Logic I exercise: Formalize “Every day each of us says the dumbest thing we are going to say that day.” Is it logically true?
Logic I exercise: Formalize “Every day each of us says the dumbest thing we are going to say that day.” Is it logically true?
Since it implies that there is a maximally dumb thing we are going to say on any given day, it’s not logically true.
Perhaps we need a limit assumption?
Well, we need that I’ll say at least one thing and that thing has an entry on the dumb scale. (If all I say on Tuesday is “ouch”,…) So hardly logically true. Of course, in my case, it is in fact true that for anything thing I said, I said an even dumber thing. And, I said at least one thing. Very talkative, I.
For all d,x,z,y there exists z'[ {NOT(x)-said-(z)-onday-(d)} OR {(x)-said-(z’)-onday-(d) AND (z’)-dumber-(z)} AND {(NOT(x)-said-(y)-onday-(d)) OR (NOT(x)-said-(z’)-onday-(d) AND (y)-dumber-(z’))}]Would that be right? Regardless, the first Anonymous got it right without formalisation. An existence-claim can never be logically true in PL.
“An existence-claim can never be logically true in PL.”Not so. (Ex) x = x is logically true.Revise that to: no interesting existence claim is logically true in predicate logic.