# Rule of Addition/Explanation

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## Proof Rule

The Rule of Addition consists of two proof rules in one.

The first of the two can be expressed in natural language as:

- Given a statement, we may infer a disjunction where the given statement is the
**first**of the disjuncts.

The second of the two can be expressed in natural language as:

- Given a statement, we may infer a disjunction where the given statement is the
**second**of the disjuncts.

The statement being added may be any statement at all.

It does not matter what its truth value is.

That is: if $p$ is true, then $p \lor q$ is likewise true, **whatever** $q$ may be.

This may seem a bewildering and perhaps paradoxical axiom to admit. How can you deduce a valid argument from a statement form that can deliberately be used to include a statement whose truth value can be completely arbitrary? Or even blatantly false?

But consider the common (although admittedly rhetorical) figure of speech which goes:

*Reading Football Club are going up this season or I'm a monkey's uncle.*