Beliefs and assumptions do not always overlap. Even a new rationalist does not need more than a few moments to prove that belief without assuming anything is possible. In spite of this, a rationalist might still find that others deny this foundational truth. There are two ways one might encounter this. The first takes the form of the self-refuting notion that nothing can be proven, and the second entails the idea that beliefs are contrary to truths, and thus truths should be embraced over beliefs.
The first of the two refutes itself so that all one must do to disprove it is grasp the inherent contradiction and dismiss it as an impossibility. Knowledge is possible only when one can demonstrate that something is true, but it is possible. Demonstrating to oneself that something is true always involves reason even when some concepts are discovered through introspective or sensory experiences. The second of the two false stances on beliefs and assumptions is not quite as self-refuting, even if it is still asinine and easy to refute.
All assumptions are beliefs, but not all beliefs are assumptions. It is both rational to believe in truths demonstrable with logic (as opposed to the idiocy of looking to hearsay, consensus, preference, or emotion) and irrational to not believe in that which one has already clarified through using reason. It is never belief that is problematic in itself simply because it is belief, just belief apart from logical proof. Again, belief in what one has used reason to prove is the only rational position to take on a given matter.
There is also the fact that beliefs are inescapable because to think that all beliefs are inherently irrational or untrue, one must believe that such a thing is true! To resist the fact that some beliefs are true by logical necessity--and that the truths at the heart of those beliefs are necessary truths like the veracity of reason and one's own existence--is to resist a demonstrable aspect of reality itself. Belief is inescapable; belief in logically necessary and provable truths is rational and all other beliefs can be avoided.
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