This post is mainly going to cover my metaphysical beliefs. Here "metaphysical" should be understood to mean that they are outside of physical explanation - they're not necessarily about physical facts and I even believe some of them more deeply than physical facts. Naturally, logical or mathematical facts fall under this category.
Some people believe they can avoid metaphysics, but rejection of metaphysics is a certain metaphysical belief (and of course, it's often correlated with other metaphysical beliefs like materialist monism, Scientism, etc).
Generally speaking, metaphysical claims can't be rejected by physical facts. Some can be, for example, Descartes' specific claim of dualism of mind and matter - where mind interfaced with matter via the pineal gland - can be rejected by noting that people who have had pinealectomies still appear to have minds. Or maybe they're p-zombies. Nevertheless, the fact that people who have had their pineal glands removed appear to have minds does not disprove dualism in general, only one specific aspect of one specific person's dualist views are rejected.
With these forewords out of the way, my general beliefs follow.
Neutral Monism and Platonism
Probably the most essential hard problem is why anything exists at all. An easy response is that things that don't exist don't exist, but this may be linguistic. Starting with the notion that some things do exist, the question becomes "what exists?".1 The dualists assert that there appears to be at least two substances in the world: mental substances endowed with (most importantly) subjective experience and material substances which appear to follow fixed laws. Importantly, some monists assert that one supersedes the other, with either material substance (hereafter matter) arising from a primordial mental substance or mental substance arising from matter. I don't think either of these are true. The relationship between the two is certainly tight: I’ve been hit on the head and lost memory so I’ve had a physical material event affect my mind. And it’s quite obvious that my mind has casual effects on the physical world - your reading an example of this. This is why I’m a neutral monist - I believe both mind and matter derive from a secret third thing.
What is the third substance? Namely, the abstract, which seems to compose logical and mathematical truths. On one hand, these truths don't seem to depend on matter: I'm not sure that 1 + 1 = 2 has anything to do with the dynamics the world of matter seems to obey. I don't think 1 + 1 = 2 depends on the existence of subjective experience2 either. It seems to entirely follow from an abstract set of rules. The distinction between mind and matter also seems to be based on abstract rules. Minds have subjective experience, they think (most notably, about themselves). Matter has properties like extension (volume), motion, and mass. Perhaps abstract rules are the basis of all things?
This is my belief. So let's get into mathematics, the study of abstract rules. To be clear, I don't believe mathematics is the basis of all things, but I do believe it is a very good map of the "space" of abstract rules, which I think are the basis of all things. I don't know if mathematics can describe all possible abstract rules or if there are some that are "unmathematizable".
A common claim is that mathematics is invented by humans. I think this can be rejected based on the fact that numerical reasoning exists across the animal kingdom, even down to insects like ants. It was even discovered that ants remember distances by counting steps. If you put them on stilts, they will walk the same number of steps back to a remembered location, which will end up being too far with their new cybernetically enhanced legs.
When humans do arithmetic, it tends to primarily be associated with activity in posterior parietal cortex. When cats do arithmetic, it tends to primarily be associated with posterior parietal cortex. Same goes for monkeys. To be clear, I'm not denying we are better at math and have *discovered* more of it. Primates certainly use a bit more of our frontal lobes for math, not too surprising given that we have more of it than cats, but the core regions are similar. I don’t think its a stretch to guess most mammals rely on these brain regions for arithmetical reasoning.
This suggests abstract rules are the product of minds in general, instead of humans in particular. This could be the case, but the physical world also seems anomalously describable with math.
Math is also unreasonably effective. Maybe this because it initially arose to describe space and geometry, natural physical things in the world. Group theory is an interesting case to consider though. True group theory initially arose when studying polynomials and modular arithmetic. These are interesting because in some ways they were divorced from the physical world - at the time they were less used to describe areas and motions and were studied for their own sake. Group theory achieved prominence for its use in proving that there were no easy ways generally to factor polynomials of degree greater than 5. Eventually, it was found that the world seemed to fundamentally have aspects that are exactly described by group theory, so that statements like "electromagnetic interaction is a principle fibre bundle with group U(1) over Minkowski space" accurately reflect some aspect of our world's processes and enables writing 20 seemingly seperate physical equations3 in a single, unified form.
