something being “first” implies existence and the statement is wrong if the something does not exist.
“everytime i’ve met yetAnotherUser, they promised me all their money” on the other hand is true, because we never met and existence of a meeting is not required.
or to look at it in a more mathy way:
“For all X y is true” is false if an x exists for which y is false, if no X exists no X exists for which y is false and thus “For all X y is true” is a true statement, but your statement is “there is an X_i from the set X=X_j for which y is true” which is false if no X_i is in the set.
That depends on whether you interpret “when” + past tense in English to also assert the reality of the temporal clause. The interpretation which allows the vacuous truth is, in my opinion, not even technically correct (by correct I mean aligns with actual spoken usage). It would amount to formalizing the sentence as
For all meetings between us, if said meeting is at a past time and it’s the first meeting (i.e. before all other meetings), you promised at that time to give me all your money.
Which is indeed vacuously true, if there have been no past meetings, or even if the meetings aren’t well-ordered in time :). On the surface this is a perfectly good interpretation, but it doesn’t really align with real usage (though I would love to see an example of “when” + past tense being used this way, e.g. in a legal document).
On the other hand, most people would interpret “when” + past to assert that the event actually happened, which in this context means
I have met you before, a “first meeting” can be identified, and at that first meeting, you promised to give me all your money.
Or even more formally
There exist meetings between us at a past time, there exists such a unique meeting which is first, and, for all meetings, if said meeting is indeed the first, you promised me at that time to give me all your money.
And this can be reduced to
There exists a unique past meeting between us such that [it’s first, and you promised to give me all your money at that time].
I think this interpretation is most closely aligned with how “when” is actually used in practice. “If” feels different, though. It can act as simple logical implication, logical equivalence, or anything in between, so it may be more interesting to study. Also note that all of this doesn’t apply to “when” + simple present, which acts very similarly to “if”.
Reason #2801 why vacuous truths are awesome.
“When I first met you, you promised to give me all your money” is a true statement because I have never actually met you.
Just be careful not to test this in court.
something being “first” implies existence and the statement is wrong if the something does not exist.
“everytime i’ve met yetAnotherUser, they promised me all their money” on the other hand is true, because we never met and existence of a meeting is not required.
or to look at it in a more mathy way:
“For all X y is true” is false if an x exists for which y is false, if no X exists no X exists for which y is false and thus “For all X y is true” is a true statement, but your statement is “there is an X_i from the set X=X_j for which y is true” which is false if no X_i is in the set.
That depends on whether you interpret “when” + past tense in English to also assert the reality of the temporal clause. The interpretation which allows the vacuous truth is, in my opinion, not even technically correct (by correct I mean aligns with actual spoken usage). It would amount to formalizing the sentence as
Which is indeed vacuously true, if there have been no past meetings, or even if the meetings aren’t well-ordered in time :). On the surface this is a perfectly good interpretation, but it doesn’t really align with real usage (though I would love to see an example of “when” + past tense being used this way, e.g. in a legal document).
On the other hand, most people would interpret “when” + past to assert that the event actually happened, which in this context means
Or even more formally
And this can be reduced to
I think this interpretation is most closely aligned with how “when” is actually used in practice. “If” feels different, though. It can act as simple logical implication, logical equivalence, or anything in between, so it may be more interesting to study. Also note that all of this doesn’t apply to “when” + simple present, which acts very similarly to “if”.
Damn it, I was trying to go for the “When” + simple present to check whether my statement worked.
I thought:
“When 1 equals 2, blablabla” is always true, therefore [my statement above] works as well.
But I should’ve thought “When 1 equaled 2, …” which doesn’t sound true anymore.
That is to say: Fuck grammatical tenses!
I love you