Something is falsifiable if if it is false, it can be proven false.
Isn’t this true of anything and everything in mathematics, at least in principle? If there is “certainly an objective truth or falsehood to P = NP,” doesn’t that make it falsifiable by your definition?
(If this is your first introduction to Gödel’s Theorem and it seems bizarre to you, rest assured that the best mathematicians of the time had a Whiskey Tango Foxtrot reaction on the order of this video. But turns out that’s just the way it is!)
I know they get overused, but Godel’s incompleteness theorems provide important limits to what can and cannot be proven true and false. I don’t think they apply to P vs NP, but I just note that not everything is falsifiable, even in principle.
Isn’t this true of anything and everything in mathematics, at least in principle? If there is “certainly an objective truth or falsehood to P = NP,” doesn’t that make it falsifiable by your definition?
It’s not always that simple (consider the negation of G).
(If this is your first introduction to Gödel’s Theorem and it seems bizarre to you, rest assured that the best mathematicians of the time had a Whiskey Tango Foxtrot reaction on the order of this video. But turns out that’s just the way it is!)
I know they get overused, but Godel’s incompleteness theorems provide important limits to what can and cannot be proven true and false. I don’t think they apply to P vs NP, but I just note that not everything is falsifiable, even in principle.