Cycle Between Learning Critical Fallibilism and Its Prerequisites

Summary: If you want to be a great philosopher, you’ll need to get really good at a bunch of prerequisites. But don’t just study one prerequisite at a time until you finish it. Instead, you should cycle back and forth between learning prerequisites and learning the more advanced knowledge that they come before. I explain how prerequisites work using a simple point-based model. I also discuss the importance of using new knowledge for your end goals to test it out.

Critical Fallibilism (CF) philosophy learning can be divided into three big areas. There’s CF philosophy itself (which deals with issues like how to think and learn effectively) and two types of prerequisites: life skills and intellectual knowledge.

Life skills include things like time management, dealing with your emotions, handling failure, resolving conflicts with your subconscious, setting goals, prioritization, and managing habits. If you’re doing poorly at these, it will be hard to learn other stuff, especially something pretty complicated, advanced and non-mainstream like CF.

Intellectual knowledge which CF builds on includes math and language. Those topics have relevant sub-topics like arithmetic, logic operators, grammar and reading comprehension. They also have sub-topics that CF doesn’t build on, like calculus and poetry.

Learning the ideas of Karl Popper, Ayn Rand and Eli Goldratt could be categorized as part of CF philosophy or as advanced intellectual prerequisites. There’s often flexibility for how to categorize things; just make your categorizations reasonable and useful.

You should go back and forth between working on prerequisites and CF. Each time you improve your prerequisites, it’ll enable you to improve your CF knowledge. Using new prerequisite knowledge to get better at CF will let you see your progress, stay motivated, and see that the way you’re doing prerequisites is effective.

Also, each time your improve your CF knowledge, it may let you understand some prerequisites in a deeper, better way.

You don’t need to thoroughly learn each prerequisite, finish it, and then move on to the next topic until you work your way up to CF. Don’t try to do that. That approach is bad. Instead, it’s important to flexibly switch between multiple topics, at different levels, in an ongoing way.

When you make a mistake, you should investigate the cause of the mistake. Often, mistakes are caused by mistakes in prerequisite knowledge, rather than being isolated issues. So when something goes wrong, that’s often a good reminder to review and improve some prerequisites.

Note: The concepts in this article apply for learning other things besides CF. They’re generic. I’ll use CF as a recurring example for the more advanced knowledge that has prerequisites.

Point System Model

I’ll explain prerequisites using a simplified point system model. When you first find CF, let’s say your prerequisites are at an average score of 40 on a 0-100 scale. 100 represents the highest skill people currently have and 0 is total ignorance. We could score each prerequisite separately to be more precise but we don’t need to right now.

40 skill at CF’s prerequisites limits your maximum CF skill to 40. So the prerequisites are needed for CF. But you don’t have to, and shouldn’t try to, reach 100 skill on the prerequisites before going above 0 skill at CF.

Your 40 skill at prerequisites lets you quickly and easily reach 15 skill at CF. When you work on prerequisites again and get up to 45 skill, then you can go back to CF and easily get up to 20, then you can get your prerequisites to 50, then CF to 25.

Your skill at CF will lag behind your skill at the prerequisites. Whenever you try to push near a maximum limit, things get harder and take more work. The more points your skill is behind its prerequisites, the easier it is to improve. If your CF skill is 30 points behind your prerequisites, it’s easy to improve, but if it’s only 5 points behind then it’s hard to make progress on CF.

If you want to get your CF skill to 40, then it’s technically possible with 40 skill at prerequisites, but that’s a bad idea. The best way is to increase your prerequisite skill to 60+ first so it won’t be very hard. It’s better to learn your 40th skill point of CF in an easy way than a hard way. You learn the same thing either way, but if it’s easy then you save effort. Having your skill level lag behind your prerequisites is efficient and reduces your error rate.

As you approach 100 skill at your prerequisites, progress will slow down and you’ll face diminishing returns on your effort. This follows the principle that as you approach a maximum limit, things get harder. Then it’ll make sense to push your CF skill closer to your prerequisite skill level. If you’re at 90 on prerequisites and 70 on CF, it’s easier to gain a CF point than a prerequisites point (CF is 20 away from a maximum limit, while the prerequisites are only 10 away).

