∀y∀x : (y & ¬y → x)
Every undergraduate logician is taught that anything follows from a contradiction.
They marvel over this for two minutes, that if one accepts a set of contradictory premises, one can prove whatever one wishes, with the full force of logical certainty. One can equally prove that nothing follows from a contradiction, but who cares.
I am reminded of this unhelpful fact as I ride my bike near Highbury Fields past a wall on which the following has been painted:
Because Υou Αre Αlive
Anything Ιs Possible
From the saddle of my bike, I have no better account of logical possibility than that it applies to those things of which we can conceive.
But who could conceive of you? And if they could conceive of you, who could conceive of you alive? Or of my bike, or of Highbury fields, or that wall or the white paint. Or of any of these things before they were?
And if this is so, against the odds, who can say what will follow next? All bets are off.
Because you are alive, anything may follow.
I reach Highbury roundabout.