You’ve just substituted a different proposition and then claimed that the implication doesn’t hold because it doesn’t hold for your alternative proposition. “We’re counting kids” absolutely implies “the count can be represented by a nonnegative int32”. If I want to show that an argument is unsound I am allowed to choose the propositions that demonstrate it’s unsoundness.
The X⟹Y implication is valid in your formulation, but then Y doesn’t imply anything because it says nothing about the distribution. I’m saying that if you change Y to actually support your Y⟹A conclusion, then X⟹Y fails. Either way the entire argument doesn’t seem to work.
Sorry but this is nonsense. JBlack’s comment shows the argument works fine even if you take a lot of trouble to construct P(count|Y) to give a better answer.
But this isn’t even particularly important, because for your objection to stand, it must be impossible to find any situation where P(A|Y) would give you a silly answer, which is completely false.
You’ve just substituted a different proposition and then claimed that the implication doesn’t hold because it doesn’t hold for your alternative proposition. “We’re counting kids” absolutely implies “the count can be represented by a nonnegative int32”. If I want to show that an argument is unsound I am allowed to choose the propositions that demonstrate it’s unsoundness.
The X⟹Y implication is valid in your formulation, but then Y doesn’t imply anything because it says nothing about the distribution. I’m saying that if you change Y to actually support your Y⟹A conclusion, then X⟹Y fails. Either way the entire argument doesn’t seem to work.
Sorry but this is nonsense. JBlack’s comment shows the argument works fine even if you take a lot of trouble to construct P(count|Y) to give a better answer.
But this isn’t even particularly important, because for your objection to stand, it must be impossible to find any situation where P(A|Y) would give you a silly answer, which is completely false.