At low scores you might leave your CF skill behind your prerequisites by 25+, but at medium scores a gap of 20 or less becomes better, and at high scores you could eventually get the gap very low. If you’re stuck at 98 prerequisites for a long time, you’d definitely want to push your CF skill over 90, and possibly even to 96 or 97.

Also, when you’re near the maximum, creating new knowledge may have a similar difficulty to learning the last remaining existing knowledge. Creating new knowledge can be thought of as pushing your score past the maximum (getting your score over 100), but you can start doing that when you’re near the maximum rather than having to wait until you’re actually at the maximum. You could be missing 3 points of knowledge, but create 5 points of new knowledge, for a total score of 102, even though you’re still missing a few things. When your score is low, creating new knowledge tends to be much harder than learning existing knowledge, and there are other problems with developing new ideas when you don’t know much. But at high scores (90+) creating new knowledge becomes more of a realistic option to consider.

Can you work on CF even though you still have a lot to learn about prerequisites? Yes. If your prerequisites are at 0 skill level, then you can’t work on CF. But you don’t need to get them to 100 skill level. They can be somewhere in the middle (no doubt, if you’re reading this, they already are) and then you can get started on CF.

This score system model uses several approximations. Don’t think of it as exactly correct. But it’s still useful.

Cycle Between Topics

If you’re actively making progress on CF stuff, you shouldn’t go a month without working on CF philosophy, on life skills prerequisites, or on intellectual prerequisites. None of those big areas should be neglected for over 30 days in a row. (This guideline is meant to prevent some actual problems that I’ve seen people have; it’s based on experience in addition to abstract concepts.)

When you first found CF, you understood and liked some parts of it. Otherwise you wouldn’t be trying to learn it. In other words, your prerequisites were already good enough to get started on CF. E.g. your prerequisites were at 40 and you found CF and learned it up to 15.

During that initial CF learning (going 0 to 15), it’s OK not to work on prerequisites at all. Since your CF skill started at 0, it needs to catch up to get closer to your prerequisite skill level. As long as you’re making easy, efficient progress, keep going. But when you start having difficulties learning CF, that means your CF skill is caught up to what’s easy to reach given your current prerequisites. Then it’s time to start cycling between studying CF and studying prerequisites.

You can also do the catch up phase on some topics – where you learn a bunch of CF at once based on preexisting prerequisites – then start cycling and improving relevant prerequisites. Then you’re saving some catching up on other topics for later. The catch up doesn’t have to be done all at once to cover everything, and realistically it won’t be. Viewing it as a single phase is an approximation.

One benefit of going back and forth is it helps you accurately identify what the prerequisites are. When you run into a difficulty at a CF task, that means there is some underlying knowledge you don’t have which would make it easier (none of the CF ideas inherently have to be very hard – in other words, there’s no CF idea that is hard for everyone regardless of their background knowledge). You can work on CF until you encounter a problem, then work on your underlying knowledge to help solve that problem. This keeps your prerequisite work relevant. While some math is relevant to CF, some isn’t, and going back and forth can help you understand which math is actually relevant to making CF progress. Or when learning grammar, you can learn the very basics first (like what a “noun” or “clause” is) and pretty safely assume it’ll be relevant. But then you should look at what will actually help you do better text analysis, not just learn anything about grammar.

Approximations

Let’s discuss some ways the point system is only approximate.

Prerequisites actually come in layers. You learn A to enable learning B to enable learning C to enable learning D. Your skill at each layer puts an (approximate) maximum on the next layer. Your B skill can’t exceed your skill at A. Your C skill can’t exceed your skill at B. And so on. But the more layers you use in your model, the smaller the point losses you get between layers, because the layers are closer together and more similar. So instead of skill levels of 40 and 15, you might model it with four layers as 40, 35, 25 and 15. The total gap from the start to the end is the same as before – adding more layers to your model shouldn’t change that.

CF has many different parts which could be scored separately. You might learn one part until you reach difficulties, then learn a few other parts before beginning prerequisites. You can have different skill levels at different parts of CF. And different parts of CF can build on different prerequisites.

There are many different prerequisite skills which could be scored separately. You might be better at math than language or vice versa. Within math, you might be better at arithmetic than algebra. Within arithmetic, you might be better at subtraction than exponentiation. When you’re learning CF, you have to pay attention to how hard different things are – how slow your progress is, how many errors you make, how confusing it is – to judge how good your prerequisites are for that part of CF. You can also directly evaluate your knowledge of a particular prerequisite, e.g. by doing practice activities then checking your work for errors.

