If and Only If

I was thinking today about the construct if and only if. It occurred to me that while it is often used my mathematicians, philosophers and logicians, it is almost never used by anybody else.

If and only if (abbreviated to iff), means exactly what it says.

  • There are fewer than 30 days in the month iff it’s February.
  • You will become king or queen iff the current monarch dies or abdicates and you are next in the order of succession.

The iff brought more meaning to those sentences than if would have alone. Not only has February got fewer than 30 days, but it is the only month that does. Not only will you become monarch under those circumstances, but those are the only circumstances under which you can become monarch.

Formally, the if denotes sufficiency, and the only if denotes necessity.

In English, we tend to use if when we mean iff, and we differentiate using context.

  • If you drop litter, you could be fined.     (if is intended)
  • You can have pudding if you finish your main course.     (iff is intended)

Much semantic and grammatical pedantry is defended with claims about clarity. One shouldn’t use less in the place of fewer as the meaning is less clear. I think the fact that we can all understand if with little confusion is a good counter-argument.

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2 Responses to If and Only If

  1. Gareth Hughes says:

    Hmmm I really don’t see the difference. If, and only if, seems to be over egging the pudding just for the sake of it.

  2. Ben says:

    Maybe we should start saying “o-if”.

    Or put the ‘only’ somewhere sensible in the sentence, “you can only X if Y”.

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