Hypothetical Propositions:
Nonstandard Forms
"p unless q"

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


"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

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