There are multiple ways to build up to the same knowledge. Most conceivable or random ways are bad, but more than one way is reasonable and effective. This provides workarounds: you can often skip a specific prerequisite skill, e.g. algebra, and find some other way to learn something without it.

As you make progress, if you use many workarounds to avoid algebra, it’ll start becoming more inconvenient. It’s unrealistic to be a great CF philosopher without learning algebra at some point. But it’s OK to delay learning a prerequisite for a while if you find it problematic. Learning some other stuff first may help make it easier. And for less general purpose skills, some of them are more permanently optional – they could be useful but you could be great without ever learning them. Algebra is basically too useful to be optional in the long run, but some other stuff could be a prerequisite you build on but is also genuinely optional.

(Note: Algebra classes commonly teach quadratics, but that’s not a core part of algebra and shouldn’t be taught to most high school kids at all. Quadratics aren’t relevant for CF. More core parts of algebra, that are more relevant to CF, include understanding variables, equations, substitution, grouping and functions.)

It’s also problematic to work around too many different topics at once. Trying to learn something while working around a dozen missing prerequisites is usually a bad idea, although not always. If all the missing prerequisites are related to math, then it can be viewed as only one missing prerequisite (math), which might be manageable even though the missing thing is a big, broad area. Having a dozen independent, unrelated, missing prerequisites is much worse.

For an example of an optional prerequisite, I know a lot about speed running video games. This is useful knowledge which provides examples of how practice, automatization, mastery and learning work. Many speed runners successfully learn to play games at very high skill levels which is interesting. But someone else could match or exceed my philosophy skill level without knowing anything about speed running. Similarly, I know a lot about chess, which is useful but optional. Someone else who didn’t know about chess, but reached my philosophy skill level, would probably know some other stuff that I don’t. There are many useful but optional topics that I don’t know about. Everyone should learn about some optional topics but which ones is basically up to personal taste. By contrast, I’d recommend that everyone learn arithmetic before they expect to be an advanced (or probably even intermediate) philosopher (but you can skip math and still get started on some philosophy because philosophy is more based on language skills than math skills).

Using What You Learn

Basically, each time you learn a chunk of prerequisite skill meant to help support CF knowledge, you should also do a CF activity where you use it, to see if it actually helps with its intended purpose. Try stuff out and see if they’re useful for you. If you don’t find something useful, then something is going wrong.

Studying prerequisite skills should be aimed to solve problems you’re having with higher level topics. After some study, you should actually make progress on some higher level problems.

But what if there are layers? Suppose you’re learning A to help with B to help with C, and C is meant to help with CF. You can take your new chunk of A knowledge and do a B-related activity to try it out. And you can try a CF activity and see if somehow you’re a little better at it. But it’s hard to directly connect A to CF. The more layers are in between, the harder it is to check whether something is useful for the final layer.

You can work your way up through the layers. Your new A knowledge helps you do a B-related task. Then you’re better at B, so you can do a C-related task better. Then you’re better at C, so you can do a CF-related task better.

You could try to find a CF task that uses C which uses B which uses A, and do it all as one test. However, not all C-related tasks use much B, and not all B-related tasks use much A. So it can be hard to find a chain where A, B and C are all key issues. If some layers focus more on some other skills, that’ll distract from what you’re trying to test.

There’s no really easy solution for this. Managing complexity with many layers is hard. If you can automatize the lower layers so they take very little attention, that helps. But people working on CF often need to improve some more basic skills, many layers down, because they initially learned those skills to normal quality standards (which are lower than CF uses). E.g. the way people think about arithmetic, algebra or grammar is good enough to pass school tests but not good enough to build up to advanced philosophy. Improving those basic skills to atypically high quality standards is relevant to CF even though it’s many layers separated from CF. Going through and improving every layer may be needed, but waiting to finish that process before seeing high level results is problematic.

