So why all the ‘α’ and ‘β’ malarky?

When we defined the meaning of ampersand with a truth-table, we said that, strictly speaking, we shouldn’t use sentence/statement letters (like ‘P’ and ‘Q’) but should instead use something else (we use Greek letters). We gave a rough explanation of why. Now we can see more clearly and accurately.

The reason is that, when we give the truth-conditions for ampersand, we are giving the truth-conditions for any ampersand phrase, including those where what’s plugged into ‘&’ are complex sentences—not just those we get by plugging in sentences that don’t have connectives in them. We want the rule about truth-conditions to apply to sentences like ‘(C & ~A)’ and ‘((A & B) & C)’, not just sentences like ‘~A’ and ‘(A & B)’. (And we also want the rule to apply to wffs which are sentential clauses in larger sentences.)