The classically valid inference according to which one may add arbitrary disjuncts to a formula without loss of truth. This is to say that if $\phi$ is true, then for an arbitrary $\psi$, $\phi \vee \psi$ is true, where $\vee$ is a disjunction. This amounts to the inference

for formulae $\phi$ and $\psi$. In the form of an axiom scheme, addition is frequently represented as:

• • $\phi \to \left(\phi \vee \psi \right)$

Some have resisted the validity of addition in general by appealing to an analytic reading of conditionals as requiring the preservation of subject-matter from antecedent to consequent. According to such a view, a conditional such as:

• • If a prime number $p$ divides $n^2$, then $p$ divides $2n^2$

may be considered true, as the subject-matter of the consequent is part of that of the antecedent. However, this condition fails for the conditional:

• • If a prime number $p$ divides $n^2$, then either $p$ divides $n^2$ or the moon is made of green cheese

because novel subject-matter not found in the antecedent has been introduced to the consequent.