Sometimes you can find a practice task where there’s a more direct connection. The number of layers between things is variable depending on what you’re doing. You can often skip some steps. Learned some grammar? You can connect that to CF via text analysis and maybe not worry about other layers much. Learned about substitution and variables in algebra? You could apply that pretty directly to text analysis too, or relate it to trees or to integrating concepts. Finding a relevant connection with only a few layers involved is often a good approach for checking that your prerequisite knowledge is actually helping you with CF philosophy.

On the other hand, for building up your knowledge to CF, having lots of small, thin layers is good. Learn lots of little chunks. Do lots of little, gradual steps. But this same knowledge can be viewed and used with fewer layers when you want to. Flexibility on how you look at layers is important. It’s the same basic issue as zooming in and out on trees, or collapsing some nodes within a tree, or (temporarily) substituting summaries for some groups of nodes in a tree. When you want to build on an idea and learn the next thing, zoom in to a higher detail level. When you want to connect what you learned to high level CF ideas and test that it’s useful, zoom out.

Automatization

Some people think the need for practice, automatization and mastery and improving their subconscious means they have to finish learning things before moving on (which is true in some sense). How can cycling between topics be compatible with subconscious automatization? You shouldn’t practice and automatize unfinished knowledge that you’re going to revise again tomorrow or next week.

The basic solution is to practice, automatize and master small chunks. You can finish learning a small chunk before moving on. If you divide your learning up into chunks that can be finished in under a week, then you can cycle between three major areas in less than a month.

You should be able to finish some small chunks within a day. In that case, you can do multiple chunks before switching topics. You can also go back and forth between CF and prerequisites more frequently, but you don’t have to. Making sure to go back and forth at least every month is just an upper limit to prevent some big problems. Going back and forth in a day or week can be good. That needs to be flexible (time to learn chunks can vary) and personalized for what works for you and the topics you’re currently studying. I can tell everyone (who is actively learning CF and is isn’t currently catching their CF skill up based on their preexisting prerequisite skills) that going a month without cycling is too long, but I can’t tell everyone a specific schedule. There isn’t a one-size-fits-all optimal schedule, but there are people who avoid either philosophy or prerequisites for months at time, which is bad.

You can also do initial learning on a prerequisite – where you learn something consciously – then cycle to working on philosophy and try it out using conscious effort. In this case, you’re dividing learning something into two separate parts (conscious and subconscious learning) which can be finished separately. Then, after confirming it’s useful for your high level philosophy goals, you can cycle back to the prerequisite and practice it in order to subconsciously automate it. Then you can cycle back to philosophy and try it again to check if those subconscious automatizations are working as intended. If it’s a burden on your conscious attention, then the automatizations aren’t done. You can practice them more, or you can try doing the next few layers.

Unfinished skills limit how many more layers you can learn, but working on just the next couple layers often helps finish automatizing a skill. It’s common to get something automatized well, so the conscious attention required is low, but only automatized extremely well (so the conscious attention it uses is very tiny) later after building some more layers on it and getting experience using it for real (not just in practice). Building additional layers and using a skill in your other work lead to additional practice and sometimes to additional understanding as you connect it with other topics more. In other words, you should often do some cycling between a layer of knowledge and the next few layers before and after it, rather than trying to 100% finish each layer of knowledge before doing any work on the next layer. One way to do this is by having a succession of sub-goals, so you can cycle after completing a goal which isn’t the final goal for that chunk.

Conclusion

People commonly interpret prerequisites as requirements that they must finish before doing something. But when the prerequisites are fairly big and complicated, you should partially finish them (in other words, finish one or more sub-parts), then work on some later layers of knowledge. Go back and forth between prerequisites and the knowledge you’re building on them. You should regularly revisit the highest layer (your final goal like learning CF philosophy) and apply things you learned to that layer to test them out and see if they actually help. You can also go back and forth between what you’re learning and adjacent layers.

Prerequisites set a maximum skill level for what comes after them. To a good approximation, you can’t be better at something than you are at the knowledge you used as foundations for it. You should revisit prerequisites when they’re causing errors or slowing progress at what you’re trying to do. You should mostly do this in a targeted way, focusing on relevant stuff that you can quickly use and see benefits from (or see that it’s not working, so you can quickly recognize and correct the problem).

This approach to prerequisites can help you use my video An Organized Plan for Learning Philosophy (explained with a tree diagram).

PS Some of this article is related to “spiral learning” and other concepts from the book Understanding Objectivism by Leonard Peikoff.