Is the difference between two ordinal variables ordinal? Is the difference between two ordinal survey responses still ordinal?

Ordinal variables are often not even numeric - the difference between ordinal variables isn't even a defined operation, much less an ordinal variable itself.
Consider three hot sauces, mild, spicy, and extra hot. How do you define (spicy - mild) or (extra hot - spicy)? There is no rationale in mapping these ordinal values to numbers and treating them as numeric variables.
If you had a rationale for claiming that the difference between mild and spicy is smaller than the difference between spicy and extra hot, you are now quantifying the differences between levels in a way that defies the definition of an ordinal variable, which indicates that you can only rank the levels but not comment on the "distance" between them. If you can quantify the size of the difference between levels, it's not an ordinal variable in the first place.
