The Chinese Room Argument

[timelets]

I'm still trying to wrap my mind around the Universal Property of Products.

Let's say, a pair of (question, answer) is a Product of all questions and all answers in all possible worlds.
When we say that there exists one (or more?) correct answer for each question we assume that there exists and Oracle X that has a unique map to the pair.

Let
D1 - questions;
D2 - answers;
D = D1xD2 - (q,a);
X - the Oracle; (correct combinations of q&a);

p1: D -> D1;
p2: D -> D2;

f: X -> D1; (question entry for the correct pair);
g: X -> D2; (answer entry for the correct pair)

m: X -> D.

If I understand it correctly, Searle's Chinese Room Argument says that if one has access to the Oracle (X and m: X->D) she doesn't have to understand questions in order to come up with correct answers.