"arbitrary constants" refers to numerical values that can be chosen freely when solving mathematical equations. These constants do not have a specific value and can be adjusted to fit the problem at hand. They are used to account for variability or unknown factors in the equation and allow for a range of solutions.
Full definition
The fact that
arbitrary constants exist, for example the strength of gravity; through science we know that these values can only be near the observable constant or human life would not exist.
No less a figure than Freeman Dyson opines that he's looked at the climate models and finds them riddled with bogus assumptions and
arbitrary constants.