[Verse 1]
If it rains then the ground is wet
This promise seems so simple yet
When logic meets our common sense
The truth can feel quite strange and dense
Rain falls down and pavement's soaked
That's true just like we always hoped
[Chorus]
Implication's just a promise made
Only broken when the price is paid
If the condition isn't even met
The promise stands without regret
Arrow pointing from the left to right
False makes everything alright
[Verse 2]
But what if sprinklers wet the street
On sunny days when there's no sleet
The statement didn't say that rain
Was the only cause of water's stain
So wet ground on a cloudless day
Still keeps our promise true they say
[Chorus]
Implication's just a promise made
Only broken when the price is paid
If the condition isn't even met
The promise stands without regret
Arrow pointing from the left to right
False makes everything alright
[Bridge]
Vacuously true sounds strange I know
When nothing happens, truth can grow
The only way to break the deal
Is when the cause is really real
But then the consequence must fail
That's when our logic starts to wail
[Verse 3]
No rain today and ground stays dry
Our promise soars up in the sky
The rain condition wasn't there
So truth floats freely in the air
This feels so wrong but here's the key
Without this rule no reasoning would be
[Final Chorus]
Implication's just a promise made
Only broken when the price is paid
If the condition isn't even met
The promise stands without regret
Arrow pointing from the left to right
False makes everything alright
When P is false then Q's free
That's how logic has to be