You're merely equating faith with belief, or with a kind of belief. Most people use the words interchangeably. You can define them and use them however you like, of course. I make a distinction between them, and I believe my use of them returns more of their original meaning. Most people don't even have a word for what I call "faith".

I first encountered these uses of the words in Alan Watts The Wisdom Of Insecurity - a great read BTW. Especially good for people entrenched in western thinking who want to understand more eastern concepts.

A true scientist doesn't just use doubt. Doubt is merely negative belief. A true scientist uses UNknowing - openness, the suspension of belief. What I call faith. You probably don't have a word for it. It begins with the words "I don't know", not "I doubt such-n-such".

In fact it is because so many scientists mistake doubt for faith that they tend to be so rigid in their thinking. Scientists are historically very slow to open to new ideas and theories, and often resist them despite overwhelming evidence. They are not open-minded (faith), but are entrenched in prior beliefs (and negative beliefs - doubts).