It is common for non-rationalists to still think they are rational, though what they erroneously consider rational is whatever strikes them as alluring at he moment or whatever seems to be true to someone who allows their worldview to be filtered by assumptions. Conversely, some people who are indeed being rational might feel as if they are making assumptions when they are not. As they go about their lives, full awareness of what they believe (for a person has direct access to their own stances and uncertainties) and of how those beliefs align with reason might not keep them from feeling like they are not being rational.
If no belief has been accepted, then no assumption has been made. Beyond just feeling like one is being irrational when one knows one is not, simply thinking or not thinking of a particular idea at a particular time does not mean that one has accepted it as true without proof, in the case of the former, or that one has made an assumption passively, in the case of the latter. To walk into a room in hopes of finding a box or a remote does not have to entail the belief that it is inside the room, even if one remembers perceiving that this was the case. To turn on a light switch does not require that someone is assuming a causal instead of a merely correlative relationship beyond the subjectivity of sensory perceptions.
Indeed, a rationalist who is deeply familiar with truths such as the epistemological irrelevance of seeing an object to it actually existing might walk into a room and pick up a box without specifically thinking every single time about how the box might not exist, or how the memory of its location could be inaccurate, and so on. Especially after years of allegiance to reason, the avoidance of assumptions and the recognition of logical truths can become practically effortless even when it might have at first seemed like there was no hope of them ever reaching this point. What misleadingly seemed impossible can become normal for a formerly irrational individual.
To make assumptions is to betray necessary truths, and doing the opposite of this is to embrace reason--to flee from assumptions and to intentionally, thoroughly align with reason, first and foremost by recognizing the inherent truth of logical axioms. With these and other logical truths, familiarity can spring up that is so holistic, so strong, and so persistent that a former non-rationalist really can avoid assumptions without even always focusing on specific examples of assumptions he or she is avoiding. To avoid assumptions, and to quickly or eventually reach this place, is something within the reach of every being that can grasp reason by distinguishing it in various ways from the rest of reality that it governs.
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