On 11 Jun 2013, at 18:28, meekerdb wrote:

On 6/11/2013 12:51 AM, Bruno Marchal wrote:

On 10 Jun 2013, at 20:04, meekerdb wrote:




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.

It has the same meaning in different theories. Without giving me your theory of humans, "Ex(x = Sherlock" has no meaning, except referring to consensual reality, but this is what we want to explain. You beg the question. In consensual reality it is just reasonable to say that Sherlock does exist only as a fictional character. But that is not what we discuss.

In the comp TOE Ex (x = sherlock) is as false as Ex (x = Brent), because Brent and Sherlock are (different probably) sort of emerging reality. Only natural numbers exist in the sense of "ExP(x)". So in the comp TOE, only numbers are NOT fiction, if basic existence is the criteria. Brent and Sherlock are different type of fiction.











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.

Classical logic formalizes machines or numbers understanding of Platonia.



"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.

My problem was just with fictionalism in math. It is fake sort of philosophy. We must avoid words like "real" or "fiction", just agree on which theory we are willing to use.

Bruno




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



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