#### Hypothetical Propositions:Nonstandard Forms"p unless q"

Another nonstandard hypothetical statement has the form, "p unless q."

Example:

"The plant will die unless you water it." This means the plant will die if you do not water it; "unless" means "if not." Thus, the following three propositions are equivalent:

p unless q.

p if not-q.

If not-q, then p.

Does "p unless q" also imply, "If q, then not-p"? Are we also saying that if you do water the plant, it will not die? No--in some contexts it might be assumed that we are also saying this, but it is not asserted by the original statement. Once again, think of the statement as a promise I have made to you. If you water the plant and it still dies, I haven't broken my promise, strictly speaking; I didn't promise that water alone would keep the plant alive, only that the absence of water would kill it. Consequently, "p unless q" is exactly equivalent to, "If not-q, then p," and should be translated that way.

"p if q" | "p only if q" | "p if and only if q"
"p unless q" | "Whenever p, q" | "Without p, then q"

Hypothetical Propositions