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I can think of "that is to say", "in other words", "put differently". And I'd like to know if there are any subtle differences in the usage of these synonyms. Can they always be used interchangeably regardless of the context?

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“i.e.” always, only, and ever means “that is”, and should always be read that way. It never means “put differently”. It is never meant to be read aloud or in your brain as eye-eee initials; it should be expanded for the abbreviation it is, and very most preferably into English not Latin.

You may be thinking of videlicet < vidēre licet, abbreviated viz. in print but originally a scribal abbreviation employing Tironian et: vi⁊. This is usually read aloud as “namely”, and has a slightly different nuance compared with i.e., which you can look up in any general reference book.

I very strongly recommend not using Latin abbreviations, because I can guarantee you that between reader and writer, someone won’t know what these properly mean. After all, look at the question you asked.

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Could you please detail the nuance between viz. and i.e.? I ended up with nothing after looking them up in several online dictionaries. – pegasusbupt Feb 19 '12 at 20:46
viz = namely, and often introduces multiple terms; i.e. = meaning, and usually gives just a single term as if in apposition – tchrist Feb 19 '12 at 21:13
+1 for a reference to Tiro, one of my favorite historical figures. – Robusto Feb 19 '12 at 21:29
@Robusto I mention him by name in the “letters lost from English” thread. – tchrist Feb 19 '12 at 21:33
I would not think 'that is' to be the same as 'put differently.' – Kris Feb 20 '12 at 7:07

i.e. is an abbreviation for the Latin id est, which means 'that (literally, 'it') is'. You can use any formulation which says the same thing. Personally, I avoid Latin phrases and abbreviations where possible. If they disappear from general use, as seems quite likely, I would say good riddance.

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Perhaps the simplest replacement is a comma:

I'm king of the hill, top of the list.

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