# Re: Fictionalism!

```On 6/11/2013 12:51 AM, Bruno Marchal wrote:
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On 10 Jun 2013, at 20:04, meekerdb wrote:

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```On 6/10/2013 10:52 AM, Bruno Marchal wrote:
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On 10 Jun 2013, at 18:25, meekerdb wrote:

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

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```On Sun, Jun 9, 2013 at 9:23 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
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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.
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Bruno, how are flying pink elephants any different from things that I
remember but am not experiencing this very moment?
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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.

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

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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.
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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).
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Actually it does. Let y="x is a prime number which is even and bigger than three". Then, if y anything; in classical logic everything follows from a contradiction. But we were talking about the metalogical relation of true/false and fictional/real. I don't think two are parallel. It's true that 17 is prime - but it doesn't follow that 17 is real. It's true that Sherlock Holmes lived on Baker Street, but it doesn't follow that he existed.
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The difference comes from the fact that in arithmetic e can prove Ex(x = 17), but we cannot prove in your "theory" that Ex(= Sherlock Holmes).
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But "E" in those two propositions don't have the same meaning. In the first it means that the axioms of arithmetic imply there is an x=17. In the second it means there was person who had all or most of the characteristics described in Conan Doyle's stories.
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Of course something described by a contradiction can't exist. But a contradiction is dependent on an axiomatic system. So a pink elephant doesn't exist, but "There is a pink elephant." is not a contradiction; it's just a falsehood and it's not the case that everything follows from a falsehood.
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It is the case that everything follows from a falsehood. (0=1) does implies
everything.
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In classical logic. But logic is just supposed to formalize good reasoning. "There is a pink elephant." may mean no more than "That looks like an elephant painted pink." It's not an axiom of a formal system. I deliberately included "flying" because it makes the identification as "elephant" problematic. If we found an animal that looks like an elephant painted pink, we'd certainly call it a "pink elephant". But if we found an animal that looked like an elephant with wings that could fly, we'd only call it a "flying elephant" metaphorically.
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Brent

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f -> q is a tautology. It is equivalent with ~f V p. that is with t V q.

"p -> everything" in all words where p is false, even if there are worlds were
p is true.
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