“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.
I have no idea why you’re being downvoted. Perhaps it’s coming off as a bit rude to some?
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.