Wittgenstein was a philosopher who arrived at several insightful questions (e.g. the private-language problem) but seemed to range from clueless to superstitious about transfinite set theory. Non-Trinitarians (and even many Trinitarians) have a hard time with distinguishing the concept of the Trinity from tritheism, or interpreting the Incarnation in a logically coherent way. On my end of things, I can think of at least two, and maybe three, abstract arguments/concepts that I do not understand to this day, try as I might: (A) the highest-level versions of the doctrine of divine simplicity (esp. modulo the Trinity idea); (B) talk of spacetime as emergent; and maybe (C) skepticism about the external world. However, for some weird reason, I feel like I can work with paraconsistent logic fairly well and incompatibilist free will has never seemed particularly mysterious (as a concept, if not as a proposition) to me.

Now, I am currently debating whether beliefs can be deterministically caused, or rather whether belief in indeterminism can be deterministically caused. But so I wonder, in turn, what specific neurological conditions might promote or inhibit understanding of various beliefs (and, in turn, agreement/disagreement with the assertions which those beliefs comprise). I've mainly seen the word neurodiversity used in connection with the autism spectrum, although I expect it might apply to the schizophrenia spectrum too, and other things besides. If it is relevant to the schizophrenia spectrum, then suppose that the reason why THC can aggravate conditions on that spectrum is less due to the dopamine hypothesis of schizophrenia and more due to the strong similarities between anandamide and THC. Insofar as anandamide (and perhaps other endocannabinoids) is (are) implicated in abstract neurological connectivity (correct me if I'm wrong but what I recall reading is that anandamide is not maintained in the system like dopamine and serotonin are, but is synthesized "on demand" when the brain tries to make certain kinds of connections), neurodiversity adverting sufficiently to variations in people's endocannabinoid systems might be reflected in different ways of handling abstract connectivity, such as would play a positive or negative role in understanding this or that conceptual scheme.

And then, in turn, other neurochemical variations might lend themselves to other problems/aptitudes when it comes to interpreting various peculiar ideas. I realize that a Google search would be liable to yield plentiful results when it comes to researching such a question, and I will do such a search as time permits, but I would like to pose the question here, nevertheless.

  • An additional factor is that if someone has proven a strong ability to grasp complex concepts but then encounters a concept that no one can make clear to him, then he is entitled to doubt whether anyone actually does grasp that concept or whether they are fooling themselves. I go back and forth on various concepts such as the Trinity and metaphysical necessity. I know the language well enough to fool anyone into thinking that I grasp these concepts, but I don't. I often suspect that everyone is in the same boat as me, but the others don't realize that they don't actually grasp it. Commented Jul 10, 2022 at 7:24
  • I've had extensive discussions with someone who claimed to grasp metaphysical necessity. I genuinely wanted to grasp the concept, but he could not make it anything more than a bare token to me. That is, I understand the consequences of P being necessary, but I cannot understand what that would consist of--how it is different from ~P being inconceivable. He eventually lost patience and accused me of faking my lack of understanding for rhetorical purposes, and the conversation went quickly downhill. Commented Jul 10, 2022 at 7:32
  • I am reminded of something Kant said about how "no one has ever been able to explain the categories of possibility and necessity," although then he attempted to explain them himself (as metaphysical, not logical, descriptions). But so I have a Scylla and a Charybdis to navigate, here: the threat of genuinely meaningless discourse, and the threat of intellectual standoffish-ness on the Internet. My experience has been that the seemingly meaningless turns out, on charitable inspection, to be otherwise, but even dialethism (for me) might turn out to be an empty notion. Commented Jul 10, 2022 at 14:19

1 Answer 1


It’s unclear if you’re taking understand and belief to be interchangeable. You start using belief in the second paragraph so I’m not sure if that’s a separate argument. Maybe you’re semi-consciously linking those two terms and it would help to disentangle them.

