Word of the day – iff

I came across today’s word, iff, in the syntax textbook I’m reading at the moment (Introduction to Government and Binding Theory). When I spotted it I thought at first that it was a typo, but have since discovered that it is used in logic to mean “if and only if”.

Iff can also be represented by the following symbols: ↔, ⇔ or ≡

Quite a few other symbols are used in logic, and to some extent in linguistics textbooks on semantics and syntax. They include:

⇒ / → / ⊃ = if … then
¬ / ˜ = not
⊕ / ⊻ = xor (exclusive or)
∀ = for all/any/each
∃ = there exists
⊢ = infers or is derived from

I vaguely remember learning some of these in maths classes many moons ago and still haven’t quite recovered! I tend to skip parts of books and articles that use them.

Source: Wikipedia

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This entry was posted in English, Language, Words and phrases.

10 Responses to Word of the day – iff

  1. Nikki says:

    I’ve known about iff for quite a long time, it always surprises me that so few others know what it means.

    “Not” (in logic in general) can also be represented by ! or a macron above (and I’ve only seen normal mid-line ~s), but it depends who, what and where. My classes used ¬ almost exclusively in semantics (finally! a use for that character other than the ¬_¬ smiley!), but the macron above almost exclusively in electronics. ! is rather popular in computing.

    How are you finding that book? I think pretty much everyone in my year is traumatised by it, it really didn’t help us at all. Maybe that’s just because we were taught a different style to what’s in the book so reading the book just confused us more.

  2. Magnus says:

    Yes, iff is quite commonly used by mathematicians as a written shorthand for “if and only if”.

    Apparently in the days when it was common for mathematicians to write their papers by hand and get them typed by a secretary it was not unusual for iff to be “corrected” to if during the typing up phase. That, of course, tends to have a very detrimental effect on the carefully polished chain of reasoning being presented.

    By the time of my own brief career as a mathematician it was much more usual for us to do our own writing up (usually typesetting on a computer) and therefore we had nobody else to blame for our logical mistakes. :-)

  3. Sol says:

    I remember getting half a mark off an otherwise perfect math test in grade 7 for accidentally writing “iff” instead of “if” in an answer. I had no idea it was a word but I haven’t forgotten it since.

  4. Arakun says:

    Similar abbreviations are sometimes used in other languages as well. The Swedish counterpart would be “omm” (“om och endast om”).

    A few more symbols, because we all like them :)

    ∧ / & = and
    ∨ / | = or
    ~ = not
    ⊤ / t / 1 = true
    ⊥ / f / 0 = false
    ∃! = there exists only one
    ∴ = therefor

  5. AR says:

    @Arakun
    I like how you used the Swedish quotation marks. =]

  6. Arakun says:

    @AR
    Heh… Those things are so small I can barely tell which way they are turned.

    Well, it was not an active choice; my computer simply does not know nor care what language I’m writing in. If I wanted English-style quotation marks I’d have to press alt-shift-n and alt-shift-m on my Swedish Mac keyboard (but I usually don’t bother). :)

  7. BG says:

    I learned iff in Geometry freshman year of high school. While some language people don’t like math, a few of my friends and I enjoy both and the connections are quite interesting. The same goes for language and music and music and math.

    As an example my friend enjoys reading Euclid’s Elements in Ancient Greek and Newton’s Principia in Latin. We even read an excerpt of Principia in Latin II, but when my friend asked our new teacher if we could read some he said “ugh”. I think it would be interesting to read something different to mix up the Aeneid with. The same friend is also trying to explain music in terms of fundamental equations as in Physics.

  8. Jim Morrison says:

    From Wikipedia:
    Other words are also sometimes emphasized in the same way by repeating the last letter; for example orr for “Or and only Or” (the exclusive disjunction).
    hence:
    I eatt chips = I eat (and only eat) chips
    ;-)

  9. Jacob says:

    nice post

  10. Simon says:

    Nikki – I’m finding the book quite heavy going and have to read each bit several times to understand it. I’ve also been reading Carnie’s Syntax: A Generative Introduction, which just confuses things even more.