“Only XYZ like ABC” is equivalent to: “Everyone who likes ABC is also an XYZ.”
Since everybody likes at least something, there is no one who likes nothing. The statement: “Everyone who likes nothing is also a man” is true because the “Everyone who likes nothing” part results in 0 people. And it’s true to say that everyone in a group of 0 people is a man. It’s also true that everyone in a group of 0 people is not a man.
But other than vacuous truths, no sentence stating “Only man like XYZ” is true.
But you’re kind of right that it’s not great that math is still a strongly male dominated field. There is not a single woman’s name in the Wikipedia article for set theory, where I first tried to find a counterexample.
Also, you don’t necessarily need set theory to arrive at vacuous truths. Logic is enough:
FALSE => [statement]
Still, I think vacuous truths are fun because they are meaningless. Especially because they have to be considered in math or else your carefully constructed proof becomes invalid.
Yes there is:
Only men like nothing.
Explanation:
“Only XYZ like ABC” is equivalent to: “Everyone who likes ABC is also an XYZ.”
Since everybody likes at least something, there is no one who likes nothing. The statement: “Everyone who likes nothing is also a man” is true because the “Everyone who likes nothing” part results in 0 people. And it’s true to say that everyone in a group of 0 people is a man. It’s also true that everyone in a group of 0 people is not a man.
But other than vacuous truths, no sentence stating “Only man like XYZ” is true.
But only men like set theory, so…
This woman likes set theory because she was involved in a set theory workshop:
https://dmg.tuwien.ac.at/sandramueller/conferences/
But you’re kind of right that it’s not great that math is still a strongly male dominated field. There is not a single woman’s name in the Wikipedia article for set theory, where I first tried to find a counterexample.
Also, you don’t necessarily need set theory to arrive at vacuous truths. Logic is enough:
FALSE => [statement]
Still, I think vacuous truths are fun because they are meaningless. Especially because they have to be considered in math or else your carefully constructed proof becomes invalid.