Transitive Incompleteness of Logical WFF's Due to Godel's Incompleteness Theorem

Question

If a set of theorems, or wff's, are used in conjunction with one another, does this have an impact on their completeness in terms of soundness?

For example, I have five theorems of logic, or well-formed formulas that are together an argument against dualism of the mind. If four of them act as premises for the fifth, which is used as a conclusion, would this argument using wff's be stronger or weaker if I instead used premises that were not wff's?

I understand that wff's are often used as lemmas to prove a final wff, but my question is exactly whether this method of proof is actually stronger or weaker than a formalized argument using premises which are not wff's.

Answer 1

The concept of a WFF (well formed formula) is a formal one and deals with syntactic validity. Any logic you pick will have a concept of WFF (just how any written language you pick has a concept of spelling).

If, in that logic, you provide a deduction that contains lines that are not WFFs, then it's easy to see that it would be weaker than using WFFs. Not only would it be weaker, but it would be nonsense.

(I'm not sure how Godel's Incompleteness Theorem fits here.)