One of the easiest kinds of logic to follow is the Hypothetical Syllogism:
IF A, THEN B
IF B, THEN C
...prove A, and we can deduce C.
Most likely you won't find that directness here. Why? Because sometimes things just aren't spelled out that clearly. The problem of defining "belief in something" you can't just pull off the shelf, hold in one's hands, and show someone is a complex task.
Suppose it was stated, from the above, that C was true. Many people would then deduce A from it. This would be an invalid conclusion (even if A was true by coincidence).
Furthermore, we can also see that NOT A does not necessarily cause NOT C either. Something else could be affecting C.
Sometimes in science we just can't prove A. But if we know something like IF-AND-ONLY-IF A, THEN B. Then we can tell A must be so because of B.
Often the only rational explanation for B, is A... and that could be defined as faith. We may not be prove it, but the only way it would make sense is if that were the case. Furthermore we can look for examples based on A, and make statistically valid assumptions that A is true.
At some point we're going to have to make some assumptions one way or another and then put those assumptions, and the rules based on them, to the test. If everything works right, we assume that our assumptions are still valid, for the time being and move on.
If we find something the contradicts our original assumptions, we will toss our assumptions aside, postulate new ones or attempt to ascertain why our initial assumption was faulted and start anew.
To search for an unknown is an incredibly difficult task. We start at square one and work forwards. Sometimes we start at an assumed goal and work backwards. Sometimes we assume the end goal is false and work looking for a contradiction.
Sometimes we create a hypothesis, test the hypothesis, and form a theory. Once a single thing comes along that contradicts a theory, we need to restart.
We must be careful not to fall into any trap. A broken theory is a useless theory (unless it can be revamped to support the contradiction). And whatever evidence surfaced showing our theory was wrong did just that one thing: it showed the theory was wrong, nothing more.
The latter is most likely the harder to accept. Something about being left with a void is disturbing, instead what we should do is look for other possible things that fit the criteria of the unknown. Or perhaps we can solve for the unknown based on the facts or testing assumptions. What we should be doing then is redefining the problem and expanding the scope of our self imposed limitation.
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