Yesterday The Donald proclaimed that, if elected this year, he would get 95% of the African-American vote in 2020. At first blush, this looks like typical Trumpian bushwah; he’s no more likely to get 95% of the African-American vote in any year than he is to become someone’s biological grandmother.

However, the propositional calculus of modern formal logic treats “if-then” statements in a fashion that leads to counter-intuitive results. “If X, then Y,” (formally, X ->Y) is interpreted to mean “It is not the case both that X is true and Y is false” (~[X and ~Y]). In the case where X is sometimes true, there’s no problem; the proposition claims that in all those cases, Y is also true, which is what we naturally mean when we say “if X, then Y.”

But a problem arises when X is always false. In that case, even if Y is never true, it is, indeed, never the case that X is true and Y is false, because it is never the case that X is true. Thus any “if-then” proposition counts as true when the “if” clause is false.

So, assuming that Donald Trump will not, in fact, win the Presidency this year, the claim that, *if* he were to win, *then* he would get 95% of the African-American vote in 2020 is also (trivially) true, just like the proposition that, *if* Trump were to win, *then* the Persians won Marathon andÂ Ï€ = 3.

Savor this moment; it may be the only instance this year when Donald Trump’s words express a true proposition. And it gives us all one more reason to work hard for the next 80 days: you wouldn’t want to make the poor man a *liar*, would you?

Cliff Wirt says

Material Implication and the Election:

<tongue mainly in cheek>If Classical Logic is true, then Donald Trump has said at least one thing (though possibly only one thing) that is true. The weirdness of Material Implication makes this one utterance true essentially by accident. However, if Relevant Logic is true, then even that one utterance is false. This is one argument in favor of Relevant Logic as a better description of Reality than Classical Logic: Donald Trump cannot possibly say anything that is true.</tongue mainly in cheek>

JamesWimberley says

The propositional calculus was developed as a way of formalising the foundations of mathematics. As an account of the everyday logic of language, it is incomplete. "If .. then" sentences are normally understood as requiring that if P is true, there is an adequate reason for holding that Q is true. The reason may be logical entailment or asserted causation or probability. In this everyday sense, Trump's if-then is false.

snideissue says

Another way it could be true would be if he manages to create conditions in his first term that effectively restrict the franchise to assure that only Trump supporters are allowed to vote or to have their votes counted. That's what the "strong leaders" Trump admires do. Having to worry about getting re-elected is one thing that "cripples" American presidents. Strong leaders also don't have to deal with hostile, dishonest reporters who can write anything they damn well please without fear of being jailed or murdered, they can torture or behead prisoners of war, and have their opponents disappeared.

JeffreyK622 says

That was my thought also. If Trump were to get 95% of the A-A vote, he would presumably get at least 96% of the Asian vote, 97% of non-white Hispanics, and 99% of whites. I think his only competition in "greatest electoral landslide ever" would be Saddam Hussein.

lcoleman6 says

"But a problem arises when X is always false."

Normally, as Dr. Wimberly points out, it's unwise to expect ordinary language use to reflect propositional calculus, but this is one case where it does: "If Trump's a savvy politician, then I'm the Queen of England." "If he wins, I'll eat my hat." Of course in that context the if-then sequence is more about X than Y, serving the communicative function of asserting the speaker's view that X is really, really, really false–or ardently hoped to be so.

JamesWimberley says

Mr. I just fake the style.

KennnethJ says

By the same analysis, if Donald Trump wins this year, in four years Professor Kleiman will be the Democratic nominee and will win in a landslide, no matter how African Americans vote.

MarkARKleiman says

As a logician said after watching a magic trick: "That's not merely impossible; it would have to be impossible in any self-consistent universe."

MattMcIrvin says

My vector-calculus prof, J. C. Sanwal, used to use the example "If the moon is made of green cheese, then my uncle is a monkey."