Here’s a more precise version of what I’ve been saying for years about
Carnap, Quine and David Lewis. It’s based on the following:

Our knowledge can be divided into two quite different parts. As best
we can, I think by seeking a theory that will be systematic and devoid
of arbitrariness, we arrive at a conception of what there is
altogether.… This conception, to the extent that it is true,
comprises our modal and mathematical knowledge. But a conception of
the entire space of possibilities leaves it entirely open where in
that space we ourselves are situated. To know that, it is necessary to
observe ourselves and our surroundings. And observation of any sort
… is a matter of causal dependence of one contingent matter of
fact upon another. (Lewis On the Plurality of Worlds, §2.4,
pp. 111–12)

1. Carnap agrees about the second type of knowledge: we find out
contingent truths, if at all, empirically. But he holds that the first
type of knowledge is knowledge of truths by convention: that is, more
or less, that the real questions in this area are practical, rather
than theoretical.

(The “more or less” is necessary because of complications about the
difference between internal and external questions. Once natural
numbers, e.g., are admitted to the language by practical decision,
there are theoretical questions about what natural numbers exist.)

2. According to Quine, this position is incoherent, because, if
conventions are supposed to do this, then empirical facts are not
sufficient to determine which convention we have chosen.

3. Lewis responds with the above doctrine. In the case of necessary
truths, we form our knowledge, to the extent that we have any, in the
way a conventionalist would suggest (seeking unity and simplicity,
etc.). But we are not choosing a convention; rather, we are choosing
what we should believe. Even if we follow the correct method, we might
be wrong.