People say "אני מאמין ש" - "I believe that ...." without actually knowing what the word means!!!
What they really mean is that they "think" or "assume" or "hope that this is true" but not "אמונה" in the true Biblical sense.
In Israel people say "ואיש באמונתו יחיה" - meaning, let every person do whatever his yetzer hara dictates!!! The actual pasuk is וצדיק באמונתו יחיה [Chabakuk 2-4] which means something completely different.
See previous post for a working definition of אמונה.
It is worthwhile keeping the following quote in mind : “Arguments follow from assumptions, and assumptions follow from beliefs, and very rarely—perhaps never—do beliefs reflect an agenda determined entirely by the facts.”