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Would anyone please enlighten me on why the author uses 'if and only if' here? It sounds to me as though just 'if' sufficed for him to inform the readers 'Cats are her favourite animals' is the truth condition.

Implicature

A communicated implication of an utterance. A speaker can intend to mean more by her utterance than what the words that she utters mean, as the philosopher Paul Grice pointed out.

Andy: I think we should get a pet.

Bess: Cats are my favourite animals.

Here Bess’s utterance is true if and only if cats are her favourite animals. However, in the context, it is likely that she conveyed more, in making her utterance, than this (and that she intended to do so). She intentionally and openly implied that she and Andy should get a cat (or cats) as pets. Pragmatic theorists would say that she implicated that she and Andy should get a cat (or cats) as pets.

[...]

(source: Key Terms in Pragmatics)

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Sssamy
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  • this is really an academic point. The author is talking about how "a speaker can intend to mean more by her utterance than what the words that she utters mean". Here, what Bess said is true only if she is speaking the truth without any ulterior motive of sending across a different signal. But as the author further points out, it here implies that she is suggesting they get cats as pets. – Darshan Chaudhary Oct 30 '16 at 11:55
  • It is simply a way of providing emphasis to if. – WS2 Oct 30 '16 at 11:59
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    There are conditions where "if" may be interpreted ambiguously. (The whole Boolean algebra problem.) The idiom removes that ambiguity. – Hot Licks Oct 30 '16 at 12:14

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Is there some reason if and only if has a meaning here different from it's usual meaning in mathematics?

From www.mathwords.com, for example:

if and only if Biconditional

A way of writing two conditionals at once: both a conditional and its converse.

For example, the statement "A triangle is equilateral if and only if its angles all measure 60°" means both "If a triangle is equilateral then its angles all measure 60°" and "If all the angles of a triangle measure 60° then the triangle is equilateral".

Biconditionals can be written using the ⇔ symbol:

A triangle is equilateral ⇔ its angles all measure 60°

So:

If Beth's statement is true, then cats are Beth's favourite animals.

AND

If cats are Beth's favourite animals, then Beth's statement is true.

That is:

Beth's statement is true ⇔ Cats are Beth's favourite animals

Beth's statement is true if and only if cats are Beth's favourite animals.

I agree that Beth appears to be saying more, that if Andy and Beth should get a pet, they should consider getting a cat, provided that cats are Beth's favorite animals.

Richard Kayser
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  • The relevant Wikipedia page says *if and only if (shortened iff) is a biconditional logical connective between statements.* I knew about OR/XOR, but until now I hadn't really registered this IF/IFF distinction. But it's obviously potentially useful. – FumbleFingers Oct 30 '16 at 12:55
  • @FumbleFingers Right re Wikipedia. I opted for what seemed a simpler reference with a good example, and I omitted iff. – Richard Kayser Oct 30 '16 at 13:07
  • I must admit that until I factored in this two-way "biconditional" concept it seemed to me the cited passage just said that a statement is true *if* the condition it asserts is true - a trite observation, within which context it seems pretty meaningless to include *and only if. I actually thought the ⇔* symbol meant something like is another way of saying, or can be restated as, but the "two-way" aspect comes into play with two assertions such as A:Beth won the lottery. B:Beth is rich, where A "entails, implies" B, but B doesn't necessarily imply A. – FumbleFingers Oct 30 '16 at 13:48
  • The terminology, "if and only if," is an unfortunate but established bit of mathematical jargon. It was fought by some mathematicians, notably by the R. L. Moore school, but it was championed by Paul Halmos, who introduced the abbreviation, iff. There is a simple gedanken experiment to see tha it is jargon. t – Airymouse Oct 30 '16 at 14:09