Do you not believe something is true, or do you believe something is not true?
Both occur. Isn't this the distinction between the theists misstatement that atheism is the belief that there is no god, when what the majority of atheists will tell you, the so-called agnostic atheists, that they don't make that claim, but rather, simply don't accept the claims of others that there is a god. This distinction is sometimes referred to as not believing versus not believing not.
If faith is required to sense the truth
Faith cannot be a path to truth since any idea or its polar opposite can be believed by faith. A path to truth would be a method that generates only correct ideas. A path like a road takes you where you want to go if you know where the road leads. As long as one continues the method of putting one foot in front of the other in a way that keeps one from going off the path, he arrives at his desired destination. Contrast that with a ship on the open seas. There is no natural path there. The ship can go in any direction. The desired destination is in one of those possible directions. Without a method such as maps and compasses to constrain the direction of movement, there is no path, and one is unlikely to sail to his desired destination.
Consider adding a column of multi-digit numbers. There is a single method that will reliably get you from addends to a correct sum. You must add pairs of digits according to a fixed and invariable rule. Every time 6 and 5 are to be added, 11 is the answer. Whenever 9 and 6 are to be added, 15 is the answer. This is pure reason, and it is a virtual path to truth (a correct sum). But allow faith to generate the sums, and there is no longer a path to truth. If 9 + 6 can be 14 one time on faith, and 17 the next time, also on faith, well, there's really little chance at getting to the desired destination.
So back to your comment, reason applied to evidence is required to "sense" the truth. No other method works. I live in walking distance to the pier. How do I get there? What is my path to the pier. I can't really know on faith. Maybe by faith I choose to believe that it is 4 blocks north. Bad guess. The lake is south. I know this empirically. I see it. That knowledge immediately constrains my choices. Suppose I discover by trial and error that the pier is 5 blocks south and 3 blocks west. If that is a fact, if that is true, then I have a reliable path to the pier.
My point is that the essential difference between faith-based beliefs and those derived from the valid application of reason to the relevant evidence is that the latter is a path to truth and former cannot be. This is why I reject all faith-based thinking and ideas. It's the surest way to accumulate wrong ideas.
Faith is a game we all play with our lives, (empirical) trust is critical in the survival of the human race.
Disagree. Trusting based on empirical knowledge is not faith. Nor is acting on partial information and having to do some guessing and hoping. If I approach a bridge and choose to cross it because I trust it will not fall with me on it based on others having successfully crossed and a visual inspection of the bridge before crossing, that is also not faith. Understanding that the bridge is likely to support me but that that is not guaranteed is also not faith. If I cross the bridge without any reason to believe it will support me yet am certain without doubt that it will, now I have a wrong idea no longer based in evidence or reason. That's faith. It's a mistake to equate that kind of thinking with reasonable thinking based on empirical support, and is tentative rather than certain. One idea is correct, the other incorrect.
Calling them both faith misses that distinction and is an equivocation fallacy, which occurs when two meaning of a word are used interchangeably, as when one argues that banks are safe place to keep money, rivers have banks, therefore rivers are a safe place to keep money. Using the word faith to mean both justified belief (this bridge is likely to support me) and unjustified belief (success is certain since God will protect me) leads to this fallacy of falsely conflating two ideas using the same word for both. It's the same thing that would happen if you named both of your daughters Faith.
