Objectivist account of cognition is inconsistent
Objectivist account inconsistently assumes: 1. The meaning of a sentence's a function that assigns a truth value to the sentence for each possible world.  2. The meaning of the parts can't be changed without changing the meaning of the whole.
The objectivist account of cognition makes two inconsistent assumptions:

  1. The meaning of a sentence is a function that assigns the truth value to the sentence for each possible world. (This is a standard definition of meaning in objective is semantics.)
  2. The meaning of the parts cannot be changed without changing the meaning of the hole. (This is a requirement of any theory of meaning.)

To see the contradiction, notice the following:
 
Changing the meaning of the parts of the sentence should change the meaning of the sentence as a whole (by 2). This implies that the truth value of this sentence will also change for some possible world (by 1).

But, we can construct a sentence in which the meaning of its parts changes but its truth value remains the same in all possible worlds.

So, we have a contradiction.

Note: in unpacking the claim, Lakoff draws on an argument by Putnam (1981), which extends Lowenheim-Skolem's theorem from first-order logic to higher order-logic.
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The Objectivist account of cognition »The Objectivist account of cognition
Objectivist account of cognition is inconsistent
The Lowenheim-Skolem theorem »The Lowenheim-Skolem theorem
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