A fully homomorphic encryption scheme has the additional counter intuitive property that, although you cannot learn anything about the encrypted data without the secret key, you can still perform arbitrary operations on it. In particular, if you have a homomorphic encryption of the source code of a program you can run that program without learning anything about it (except how long the source is), but the output of the program will be homomorphically encrypted.
The second sentence doesn’t follow from the first. Being able to perform arbitrary operations on the encrypted data doesn’t enable you to perform operations without knowing what operations they are.
The second sentence doesn’t follow from the first. Being able to perform arbitrary operations on the encrypted data doesn’t enable you to perform operations without knowing what operations they are.