Maybe it would be useful to take an intentional point of view on this and distinguish between faith itself and faith-with-an-object (referring to the latter as a form of belief). Faith itself would not be something that could be given a precise rational definition, more along the lines of what Kant called an aesthetic idea: “...by an aesthetic idea I understand that representation of the imagination which occasions much thought; without, however, any definite thought, i.e., any concept, being capable of being adequate to it; it consequently cannot be completely compassed and made intelligible by language. We… see that it is the counterpart of a rational idea, which conversely is a concept to which no intuition (or representation of the imagination) can be adequate.”
Would you give an example of that type of faith? That language sounds vague to me. Many believers I’ve met describe “faith” in their gods as more or less like faith in the future or faith in a spouse, but that doesn’t sound right to me.
I’ll start off with just examples:
Aesthetic idea: The cognitive (mental, emotional) experience one has when viewing a work or art like the King Tut funeral mask; or when listening to music (Beethoven’s 9th).
Rational idea: the concept of number, the concept of a triangle.
I think you’ll agree that these fit into Kant’s definitions.
For faith, feelings of confidence and security experienced physically in the upper chest and projected onto aspects of the world (which, as a mental extension of this, one then says that one has faith in—the ideas, thoughts, beliefs, and so on that get attached to this all being, in the end, inadequate and at bottom superfluous).