Observations like these point me to the conclusion that our universe is essentially one particular set of (mathematizable) rules. Going back to materialism versus idealism: I think both the mental and the material emanate from this deeper world of Form. The use of the word "Form" here is a reference to Plato and platonism: while my views are certainly different from Plato's, they share the commonality in believing the abstract has an independent existence from material and mind. Going beyond this, my belief is that material and mind are actually downstream of this realm of Form. They both exist as particular realms among the Forms with their own rules and have a particular correspondence between themselves that allows for "simulation". Simulation or correspondence is one of the core characteristics of the Forms.
Quickly going back to the question of existence, why should Forms or abstract rules or whatever I call them exist? I can't answer that, except by again stating some nonsense like "nonexistence doesn't exist". What I can say is that conditional truth seems to exist. In other words, given a set of axioms assumed to be true, other true statements will be true conditional on the truth of those axioms. You can also say they "follow" or spring into being from these axioms.
As an example, consider geometry. You might know that the parallel postulate, the claim that parallel lines can never converge and always maintain their distance from one another, was an assumption of Euclidean geometry. A whole (infinite) set of theorems/truths follow from this assumption combined with four other geometric axioms. But we can also assume it's not true and replace it with other axioms, this leads to other types of geometry, some of which better describe our universe in the large scale! The truths of Euclidean geometry are still true in their domain though.
So you can view this as an extreme multiverse claim: there is some infinite,varied network of "axioms" and dependent truths. Restating a core point: I think the physical universe is one of these.
Some rules are more basic than others though. The natural numbers seem to spring up almost anywhere, as long as you have a notion of one thing succeeding another, you can find them in another abstract rule system. The natural numbers are a Form that is easy to instantiate or simulate in other Forms.
An example of simulation is that of a computer. Fundamentally, the electricity in the silicon chip of a computer obeys the same laws as lightning striking a sand dune. The difference between them is that the constraints in how electricity can flow in a chip correspond to a set of rules in the realm of Form. We might refer to these as "Boolean logic" or something4. The rules of another world have been instantiated in our own, by carefully constraining how the rules of our world can act (one may compare Turing universality here).
This is where the power of simulation lies. We can implement a computer with more than silicon chips and transistors. They can also be implemented with RNA and ATP, with pool balls, or in Minecraft. The key feature here is correspondence: there is some correspondence between the rules characterizing one system and another. A computer based on pool balls uses the laws of Newtonian mechanics to instantiate the laws of Boolean logic. This also raises another point: simulations don't need to be perfect. If you really tried to build a pool ball computer, you would find the computation breaks down after about 40 logical operations due to the uncontrollable influence of tidal forces from the gravitation of distant stars (yes, actually).
But why can the Forms be observed at all?
Some Forms support Life
One old idea is that of the difference between the world of Being and Becoming. Being is static, it's where unchanging things like the numbers live. On the other hand, we are incarnated in the world of becoming, which is ever-changing. A misconception is that only the former corresponds to the world of Form. In fact, Forms are perfectly capable of being in flux, the mathematical study of these Forms is called "dynamical systems theory" and covers many popular concepts like chaos and control. Put another way, these are Forms that have some notion of time or change.
So in this great world of Forms, some have a process by which they evolve and change. Furthermore, some are organized so that parts of them can maintain themselves and copy themselves.
I'm not going to define life here - capacity for self-replication seems important, but I don't think I could reasonably say an adaptive creature that maintains itself without copying itself is not alive. The origin and nature of life is unquestionably a hard problem (but one that is generally amenable to scientific methods).
Something we can say with certainty: there seem to be rules that allow self-replicating beings which grow in complexity over time. The rules of our world are one case. So some rules exist which produce beings capable of maintaining themselves over time. Interestingly, this observation could actually lead to a testable metaphysical claim: if there are many possible rule-sets that can support living beings, we might expect ourselves to occur in a simpler one5! The existence of Forms that self-replicate provides the basis for objects in the realm of Forms to describe the realm of Forms (as I, a Form, am doing now).
Unknown to many, there has been significant work on the rules of self-replication. In 1944, the great John von Neumann worked out many of the rules from first principles and came to an important conclusion: to copy itself, something needs a coded representation of itself and the tools to build what is represented. The central dogma of molecular biology was first stated in 1957: DNA blueprints represent proteins, which produce and copy DNA blueprints and protein. An interesting modern approach to self-replication can be seen through the lens of constructor theory, for example in Chiara Marletto's work. The duality between self and self-representation is still present.
I think self-representation, in addition to being critical for life, is critical for the mental substance or "consciousness".
