One of the stranger misconceptions of rationality/intelligence--the extent to which someone intentionally, consistently grasps the laws of logic and roots their beliefs in them--that I have heard from others is the idea that if someone thinks they are intelligent, they are not. That this does not logically follow because being rational and knowing one is rational are distinct things that could easily overlap; the former is true when applicable whether or not the latter is something a person focuses on or fully accepts. Of course, being educated, having a strong memory, and being able to easily put words to thoughts and concepts are not intelligence, so anyone who thinks they are rational for these reasons is an irrationalistic fool, but avoiding assumptions, understanding logical axioms and what logically follows or does not follow from various truths or ideas, and recognizing the intrinsic philosophical nature of logic and everything else makes someone rational whether or not they or anyone else admits it to themselves.
Perhaps this person who erroneously thought that no intelligent person thinks he or she is intelligent confused a lack of self-awareness or rational recognition of one's rationality (the irony in intentionally avoiding this kind of self-awareness even as a rationalist is strong) for humility. Humility, though, is not ignoring one's talents, rationality, or gravitation towards deeper matters or mistaking them for something trivial. Moreover, it it was, then humility would be irrational and thus only someone disconnected from grasping reason fully would pursue humility. This is not the case. In fact, not making any assumptions, including about one's own rationality, is an expression of humility, and it would be an assumption to blindly believe that one is or is not rational without understanding reason or oneself.
Now, there are only two small categories of things that are logically self-verifying and that necessarily are the epistemological and metaphysical foundation of all else. The inherent epistemological truth of logical axioms and the fact of one's own conscious existence are the only self-evident things. While the existence of one's various feelings and many of one's thoughts is not self-evident in the way that one's own existence as a consciousness is, for one's consciousness is a metaphysical prerequisite to having thoughts and an epistemological prerequisite to knowing one's further thoughts or feelings, the contents of one's mind are absolutely certain: if I feel something or think about an idea other than logical axioms or my own existence, I cannot be mistaken that I am experiencing such a thing. I and everyone else can infallibly know their own worldview, personality, and perceptions by merely looking to reason and then introspecting without making assumptions. If a rationalist examines their own alignment with reason, he or she can directly know it without any misperceptions, assumptions, or great difficulties, meaning they can know their own rationality (intelligence is nothing besides this).
There are even analogies that could help some better understand or appreciate why believing one is rational, which can be easily proven or disproven to oneself, does not mean one is not intelligent (given that one really is a rationalist). Is a tall person not fall if they believe they are? Is a kind person not kind if they believe they are, rightly or wrongly, though, again, this is something rationalistic introspection can easily reveal? Of course not! In fact, you cannot know you are tall, only that you perceive yourself to be tall by comparison to something else using senses that might not be seeing the external world as it is to begin with. On the contrary, since reason is necessarily true and introspective perception is by necessity absolutely certain in that one cannot not be experiencing the contents of one's own mind, one's rationality is not difficult to discover given that one just avoids all assumptions and looks to reason to do so. It is still true that the difference between being tall and believing one is tall illustrates by analogy how believing one is something does not mean one does not have the characteristic in question.
One's own intelligence is directly knowable without any distortion of the truth or any experience of confusion. A rational person even knows to some extent that he or she is rational, just as an emotionally conflicted person can easily know they are emotionally conflicted without focusing on the issue directly. It would be impossible for a rationalist to have no idea at all that he or she is rational, though there are differing degrees of awareness, focus, or acceptance of this fact. At the very least, that reason and introspection are absolutely certain, directly knowable, and universally accessible means that no one needs to expend great effort to understand their own rationality. The laws of logic that dictate possibility and necessity and proof, governing the whole of reality, are known directly without anything more foundational than logic itself, and one's mind is ever before oneself. There can be no reason a person fails to thoroughly recognize their own intelligence in light of these truths besides focusing on something else, apathy, or sheer irrationality.
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