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(5*t*) + β *t* exp(5*t*)

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(5*t*), 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”.