Well, that saying only makes sense if it has the exact same implication in both terms (and then their respective conclusions has to be about different propositions), otherwise one is just claiming the equivalent of:
“One guy thinks A implies B, another thinks B implies A.”
And that is not a very good saying. It just sounds like something a post-modernist would say.
If you make A → B only with some probability, then B becomes probabilistically dependent on A as well; i.e. if you make logic probabilistic then this actually becomes true in a sense.
It is certainly true that if we know A implies B, then knowledge of B will also confer knowledge of A. However, this is not enough to call it a logical implication, and given that the original saying used the terms modus ponens and modus tollens, a logical implication is obviously what is meant in this setting.
Well, that saying only makes sense if it has the exact same implication in both terms (and then their respective conclusions has to be about different propositions), otherwise one is just claiming the equivalent of:
“One guy thinks A implies B, another thinks B implies A.”
And that is not a very good saying. It just sounds like something a post-modernist would say.
“One man’s modus ponens is another man’s modus ponens… in the other direction.”
If you make A → B only with some probability, then B becomes probabilistically dependent on A as well; i.e. if you make logic probabilistic then this actually becomes true in a sense.
It is certainly true that if we know A implies B, then knowledge of B will also confer knowledge of A. However, this is not enough to call it a logical implication, and given that the original saying used the terms modus ponens and modus tollens, a logical implication is obviously what is meant in this setting.