Eliezer already conceded that trivial instances of such problems can be solved. (We can assume that before he made that concession he thought it went without saying.)
The point can’t be confined to “trivial instances”. For any NP-complete problem on some reasonable computing platform that can solve small instances quickly, there will be instance sizes that are non-trivial (take appreciable time to solve) but do not require eons to solve. There is absolutely no mathematical reason for assuming that for “natural” NP-complete problems, interesting-sized instances can’t be solved on a timescale of months/years/centuries by natural processes.
The dichotomy between “trivial” and “impossible to solve in a useful time-frame” is a false one.
The point can’t be confined to “trivial instances”. For any NP-complete problem on some reasonable computing platform that can solve small instances quickly, there will be instance sizes that are non-trivial (take appreciable time to solve) but do not require eons to solve. There is absolutely no mathematical reason for assuming that for “natural” NP-complete problems, interesting-sized instances can’t be solved on a timescale of months/years/centuries by natural processes.
The dichotomy between “trivial” and “impossible to solve in a useful time-frame” is a false one.