"My function is indeed incomplete...and it happily proceeds by objectively classifying countries as 'free', yes or no"

Any idiot can proceed"happily" along if they ignore the complexities of an issue.

taabarang wrote: ↑Tue May 02, 2017 2:34 pm "My function is indeed incomplete...and it happily proceeds by objectively classifying countries as 'free', yes or no"
Any idiot can proceed"happily" along if they ignore the complexities of an issue.
Berliner expression: Wat ist meins ist meins, wat ist deins ist och meins.

The fact that the Russians raped someone's mother in the ruins of Berlin, does not make him smarter either, does it?
I thought that the first thing that you learn when you lose the war, is to shut your mouth?

"The fact that the Russians raped someone's mother in the ruins of Berlin, does not make him smarter either, does it?
I thought that the first thing that you learn when you lose the war, is to shut your mouth."

First, I was never in a war and I'm not German. Not only is your "foolproof" logic simplistic, but your extrapolations of what you presume to be facts aren't related to reality. Have a nice day.

taabarang wrote: ↑Tue May 02, 2017 3:14 pm... your extrapolations of what you presume to be facts aren't related to reality ...

Relating to reality is a requirement for falsifiability/testability ("science") but not at all for provability ("mathematics"). On the contrary, in provability, it is considered a constructivist heresy to relate anything to reality. Provability is NEVER about reality. The basic building bricks in provability (numbers, sets, types, functions, combinators, ...) have no physical incarnation and NEVER exist as such in reality. For example, the number 5 does not exist in the real world. It is a non-physical abstraction. Anything provable that we may say about the number 5 has absolutely no relationship with reality. Deriving any statement at all about comparing to reality, is utterly wrong in provability. This may only be done in falsifiability/testability. But then again, if the statement is testable, it can never be provable, nor the other way around.

"Shouldn't that be, 'ist auch meins'?" In high German-yes, in Berlinerish no.

High German: Das ist ein Ding was ?
Berlinerish: Det is'n Ding wa ?

Translation: That's a bummer isn't it?

"Provability is NEVER about reality"
In my world it is.

"Freedom is free of the need to be free". - George Clinton

taabarang wrote: ↑Tue May 02, 2017 3:52 pm "Provability is NEVER about reality"
In my world of is.

It is not possible to do what you want to do.

It is not permissible in provability to use building bricks with a physical incarnation, aka, things that appear in reality. For a statement to be provable, it is a requirement to visit all elements in the set concerned. That is why you will find the "for each" symbol all over the place. If the set's elements are part of reality, it would require infinite energy to visit all of them. However, if you do not visit all of them, then your statement cannot be provable ("math"). In that case, you would just have sampled the set, and then your statement will be at best testable/falsifiable ("science").

You cannot visit every possible case in the real world, while you can perfectly do that in your mind. However, that requires the things to visit, to be abstractions of the mind. Something cannot simultaneously be an abstraction of the mind and a real thing in the real world. So, your approach can only fail.

Look Eric we should both be happy we don't share the same world. Even if according to you I can't prove it, I'm still happy.