The crucial point here is that Ramsey sentences don’t define concepts like belief, but eliminate them. They give us a way of saying what our everyday theories say without using the relevant concept (there is a kind of state that is caused by perceptions …) If we want definitions, then we need “Carnap sentences”, not Ramsey sentences (Lewis 1970). The Carnap sentence corresponding to “\(\exists!\Phi(T(\Phi))\)” is “If \(\exists!\Phi(T(\Phi)\), then \(T(F)\)”.  (If there is a kind of state that is caused by perceptions …, then it’s belief.) Carnap sentences can plausibly be viewed as akin to stipulations that fix the reference of the relevant concepts, and to that extent as analytic claims that can be known a priori. But this certainly does not mean that Ramsey sentences, which make substantial claims about the actual world, are also knowable via a priori analysis. (Note how you can accept a conditional Carnap sentence even if you reject the corresponding unconditional Ramsey sentence. You can grasp the folk concept of belief even if you reject the substantial folk theory of belief.)