The Classic Hard Problem
Returning to the notion of simulation, another point worth considering is representation. Consider triangles. By my belief, a given triangle consists of a given Form. There are many ways we can represent this single Form. We can draw it on paper (a lower fidelity simulation). We can describe it by a list of angles. We can write a computer program that represents this triangle (things get messy with real numbers here, but still it is representable). We can describe it symbolically with a few equations. That is, instantiating a given triangle can be done via a few routes. So a representation is one particular way a Form can be instantiated within another Form. A triangle does not engage in self-representation though. The processes of (at least) animal brains do engage in self-representation. I think self-representation is the core feature of consciousness and that self-representing Forms are a particularly interesting variety.
A physical instantiation of a Form (a simulation) is always a representation of that form. Forms that engage in self-representation are unique in that regardless of their physical instantiation (representations) they always contain another representation of themselves (by definition). I think this IS subjective experience. A triangle Form can only be accessed via representations of it, but because self-representing Forms always have their own representation, they are directly experienced.
One point of clarification here is that "self-representation" is not easy to define. For example, a computer can have a blueprint of its construction or functioning stored on it, which is certainly a self-representation, but I don't think this type of self-representation reasonably entails consciousness. I do have some ideas about what "non-trivial" self-representation that does entail consciousness is, unfortunately these ideas fall into the class of knowledge that is practical in the real-world, which I've been trying to avoid here. Suffice to say, a key part is that the self-representation has causal power.
Another clarification I want to make: this "non-trivial" self-representation is present in all living beings, even bacteria6. It's much more basic than commonly used notions of self-awareness like "recognizing that you have a mark painted on you in the mirror" (which I think relates more to social self-awareness than true self-awareness, which is quite essential to living beings in my view).
What are some claims of this belief on consciousness and self-representing Forms? One is that the physical structure of brains can indeed be responsible for our consciousness, which nicely agrees with such observations like "electrical stimulation of the claustrum leads to disruption of consciousness"7 or "electrical stimulation of the premotor cortex shuts down awareness of voluntary actions". Additionally, by this argument based on Forms, any simulation of the brain should also produce the same conscious experience! After all, it's a correspondence between a physical Form and a self-representing Form.
In this way, I do believe in "souls". They are the self-representing Forms, and they are indeed immaterial (as they are not physical, even if they are typically physically instantiated).
Ideas about consciousness always start with properties of consciousness (real or perceived) and try to explain consciousness based on these properties. Some common ones that get emphasized are its "unity", its "self-representation", its "ineffability" etc. I'm not convinced that any property other than self-representation is fundamental to consciousness. Self-representation, in addition to being the method by which consciousness talks about itself at all, is the strangest property we can imagine a non-conscious agent to have. Here I mean p-zombies. It's not that strange to imagine a non-conscious being who can paint a house or give directions. It is VERY strange for a non-conscious being to start referring to it's own subjective experience or its own consciousness8 i.e. self-representation.
Note this is not a true "solution" to the hard problem of consciousness. I basically said "it is what is". I am okay with this. Nonetheless, it does provide some important claims. Beings in our universe and in an identical simulation of it should have identical subjective experience (down to the flavor of their qualia) because they are instantiating the same Form. If one self-representing Form is an elaboration on another we should expect the shared elements to be identical (aka: in this belief system, my red really is your red due to our mostly identical brains, barring any opsin mutations that really change one of photoreceptor's preferred frequency tuning).
I believe in punctuation outside of quotations when it is not part of the quotation.
I emphasize subjective experience because it is the most unique characteristic of mental substance.
Heaviside, Gibbs, and Hertz summarized Maxwell’s equations to the four we know and love today, Maxwell himself had reduced 20 seperate equations to 8.
A great article on what it means for a computation to be physically instantiated is this one. Boltzmann brains BTFO. I don’t go into counterfactuality here but it is also important in the idea of simulation, the article covers it in detail.
But Occam’s razor is not law…
This article may give you an idea of why this is (though technically speaking, it’s not about the ways bacteria represent things). Staring at this article hard enough may hint at what non-trivial self-represenation consists of.
btw the claustrum is a brain region involved in self-representation that contains a little map of the rest of the brain, ain't that quackin' crazy? it also has the highest density of 5-HT2A receptors, the ones targeted by psychedelic drugs
This inevitably leads to the question "are large-language models conscious?". My answer is (a very slightly uncertain) no, they seem to consistently fail at tasks involving self-representation that aren't well-represented in their training set. As you may guess, I'm almost certain future ML systems will circumvent this issue and engage in genuine self-representation.