Back to the basics

Aidoe

Does "A is always the Best Student" mean "A --> Best Student" or "Best Student --> A" ?

Does "A is the only Best Student" mean "A --> Best Student" or "Best Student --> A" ?

I get a bit confused when "is" or other referents are used in conjunction with Group 1 - 4 logical indicators. I know the convention is to follow the rule of the indicators, but when I think about what the sentence is saying instead of just blindly following the rule, I'm not always so sure.

Wind-Up Bird

Here's how I mapped it:

A is always the best student ("B") = A <---> B
I think this is a special case. If you're operating under the reasonable assumption that there can only be one "best student", then the arrow goes both ways. If you're asked about A, you know that they're the best student. If you're asked about the best student, you know that it's A.

However, a sentence like "dogs are always cute" would be represented as "dogs --> cute". The arrow only goes one way, since you now know that if you have a dog, it's always going to be cute. However, the arrow doesn't go the other way, since you don't always know if a cute thing is going to be a dog.

Your second statement is just a classic group 1 example ("the only"). "A is the only best student" = "the only best student is A". Therefore, if you have a "best student", you know it's going to be A (best student --> A).

Not Ralph Nader

Always is a necessary condition indicator so the first sentence "A is always the Best Student" mean "A --> Best Student" in plain English if A is in the class then A is the best student in that class.

Second sentence is a normal conditional statement " Best Student --> A
"A is the only Best Student" the only is sufficient condition indicator so it means if we have a best student in that class then it is A. "

TBH I am not very sure about the second sentence, it would be great if one of the Sages or Mentors comment on this thread.

Alejandro

what @"Not Ralph Nader" said!