I look to formalism and fictionalism of math as an example of how that might look. It does not require specific belief in how formal languages apply to the world to understand formal languages. Only the belief such study is worthwhile is necessary to understand a formalism.

When Poincare “rejected the actual infinite” and called impredicative definitions (a collection that contains the defined entry) viscously circular[1], I do not take that to mean he could not work under such a system if properly motivated. To work in a formal system is to understand, just look to the late Ed Nelson who was a formalist at the highest levels of mathematics. And he worked on trying to show PA was inconsistent, on a belief that it was a worthwhile investigation. This is why I doubt Poincare would have trouble with any mathematics a realist could throw at him if he were so inclined to study it.

So we have to clarify, is it a lack of belief or a lack of understanding? I dare say you’d probably pass any quiz given to the average church-goer on the trinity. Even though your understanding is par or better to the average church attendee, your beliefs may be wildly different and unique from anyone else’s. Who knows the path anyone takes to understanding. Maybe you were motivated by pure incredulity yet acquired the skills to pass any quiz given to a parishioner.

I think to deny this separation of belief and understanding is to deny the fictionalist and perhaps nominalist accounts.

Now separation doesn’t mean something biological or environmental isn’t at play. But it means the proper “diagnosis” is important. Is it belief or understanding or both you lack? If you understand any Earthly quiz, what more could you ask for? Ed Nelson understood the Earthly public domain at the core of his field. At that point belief becomes nigh-superfluous. To reach that point requires properly motivating beliefs toward understanding, but which belief doesn’t seem to matter nor does belief serve much purpose after the core is mastered.

So I do think it plausible brain chemistry plays a role in belief and understanding. But honestly, why be troubled by having more difficulty in motivating certain study? At some level beliefs become superfluous, and wildly different beliefs can lead to the same understanding.

I think what I’m saying is understanding is of the same concept by being public, belief is idiosyncratic. It is possible our innate or early beliefs prevent us from proper motivation and study. But beliefs, by their nature of being possibly superfluous once understanding is reached, and creating wildly divergent paths to the same understanding, shouldn’t substitute for proof. You should not believe understanding impossible as understanding something in public doesn’t require specific belief.

[1] Shapiro, thinking about mathematics, 2000. Pg. 10

  • In the abstract context of philosophical concepts, it seems as if there is a vague boundary between, "Understanding proposition X," and, "Believing proposition X is possibly true." (There IS a boundary, but also some abstract questions seem as if their answers would be given, here, directly from ambient understanding.) From a truth-functionalist standpoint on semantics, representing the definitions of lexical concepts adverts to interpretation of their entire sentential context. Also, though: answer upvoted, under consideration for acceptance. I'll see what others say but then... Commented Jul 9, 2022 at 17:01
  • One other consideration: but how likely is it that Poincaré would have ever made any contributions to the theory of the higher infinite? Contributions, that is, besides some theorem-level permutations of axioms he would not have come up with (e.g., I doubt the question, "Do embedding-theoretic cardinals exist?" would have occurred to him, quite). Commented Jul 9, 2022 at 17:04
  • Re: belief vs. understanding, another illustration might be the intersection of, but also the difference between, knowing how to play a given game, and knowing how to invent a new game. Commented Jul 9, 2022 at 17:16
  • @KristianBerry (Comment 1) What exactly are you being asked of in prop logic? Much more than, if I use a certain algorithm on a limited domain of sentences I get propositions which can be studied formally by a new algorithm? If it was much more than that I missed the memo and still did well. (Comment 2) Definitely Poincare would study something else. Beliefs may orient our study and lead to different understandings. But he could learn higher set theory with the right motivators right?
    – J Kusin
    Commented Jul 9, 2022 at 17:33
  • @KristianBerry (Comm 3) this goes back to my comment about prop logic. What exactly does learning a game entail and require? I would argue little. If you love chess and are a grand master, you understand it bar none and yet don’t want to invent another game.
    – J Kusin
    Commented Jul 9, 2022 at 17:36

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