1.4 Two philosophical methods

1.4.1 Philosophy consists of updating the highest-level concepts of the mind. As discussed above, this 'updating' process can ultimately involve anything in the mind. That said, when undertaking philosophy as an intentional project, we can distinguish two methods. These are not opposed strategies, but complements; doing philosophy well may require both.

• 1.4.1.1 Firstly, we can try to draw out connections among existing concepts, showing, e.g., that they contradict each other, or that two seemingly different concepts can be unified. This is what is usually called 'philosophy'.
• 1.4.1.2 Secondly, we can can learn things, or have experiences, which are especially likely to help with the updating of the highest-level concepts.
  • 1.4.1.2.1 Learning new things can be useful for several reasons. They could refute an existing high-level concept; they could suggest a common pattern; or they could give a model for how to compress ones' existing knowledge, even if this was already possible earlier.

1.4.2 If we are aiming to follow the second strategy, what sort of experiences or concepts are most useful to have? This is a difficult thing to determine since our goal is to update the highest-level concepts, so we can't choose on the basis of a yet-higher concept.

• 1.4.2.1 Given this, one strategy might be to study the areas which we are currently maximally uncertain about. Another might be to try to learn as many novel ideas as possible.
• 1.4.2.2 But we should not choose the above areas or ideas purely at random; rather, the areas should be chosen based on how near they are to our current conceptions of the highest-level notions of reality, goodness, etc.

1.4.3 Given the prominence of science and mathematics in determining our world-view, studying these areas seems like a natural choice. This will be the strategy we pursue here. Thus it seems worth saying a bit about how I think the epistemic process works in these domains.

1.5 Math & Science: flywheels of modernity

1.5.1 Modernity has seen an explosion of our scientific and mathematical knowledge. The core mechanism behind this can be described as follows: virtuous feedback loops between conceptual progress and empirical/calculational flywheels.

1.5.2 What is a empirical/calculational flywheel? By this I mean a set of well-defined procedures and technologies which enable one to pose precise questions and problems about some aspect of physical or mathematical reality.

• 1.5.2.1 As an example, in astronomy sextants enable precise records of the position of objects in the sky. This allowed Tycho Brahe to record the motion of the planets and led to Kepler's laws.
• 1.5.2.2 In biology, empirical flywheels include Mendelian breeding experiments. Fields can also provide empirical tools to be used in another, as in the X-Ray diffraction experiments which revealed the structure of DNA.
• 1.5.2.3 In mathematics, the distinction between "empirical" and "conceptual" research is not as clear. Roughly speaking, explicit calculations and proofs using a given set of definitions could be considered a "calculational flywheel".

1.5.3 The full process of science consists of an alternation between discovery/work within one of these flywheels, and developing new high-level concepts on the basis of the results obtained from doing this. These new concepts in turn suggest new ideas for experimental paradigms, technologies, and calculational techniques.

• 1.5.3.1 These feedback loops are themselves enmeshed in larger loops of engineering technology, political change, etc. which define modernity in full.

1.5.4 Notably, the concepts discovered in the course of investigating a given flywheel can be surprising. The process of investigation takes on a life of its own and shows you things you didn't know would be there.

• 1.5.4.1 An obvious example is quantum mechanics, a theory whose conceptual interpretation is still not clear to this day, despite being ubiquitously and successfully applied. QM was initially as a solution to technical problems in the theory of radiation.
• 1.5.4.2 It might seem that this would be less the case in mathematics. But in fact calculations are constantly giving rise to surprising results that naturally suggest radical new concepts. Take complex numbers. It's natural to try to find roots of cubic and higher order equations: this leads to the introduction of the imaginary unit i. Extending differentiability to this new number system gives rise to the amazingly rich holomorphic functions.
  • 1.5.4.2.1 Mathematicians' sense of the richness of an area largely consists of the extent to which investigating it tends to lead to surprising new concepts "naturally" coming up in the course of an investigation.

1.5.5 These examples suggest to me the mental image: when investigating, do not merely doggedly pursue the answer(but do pursue it, to be clear). When stuck, let the phenomena take you by the hand and guide you to the correct concepts.

1.5.6 The above "virtuous circle" between conceptual analysis and experimentation bears some resemblance to my description of ideal philosophy. Indeed, I think the activities are similar.

1.5.7 My project in this text is to attempt to do philosophy -- that is develop new concepts describing very high-level structures of the world, and our existence within it -- by examining the mathematical structures discovered by physicists.

• 1.5.7.1 Relative to this lofty goal, I have only really succeeded at producing a sketch of some concepts which might be a useful description of the world.
• 1.5.7.2 As a secondary goal, I wish to introduce some new "flywheels" that might be especially productive in generating new concepts in this area.

1.6* The Usefulness of Philosophy

1.6.0 You might be thinking: "That's all well and good, but who cares about having good high-level concepts? Isn't it basically useless? Philosophers aren't exactly super effective at getting stuff done in the world."

• 1.6.0.1 (If you're not thinking that feel free to skip to the next section where I actually start talking about physics)

1.6.1 I think that having good high-level concepts can be very impactful. In slogan form: "philosophy helps you choose a good direction to move in; doing a good job at moving in a direction depends on attention to detail and work ethic. But a good direction can be very impactful".

1.6.2 Let's consider some examples.

• 1.6.2.1 The nature of the mind. Materialism posits that the mind is instantiated by processes in the brain; combined with the Church-Turing thesis, this implies that making an artificial mind that runs on a computer should be possible. Thinking through the consequences of this naturally implies that AI development is a very impactful area to study. These considerations motivated people to work in AI decades before LLM-like systems made it obvious that such a thing is possible.
• 1.6.2.2 The nature of political power. European societies in early modernity believed that political authority was held by royalty, derived from natural law or divine sanction. Social contract theory instead viewed political power as the result of an explicit or implicit negotiation between people; this contributed to the revolutions in Europe and America in 17th-19th centuries.
• 1.6.2.3 The nature of money. From where does money derive its value? One answer: it is an arbitrary yet consistent fixed-point in valuing-space, emergently useful for coordination. This -- in contrast to other answers such as that money's value derives from the state -- reveals that something like bitcoin should be possible.

1.6.3 Good highest-level concepts are not so different from low-level concepts in this regard; both should enable better understanding of, and action in, the world.

1.6.4 Can the world be fully grasped through concepts? Can we fully analyze the redness of red, the feeling of a late-summer breeze, yearning and nostalgia? Or even what it's like to go swimming, or fix an old bike, or use a word processor? Perhaps not.

1.6.5 And yet, taking a step back, I often find it remarkable how well abstractions I read and pondered out of intellectual curiosity, have turned out to describe in miniature the great arc of history, the pattern of peoples' lives, real opportunities and tragedies.

1.6.6 Thus I adopt philosophical analysis not as a game, but out of belief that the world rewards careful attention to its structure and the conviction to act upon it.

• 1.6.6.1 In particular: as mentioned in the introduction, I believe that AGI might come soon. If this is the case, a theory of abstraction and the mind could be key to influencing its trajectory. I believe that the ideas outlined here are very promising as paths to such a theory.