I see that in my definition of “tall” on handout 4b, I left out something relatively important. The definition should be:

[tall]^M = λP[λx[P(x) ∧ x is tall compared to {y:P(y)} in M]]

The important difference between what is on the handout and what I have here is that the definition here requires not only that a tall elephant be tall for an elephant, but that it actually be an elephant.

In case this wasn’t clear, P(x) will be true if property P holds of x. So if P is λx[x is an elephant in M], then P(x) will be true when x is an elephant and false otherwise, and {y:P(y)} would be the set of elephants in M (all of those individuals with the property of being an elephant).