Hypothetical Propositions:
Nonstandard Forms
"Without p, then q"

Another nonstandard form is "Without p, then q."

Example:

"Without distribution requirements, most students would take too narrow a range of courses."

Here we do not have two component propositions; the phrase beginning, "without" does not contain a whole statement. Yet it is easy to turn that phrase into a whole statement: "If distribution requirements did not exist, most students would take too narrow a range of courses."

In general, "Without p, q" can be translated as, "If p does not exist (or occur), then q."


"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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