One of the mysteries of the English language finally explained.
If and only if.
- ‘Let us say that I could have rendered a proposition false in the weak sense iff I was able to do something such that, if I did it, the proposition would have been falsified (though not necessarily by my act, or by any event caused by my act).’
- ‘Thus the sentence ‘Snow is white’ is true iff it corresponds to the fact that snow is white.’
- ‘Let the letter ‘M’ represent this operator, and add to the axioms of classical propositional logic the modal axiom M (p v q) iff Mp v Mq.’
- ‘Minimalism allows us to generate a minimal truth condition for any meaningful indicative sentence, such as ‘Lying is wrong’ is true iff lying is wrong.’
- ‘The truth conditions for negation are: A is true iff A is not true.’
1950s: arbitrary extension of if.
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