Coextensive properties that are not the same property. There are some biological facts like these. Probably not remembering correctly but for example B=”animal has heart” A=”animal is mammal” it can easily be that all mammals in fact have hearts but you couldn’t still say that it would be impossible for a mammal to be heartless (and for example have a blood circulation system that is evenly distributed all over the veins (which they kinda partially do but be totally reliant on those kind of mechanism)). The deduction of “It is a mammal, it must have a heart” is false for plenty of reasonable senses of “must”. It is true for the probabilistic sense of must but implication has more senses than the probabilistic one.
If it’s a given that all mammals have hearts, then being a mammal implies it has a heart. If it’s not known that all mammals have hearts, then P(B|A) < 1.
Coextensive properties that are not the same property. There are some biological facts like these. Probably not remembering correctly but for example B=”animal has heart” A=”animal is mammal” it can easily be that all mammals in fact have hearts but you couldn’t still say that it would be impossible for a mammal to be heartless (and for example have a blood circulation system that is evenly distributed all over the veins (which they kinda partially do but be totally reliant on those kind of mechanism)). The deduction of “It is a mammal, it must have a heart” is false for plenty of reasonable senses of “must”. It is true for the probabilistic sense of must but implication has more senses than the probabilistic one.
If it’s a given that all mammals have hearts, then being a mammal implies it has a heart. If it’s not known that all mammals have hearts, then P(B|A) < 1.