Socionics perpetuates the myth that Te and Ti are logical functions, while Fe and Fi are not. All judging functions are logical, because logics is just a set of rules to process information.

Ti is boolean logic; it works with absolute true and false. Fi, however, is diffuse, and thus can handle intermediate values between true and false. For example:



The girl above, is she wearing blue pants?

Ti answer: no.
Fi answer: she's wearing pants, but not blue.

According to Fi, it is true to some extent, or, in other words, it is a half truth.

It's the ability to handle partial truths what gives Fi types the diplomatic intelligence. They often look at other's point of view and find something useful, so they find it easy to build bridges of agreement between them an others.

The difference between Fi and Ti is explained here: