Post #4043865

Replies (1)

• @FishFace@ioc.exchange 2026-07-23 19:01

  @rzeta0@mathstodon.xyz this is a good question. It's a question of language - of translating natural language into formal language and respecting the intent. And, since you aren't quite convinced of the intent behind the natural language statement, this justification may not work for you (i.e. it may feel circular or like it's begging the question), but I'll give it anyway: "There exists x such that P(x)" is supposed to mean, well, what it says. But if P is an implication (i.e. P(x) ≡ Q(x) --> T(x)), then as long as Q(x) is false for some x, the existential statement is true. That is, take P(x) ≡ "x is even --> x^2 = 9", i.e. we're talking about "there exists an x such that x is even implies x^2 = 9". Then this is *true* because pick any odd x, and P(x) is vacuously true! But this does not reflect our intuition - or at least not *my* intuition - about the sentence, "x^2 = 9 for some even x". Does that make sense? Happy to cook up more examples :)

  Open ##4043864