you don't have precise memory of having actually seen a
```Flying Pink Elephant in your life, except in cartoon or dreams.

For example, I've
been to Brussels but I'm not there right now. Brussels is an
abstraction in my mind, but I believe it's the capital of Belgium.
That's part of the Brussels abstraction, in the same sense that being
pink is part of the flying pink elephant abstraction. No?

I do not dispute that fact. Pink elephant are pink.

```
But the pink elephant on this planet happens also to be brown rampant worms.
```And I'm afraid that is only a classical logician's joke.

```
(x = Flying Pink Elephant) -> (x = Brown Rampant Worms) is true on this planet because (x = Flying Pink Elephant) is false for all x, on this planet
```(I think),

```
But (x = Flying Pink Elephant) is false for all x, is an empirical proposition.
```
I agree.

```
Not one you can prove from arithmetic or logic. But the point was that true propositions, like "Flying pink elephants are pink" don't imply the existence of anything; just like "17 is prime" doesn't imply the existence of 17.
```
But how do you formalize "flying pink elephant are pink" ?

```
I am simpled minded, so I formalized it in a first order logical formula:
```
if x is an elephant which is pink and which is flying then x is pink.

```
This does not entail Ex( x = an elephant which is pink and which is flying)
```
For the same reason that:

```
"if x is a prime number, which is even, and bigger that 3" then x is bigger than 3"
```
does not entail Ex(x = even prime number bigger than 3).

Bruno

Brent

and in classical logic f implies everything.

If you want,

"(x = Flying Pink Elephant) -> (x = Brown Rampant Worms)"        is an
expression equivalent

```
to "f -> <whatever>" which is a tautology. It is the way to diplomatically assert that we do not believe in the existence of some x which would be equal to a flying pig elephant. The popular saying "with "ifs" and "buts"
```you can put Paris in a bottle express a similar thing.
Ok, I'm convinced.

Telmo.

--
```
You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com.
```
To post to this group, send email to everything-list@googlegroups.com.
```
Visit this group at http://groups.google.com/group/everything-list?hl=en .
```For more options, visit https://groups.google.com/groups/opt_out.

http://iridia.ulb.ac.be/~marchal/

--
```
You received this message because you are subscribed to a topic in the Google Groups "Everything List" group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/everything-list/_ONFIcyntY4/unsubscribe?hl=en . To unsubscribe from this group and all its topics, send an email to everything-list+unsubscr...@googlegroups.com .
```To post to this group, send email to everything-list@googlegroups.com.
```
Visit this group at http://groups.google.com/group/everything-list?hl=en .
```For more options, visit https://groups.google.com/groups/opt_out.

--
```
You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com.
```To post to this group, send email to everything-list@googlegroups.com.
```
Visit this group at http://groups.google.com/group/everything-list?hl=en .
```For more options, visit https://groups.google.com/groups/opt_out.

```
```
http://iridia.ulb.ac.be/~marchal/

--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email