OK so I completely forgot what Ramsey sentences are.
On point 2, supposing that every a priori proposition is analytic, then it seems each only needs one term replacing
Let's say we want to explain what the different parts of a car are...
First, we transform our Car Theory into an existentially quantified
sentence, quantifying out all the bold terms our audience doesn't yet
x1 x2 (...and x1 mixes gasoline and air and sends the mixture to x2,
which in turn...and that makes the wheels turn.)
This is called the
Ramsey Sentence for our Car Theory (after the philosopher and
mathematician Frank Ramsey). Next we can define what it is to be a
carburetor and an ignition chamber as follows:
A carburetor = an x1 such that x2 (...and x1 mixes gasoline and air
and sends the mixture to x2, which in turn...and that makes the wheels
So supposing that the sum of analytic facts do not add up to anything which cannot be expressed in an analytic proposition, their sum only expresses something non-relational, like:
- every x is an unmarried man.
I think the sentence is non-relational because all analytic propositions tell us is a definition: of a term which is now eliminated.