Why do we spell naive with two dots on the i ?

Answer 1

Normally you dot the i. The name for the dot over the lower case letter I is called a tittle.

In some cases, instead of a tittle, you use two diacritical marks over the lower case i. The double dots are called an umlaut: ï

The umlaut is a diacritic ( ¨ ) which indicates the phonological phenomenon of umlaut in German. The umlauted vowels are ä, ö, and ü. The same name is used in other languages which have borrowed these symbols from German. (Including French and English)

Usually the umlaut occurs when two vowels are beside each other, and instead of joining in a single sound, they make different syllables. In other words, "ai" does not join to make a single sound.

(nä-ēv')

So that even without ever hearing the word, you would know by the umlaut that naive is not pronounced nave but
as this recording indicates:
http://www.bartleby.com/61/wavs/46/N0004600.wav

Answer 2

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RE:
Why do we spell naive with two dots on the i ?

Answer 3

I don't think most people do that, but sometimes the double dot thingy is put on there to remind people that the "i" is pronounced separately from the "a' - we pronounce it ny -eve instead of nave.

Answer 4

french.
The ï in french is pronounced like the Y in english