Highjacking mathematical notation for political statements? Is nothing beyond the reach of politics?
Well, in logic, ⊥ is used to denote falsehood, hence the name falsum.
So “⊥” is equivalent to “A ∧ ¬A” or “2 + 2 = 5”. Whenever you say “⊥” as a single statement by itself, you are either lying or you are badly confused.
It’s interesting to use it together with logical implication (“⇒”). The interesting thing about logical implication is that anything can follow from a falsehood.
“If 2 + 2 = 5, then I am the pope” is a true statement regardless of whether I am actually the head of the Catholic Church or not.
⊥ ⇒ Obama wiretapped the candidate
can be read as “Trump says, Obama wiretapped the candidate”.
Note this is true regardless of whether Trump is lying, making things up, confused, or telling the truth for once. He said it.
If we flip things around, they’re different:
Obama wiretapped the candidate ⇒ ⊥
(Read as “Obama wiretapped the candidate, says Trump”)
This actually means that Obama didn’t wiretap the candidate.
In denotational semantics of programming languages, ⊥ is called “bottom” and denotes the result of a program that fails to compute a value. Programs that terminate with an error, and programs that do not terminate at all. Meaningless programs.
So, if ⊥ is the president of the US, that means that this is an abnormal condition, either American democracy has crashed or it is caught in a never-ending infinite loop.
One more warning about ⊥: There are some programs which are obviously ⊥, and others which are obviously not ⊥. But in general, it is impossible to tell. You can run a program, and if it produces a result, you know it’s not ⊥. But if it hasn’t produced a result yet, you cannot know if it will produce a result tomorrow or never at all. This is known as the “Halting Problem”.
For politics, this means that you can never know if a politician is going to bring about world peace and happiness soon, or if he’s equivalent to ⊥rump.