On 11 Jun 2013, at 23:18, John Mikes wrote:
Laughing stock: how can so many excellently educted and smart(est)
scientists SERIOUSLY debate on farces like flying pink elephants?
Those are test cases, extreme case, to argue more easily on the
question of existence, which is not obvious.
Of course we are not discussing on the existence of flying elephants
at all.
Bruno
JM
On Tue, Jun 11, 2013 at 12:28 PM, meekerdb <meeke...@verizon.net>
wrote:
On 6/11/2013 12:51 AM, Bruno Marchal wrote:
On 10 Jun 2013, at 20:04, meekerdb wrote:
On 6/10/2013 10:52 AM, Bruno Marchal 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).
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.
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).
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.
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.
It is the case that everything follows from a falsehood. (0=1) does
implies everything.
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.
Brent
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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