Contradiction and lies - part 2

Why don’t we trust people who contradict themselves? This is a no-brainer: because one of their statements must be a lie:

 

Face masks protect against infection. (P)

Face masks do not protect against infection. (Not P)

 

But another reason, less often articulated though grasped intuitively by any sane person, is that anything follows from a contradiction, including a lie.

 

If someone is known to have said both of these statements in public, they might want to defend one of them (no matter which) by smuggling in another statement:

 

Either that or bleach is a cure for viral infection. (Q)

 

We defend the truth of one statement by disjoining a new statement to it (more on that in the previous post). By the rule of disjunctive syllogism, the new statement will be stripped of company and made to stand out unsupported. Contradictory statements cancel each other out. 

 

Premise 1: P

Premise 2: Not P

Addition 3: P or Q

Inference: Therefore, Q.

 

A lie abhors a solo appearance. It likes company. For a lie to thrive, it likes to be shielded by truths (and other lies alike).