Everyone operates under a belief system.
They have certain core pillars they believe, and everything flows from that.
For some, their core belief is that if science cannot demonstrate it is true with convincing evidence, it is not true. What flows from this, is the belief the supernatural does not exist, only the natural world exists.
We might call this the rationalist approach.
They also believe all things that can be known, can be known with logic, and reasoing based on the first pillar (empirical evidence for all things known).
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There are two ways to look at suppport for this belief system.
One, is that they take it on faith, that their pillars are true, valid, in harmony with reality.
The other, is some form of circular reasoning, that says "I believe these things are true, because they show themselves to be true."
This second can have many forms, but it is self supporting.
Circular reasonig and self supporting systems are fallacious, and suspect.
All belief systems are fallacious, and suspect, but most especially to those of other belief systems.
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Those who are religious, accept that some things are known by faith.
This is a core pillar to their belief system, and their logic will be built on this.
Since faith, by definiton, is not rational, it could be said that their logic is not rational.
However, since the rationalist's belief system has a fallacious foundation, it is also irrational, at the ground level.
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There is a third way of knowing, that is not faith, and not rational.
Some say knowledge can be intuited.