(live-blogging Xprag)
In his introduction, Kai von Fintel tells an anecdote that I think sums up why it is sometimes difficult to explain what it is we do. Some time ago, Emmon Bach wrote a book for Cambridge University Press on if/then conditionals. The copy-editor sent it back, replacing every use of "if and only if" with a simple "if," saying the "and only if" was redundant.
As it turns out, although people often interpret "if" as meaning "if nd only if," that's simply not what the word means, despite our intuitions (most people interpret if you mow the lawn, I'll give you $5 as meaning if and only if you mow the lawn...).
Part of the mystery, then, is explaining why our intuitions are off. In the meantime, though, explaining what I do sometimes comes across as trying to prove the sky is blue.
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1 comment:
If and only if (iff) is distinct from simple if even in our intuitions. Iff implies that for no other reason would the consequent (the then clause) be true. Simple if only indicates one way the consequent could happen. To clarify, I'll use your example.
"If you mow the lawn, I'll give you $5."
If you mowed the lawn, I can safely say you were given $5. But if you were given $5, I could suspect but not be certain that you mowed the lawn.
"If and only if you mow the lawn, I'll give you $5."
If you were given $5, I can know for certain that you mowed the lawn: If the proposition is true, then for no other reason would you have been given $5. (Note that "iff the proposition is true" would be innapropriate because several antecedents (if clauses) could have that very consequent.)
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