Re:University of Tokyo Graduate School Entrance Exam – Mathe...
by Smaug123 on Thursday March 16, 2017 @11:46AM
(#13885977)
> > The things you say are always falsifiable.
> is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work.
Broadly speaking, if things aren't falsifiable, they're either provably not falsifiable (so everyone knows that debating their truth isn't particularly fruitful, like the case of Choice), or they're precise but not provably unfalsifiable (Gödel might permit this, but we have never yet found a plausible example of such a statement), or they're imprecise (in which case they're recognised as being "not yet rigorous").
> is that necessarily absolutely true? i myself would take a deep breath before making such a wide-sweeping claim. first thing that pops into my mind is the axiom of choice and also godel's work.
Broadly speaking, if things aren't falsifiable, they're either provably not falsifiable (so everyone knows that debating their truth isn't particularly fruitful, like the case of Choice), or they're precise but not provably unfalsifiable (Gödel might permit this, but we have never yet found a plausible example of such a statement), or they're imprecise (in which case they're recognised as being "not yet rigorous").