This story was a bit weird, main characters seemed to take it a bit too strongly that arithmetic failed.
I mean, there is some sense in which 1 does not equal 2. Even if arithmetic fails to define a framework where they’re separate, that would simply mean that we need to redefine stuff, figure out a better way to describe our intuitive way of understanding how they’re different, and thus changing the framework towards that intuitive understanding.
It would of course be a bit embarrassing, when much of the work had to be revisited and all that sort of stuff. But the characters seemed to be plain overreacting.
Even if arithmetic fails to define a framework where
they’re separate, that would simply mean that we need to
redefine stuff, figure out a better way to describe our
intuitive way of understanding how they’re different, and
thus changing the framework towards that intuitive
understanding.
Man that would be hard, though!
I imagine that if this happened, math would become, at least
for a while, an empirical science. People would study the
derivations that led to contradictions. Proscriptions of
such derivations would be taken as provisional,
“this-is-how-our-universe-seems-to-work” axioms.
(Of course I don’t actually expect arithmetic to ever be shown to be
inconsistent.)
This story was a bit weird, main characters seemed to take it a bit too strongly that arithmetic failed.
I mean, there is some sense in which 1 does not equal 2. Even if arithmetic fails to define a framework where they’re separate, that would simply mean that we need to redefine stuff, figure out a better way to describe our intuitive way of understanding how they’re different, and thus changing the framework towards that intuitive understanding.
It would of course be a bit embarrassing, when much of the work had to be revisited and all that sort of stuff. But the characters seemed to be plain overreacting.
Man that would be hard, though!
I imagine that if this happened, math would become, at least for a while, an empirical science. People would study the derivations that led to contradictions. Proscriptions of such derivations would be taken as provisional, “this-is-how-our-universe-seems-to-work” axioms.
(Of course I don’t actually expect arithmetic to ever be shown to be inconsistent.)
ROT13: Uhu? Bar znva punenpgre gbbx vg uneq. Rirelobql ryfr jrag “uhu, gung’f jrveq”, naq pbagvahrq ba. Guvf znva punenpgre jnf n zngurzngvpvna jub unq onfrq ure frafr bs gehgu naq pbeerpgarff naq zrnavat ba zngu—zngu juvpu unq qvfcebirq vgfrys.