I don’t know if there’s a name for the position that the meanings of our terms is pinned down by facts about the brain. The closest I know is *semantic internalism*, but a semantic internalist could think that meaning is pinned down by facts about qualia, which happen to not be facts about the brain. So I’ll make up a name for this position: call it **physicalist semantic internalism**.

Now, here’s an argument against physicalist semantic internalism that seems totally right to me.

What I mean by “second-order logical concepts” is the concepts of “and”, “or”, “not”, second-order quantifiers (“for all” and “for some”, ranging over not just objects but properties of objects), and the notions of functions, relations, and concepts.

- The semantics of second order logic captures what I mean when I use second-order logical concepts.
- No finite set of rules (and correspondingly no finite machine) can pin down the semantics of second order logic.
- So no finite machine pins down what I mean when I use second-order logical concepts.
- My brain is a finite machine.
- So my brain does not pin down what I mean when I use second-order logical concepts.

And here’s another argument along similar lines:

- The truth values of sentences about integers are determined by what we mean by integers.
- The statement of the satisfiability of each Diophantine equation has a determinate truth value.
- The statement of the satisfiability of each Diophantine equation is a statement about integers.
- So the satisfiability of each Diophantine equation is fixed by what we mean by integers.
- No finite machine can fix the satisfiability of each Diophantine equation.
- Our brain is a finite machine.
- So the meaning of integers is not contained in the brain.

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