Lakoff made another comment later on that really surprised me:
Any theory of meaning at all, model-theoretic or not, must obey the following constraint:
[...] The meaning of the parts cannot be changed without changing the meaning of the whole.
This seems like a very strong strictness condition, but I can't think of any counterexamples which would not admit reasonable objections. The recurring problem, when I try to imagine a dialogue between a supporter and detractor of the claim, is that the supporter seems to always be able to weasel around about what the parts mean.
For instance, if I say that "This microwave has a thingumabob to set the temperature" has the same meaning as "This microwave has a widget to set the temperature", then the supporter says, "well, then thingumabob and widget are both nonsense words of equal standing, therefore they have the same meaning". However, I could easily say "the thingumabob is above the widget, turn the thingumabob ninety degrees to the right", and in this case they clearly mean different things.
I really hope I'm setting up a strawman, though, because Lakoff clearly can't in good conscience think that the "parts" have an objective meaning inependent of the context-providing "whole", can he?