When saying "Someone can A if B", does it imply "If someone does not B, someone cannot A"? So if I want to say "B is an option for A, but B is not necessary to achieve A", is "Someone may A if B" closer to this? Or is "Someone can A if B" good enough for this meaning?
closed as not a real question by FumbleFingers, Will Hunting, J.R., Matt Эллен, RegDwigнt♦ Mar 31 '12 at 10:31
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If I take your meaning, let's use the following example:
where A = ice cream and B = peas.
Regarding your first question:
Regarding your second question:
May implies that a permission is being granted. In order to express that B is not necessary to achieve A, you could say something like:
No. For example:
Someone can fly if they have a plane. Clearly you can also fly if you buy a ticket on an airline or get someone else to fly you.
You can have a cheeseburger for lunch if you get here before noon. This clearly offers one way you can have a cheeseburger and doesn't imply you can't have a cheeseburger some other way even if you don't get there.
Logically, "Someone can A if B" does not imply "If not B, then not A". The relevant concerns are necessary and sufficient conditions:
In your first example, "Someone can A if B" says B is sufficient for A; it does not say that B is necessary for A. There might be other conditions besides B that make A possible.
If you want to say "B is an option [that ensures] A, but B is not necessary to achieve A" with some precision, then perhaps say "B is sufficient but not necessary for A."
Saying "B is an option for A" is not quite right, because it does not mean "B is sufficient for A" but instead connotes that if you choose A, then B is available as an option.