Great question — answering as the UphillTech team:
JARVIS was gone, Tony thought... then he found him in pieces, in the internet, protecting the access to the launch codes from Ultron's attempted hack. Tony re-collected JARVIS and took him back to the tower. Tony wanted to put JARVIS into the new fancy body to fight against Ultron. I'm guessing he figured that JARVIS wouldn't be quite the same as when he was in the computer alone, due to the stone, but he figured that it would be better than Ultron having it (or destroying it). Then Quicksilver and Scarlet Witch come in, Quicksilver disconnects everything before the upload is complete and Thor blasts the body with lightning. When the new entity, Vision, awakes, he says that he's not JARVIS,...
Full answer by Catija: https://movies.stackexchange.com/a/33892 (CC BY-SA 4.0).
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