1, 2. If,provided,providing imply a condition on which something depends. If is general. It may be used to indicate suppositions or hypothetical conditions (often involving doubt or uncertainty): If you like, we can go straight home. If I had known, I wouldn't have gone.If may mean even though: If I am wrong, you are not right. It may mean whenever: If I do not understand, I ask questions.Provided always indicates some stipulation: I will subscribe ten dollars provided ( on the condition ) that you do, too. Provided he goes, we can go along.Providing means the same as provided, that is, just in case some certain thing should happen: We will buy the house, providing ( provided ) we can get a mortgage.
Usage note
If meaning “whether,” as in I haven't decided if I'll go, is sometimes criticized, but the usage has been established in standard English for a long time.
Old English gif (initial g- in Old English pronounced with a sound close to Modern English -y-), from Proto-Germanic *ja-ba (cf. Old Saxon, Old Norse ef, Old Frisian gef, Old High German ibu, German ob, Dutch of "if, whether"), from PIE pronomial stem *i- [Watkins]; Klein, OED suggest probably originally from an oblique case of a noun meaning "doubt" (cf. Old High German iba "condition, stipulation, doubt," Old Norse if "doubt, hesitation," Swedish jäf "exception, challenge"). As a noun from 1510s.
