The Greek letter paradox is seeing the same symbol in two contexts and assuming it means the same thing. Maybe it’s used in many contexts, but I first heard it in the context of comparing statistical models.
I used the phrase in my previous post, looking at
α exp(5t) + β t exp(5t)
and
α exp(4.999 t) + β exp(5.001 t).
In both cases, α is the coefficient of a term equal to or approximately equal to exp(5t), so in some sense α means the same thing in both equations. But as that post shows, the value of α depends on its full context. In that sense, it’s a coincidence that the same letter is used in both equations.
When the two functions above are solutions to a differential equation and a tiny perturbation in the same equation, the values of α and β are very different even though the resulting functions are nearly equal (for moderately small t).
Alfred Korzybski loves you (or might have if your mortal realities intersected).
It doesn’t have to be Greek letters.
I saw a problem on math.stackexchange where they were solving linked 2nd-order DEs, and they used C_1 and C_2 for the writing x(t), and then re-used C_1 and C_2 for writing y(t) – because, of course, the general solution, before fitting initial conditions, uses C_1 and C_2.
The paradox is so strong that I couldn’t get people to recognize this error, and the accepted answer was “must have dropped a sign somewhere”.