> Is this what you are talking about with 1 or 0.

It mostly has to do with the zeroes. Take Bayes' theorem:

P(A|B)=P(B|A)P(A)/P(B)

The prior for some hypothesis A is P(A)

If you start with no knowledge, P(A) can be something like 1/n, where n is approximately the number of competing hypothesis.

B is the "data" part, a weighed compbination of all data used to update P(A).

P(A|B) is the posterior probability for A, given the data B. This posterior is then used to update your prior P(A) before you are exposed to new data.

Take the hypothesis "God exists as a male person". Before any data, maybe you give this a 1/4 prior probability. Add the Bible as your only source of data, P(A|B(ible)) may go to 9/10. Add all other religious texts, and maybe it goes to 1/2. Add all of Science, and maybe it goes a bit lower.

Now what happens when we set a probability to 0?

If P(A)=0, then P(A|B) stays at 0 regardless of how much data you pile into B. A prior of 0 makes it completely impossible to convince you that A is true.

Or, lets say you have two competing hypotheses:

A1: God is exists as a male person:

A2: Hypothesis A1 is false. (God either does not exist or is not male or not a person).

Since A1 and A2 cover all possible states, P(A1)+P(A2) = 1.

In other words, if you set P(A1) to 1 you simultaneously set P(A2) to 0.

And as above, when you have a prior of 0, it will never get updated using bayesian logic, so regardless of any evidence to the contrary, P(A1) will remain 1.

Only in a situation where P(B|A1) is also 0 could you ever doubt A1. When this happens, a person may live through severe cognitive dissonance or crisis, as if all of reality falls apart. The person will have to choose to discard A1, or to find some reason to ignore the data B.

For instance, if you believe 100% that some organization (any organization, but let's pick Hamas this time) are the good guys (hypothesis A), and some event B (like a massacre of civilians) seems to strongly oppose that belief.

Lets say P(B|A) is very low in this case.

If you have built your existence and identity around P(A)=1.

Now, instead of believing B really happened, you can introduce an alternative (conspiracy theory) view on the data, for instance:

C: It was really Mossad that tricked Hamas into attacking Israel.

In this case, P(C|A) can be quite a bit higher than P(B|A).

Now, if you extend this, you can even turn this around. If you see A as the DATA not as the Hypothesis, you can set up

P(B|A) = P(A|B)P(B)/P(A)

P(C|A) = P(A|C)P(C)/P(A)

While other people take B simply as data, you have now turned it into something to be disproved. And if you are certain that P(A)=1, you can believe almost any conspiration theory C as long as P(A|C) > P(A|B).

And this can cascade. If P(A|B) is small enough, then you can end up being certain that P(B) = 0 and eventually that P(C)=1.

Anyway, the above type of reasoning is at the root of religious and dogmatic thinking. In fact even a single false belief held with a prior probability of 1 can be used (through Bayesian logic) to prove almost anything.

And this is not limited to happening by accident. A skilled demagogue who can trick the audience into accepting (with no room for doubt) a single false or inaccurate claim, can then use to manipulate them into believing almost anything.

(Obviously, in the Hamas/Isreal conflict, this goes both ways.)