This was a recent question at Quora – What are some concepts only people with high IQ’s can understand? – and this was the answer provided by Bruno Campello de Souza, Professor at Federal University of Pernambuco in Brazil. I don’t necessarily agree with any of these myself, but it is a very interesting list.

It is hard or perhaps even impossible to state something that “only” the very intelligent will understand, but there are certainly things which most people struggle with that those with high IQs are more likely to grasp.

In my own personal and anecdotal experience, the following ideas and notions are unknown, misunderstood and/or rejected by the vast majority of those with normal IQs (90–110) and even by most of those with above-average IQs (111–125), but are far more likely to be known, correctly understood and/or embraced by those with a gifted-level IQ (126+). In no particular order:

• If you agree to the premises, then you have, wittingly or not, agreed to their consequences or implications, and the only way to revert this is to go back to the premises and disagree with at least one of them;
• It is possible to predict and, yet, not control, i.e., there is a difference between correlation and causation, i.e., knowing “how” does not tell you “why”;
• There are statements that are always true no matter what, and they are utterly useless precisely for that reason (tautologies);
• One cannot “prove” a scientific hypothesis empirically no matter how many confirmations are observed, but only “disprove” it through counterexamples (which may be just a single trustworthy case), proofs only existing in Logic and Mathematics (Modus Tollens);
• By definition, conspiracy theories cannot be falsified, for it can always be said that any evidence that would contradict them was secretly fabricated by the hidden powers that be in order to hide the truth, therefore, they are logical fallacies;
• In random independent events, no matter how unlikely a given series of observations is, this has no bearing on the likelyhood of the next element in the series, even if the next element makes the increased series much less unlikely (ex: in a fair coin toss, obtaining a series of 100 “heads” in a row does not change the chance that the next toss will come up “heads” as well);
• Natural selection does not work through environmental challenges leading to the an increased rate of offspring born with the capacity to overcome such challenges, but rather through an increased chance of procreational success (intergenerational genetic transmission) of specific random mutations that happen to coincide with a higher ability to overcome said challenges;
• Predictability has no bearing whatsoever on free will, for the existence of a pattern for one’s behavior, even at the level of preferences and decisions, does not imply that such behavior was not a choice, for the possibility of choosing according to one’s preferences is the very definition of free will;
• Any and all things are quantifiable, even love, justice, and beauty, among all other things, for different instances of the same phenomenon vary in amount and/or intensity, which is not to say that such quantification is always easy;
• “When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be” – Lord Kelvin;
• Mathematics is not science, but there is NO science without Mathematics, with human and social sciences being no exception (there are no exceptions);
• The fundamental rules of the scientific method do not change according to the subject or phenomena under study, be it Physics, Chemistry, Biology, Psychology, Sociology or any other field, and straying from that method is always bad science, regardless of the field;
• Electron, force, mass, gravity, space-time and any other concepts from Physics or any other natural science have the same nature as those of motivation, emotion, unconscious, intelligence or any other concept from Psychology, i.e., they have no objective existence, being purely made-up abstract ideas put forth to explain observable phenomena;
• It has always and will always be impossible to tell fact from perception, i.e., whatever is considered to be known about any empirical phenomenon can always be false, no matter what the evidence, i.e., one cannot separate Metaphysics from Epistemology;
• The inevitable fallibility of all empirical knowledge, along with the psychological and sociocultural nature of knowledge, are no justification for a “free-for-all” or “anything goes” epistemic nihilism;
• It is impossible to truthfully state that someone is making a misleading argument based on sophisms and/or fallacies unless one clearly points out said sophisms and/or fallacies, in other words, one cannot say that they are losing an argument solely because of rhetorical “cheats” or “tricks” from their opponent unless such “cheats” or “tricks” are explicitly identified (otherwise, the statement becomes unfalsifiable and, therefore, tautological and useless).

Due to their logical-mathematical nature, which is not subject to empirical validation, none of the above statements is an “opinion”.

Even among those with a very high IQ it is not uncommon to find someone with difficulties regarding one or more of the aforementioned statements . This is a particularly annoying case, for not only one expects such individuals to be more able to deal with the concepts involved, but also they tend to be very good at rationalizing their viewpoints through convoluted arguments which, of course, are wrong, but often require considerable time and effort to debunk.