Justin Attempts to Understand Part of “The Fabric of Reality”, Part 2

This post is part 2 of my attempt to understand the discussion of Godel’s incompleteness theorem presented in The Fabric of Reality by David Deutsch (DD). See Part 1 here.

Below is a summary of what I thought the relevant parts of Chapter 10 were. I included a big chunk of the beginning of the chapter cuz it seemed like relevant context to understand the problem situation Godel was facing.

David looks back on his discussion of Cantgotu environments and asks:

I have said that there exist infinitely many [Cantgotu environments] for every environment that can be rendered. But what does it mean to say that such environments ‘exist’? If they do not exist in reality, or even in virtual reality, where do they exist?

DD asks whether abstract, non-physical entities like numbers & laws of physics exist. He wants to distinguish things that have an independent existence vs. things that are features of our culture, arbitrary, etc.

DD says if we want to know whether a given abstraction exists, we should ask whether it “kicks back” in a complex, autonomous way. He talks about natural numbers as an example. We came up with them as an abstract way of expressing “successive amounts of a discrete quantity.” But after we made them, it turns out they have all these properties we have to figure out (like characteristics of the distribution of prime numbers.)

Since we cannot understand them either as being part of ourselves or as being part of something else that we already understand, but we can understand them as independent entities, we must conclude that they are real, independent entities.

DD says abstract entities are intangible and don’t literally kick back. He says proofs play the role in maths experiment and observation plays in science, and says that mathematicians are big on thinking proofs are absolutely certain.

DD talks some about Pythagoras and Plato. Pythagoras thought regularities in nature were expressions of mathematical relationships in natural numbers. Plato thought the physical world wasn’t real and thought things we experience in our world were reflections from the world of Forms (the Forms including numbers like 1,2,3, mathematical operations etc.) DD also mentions Plato’s theory of in-born knowledge.

DD says that mathematicians agree “mathematical intuition” is a source of absolute certainty, but then disagree about what mathematical intuition tells them, heh. He gives the example of imaginary numbers. There were proofs about real numbers that involved imaginary numbers, and some mathematicians objected because they said imaginary numbers weren’t real. Good example.

DD talks about a crisis in mathematics. Aristotle had figured out the laws of logic and syllogisms, and said that all valid proofs could be expressed as syllogisms. He hadn’t proved this though. And DD says the crisis was modern mathematical proofs weren’t expressed syllogistically and involved tools outside the classical logic rules. So this proved that Aristotle’s rules were inadequate. And people were worried that maybe the new stuff wasn’t absolutely certain.

DD talks about responses to this crisis. One was intuitionism, which tries to construct intuition in a super narrow way only based on supposedly unchallengeable, self-evident aspects. This leads to them denying infinite sets.

DD says intuitionism had some value (like inductivism) in that it dared to question some received certainties. But it ultimately involved retreating into an inner world/domain that actually makes explanation of even that inner domain harder. E.g. intuitionists deny infinities. So there must be finite natural numbers. How many? And then why can’t you form an intuition about the next natural number above that one? Intuitionists reply to this by denying logic, specifically the law of the excluded middle, which says there’s no third possibility between a given proposition and its negation.

DD says:

…by severing the link between their version of the abstract ‘natural numbers’ and the intuitions that those numbers were originally intended to formalize, intuitionists have also denied themselves the usual explanatory structure through which natural numbers are understood. This raises a problem for anyone who prefers explanations to unexplained complications. Instead of solving that problem by providing an alternative or deeper explanatory structure for the natural numbers, intuitionism does exactly what the Inquisition did, and what solipsists do: it retreats still further from explanation. It introduces further unexplained complications (in this case the denial of the law of the excluded middle) whose only purpose is to allow intuitionists to behave as if their opponents’ explanation were true, while drawing no conclusions about reality from this.

DD then turns to Godel:

Thirty-one years later, Kurt Godel revolutionized proof theory with a root-and- branch refutation from which the mathematical and philosophical worlds are still reeling: […] Godel proved first that any set of rules of inference that is capable of correctly validating even the proofs of ordinary arithmetic could never validate a proof of its own consistency. […] Second, Godel proved that if a set of rules of inference in some (sufficiently rich) branch of mathematics is consistent (whether provably so or not), then within that branch of mathematics there must exist valid methods of proof that those rules fail to designate as valid. This is called Godel’s incompleteness theorem. To prove his theorems, Godel used a remarkable extension of the Cantor ‘diagonal argument’ that I mentioned in Chapter 6. He began by considering any consistent set of rules of inference. Then he showed how to construct a proposition which could neither be proved nor disproved under those rules. Then he proved that that proposition would be true.

So basically Godel showed that we can have no fixed way of knowing if a mathematical proposition is true.

Skipping ahead some in the chapter…

DD says one of Godel’s assumptions was that a proof can have only a finite number of steps. DD says this is correct as far as we know according to quantum theory.

DD says Godel inherited Greek conception that a proof was a particular type of object (a sequence of statements that obey rules of inference.) But really it’s better thought of as a process. He says that with the “classical theory of proof or computation” this distinction isn’t hugely significant because you can just make a record of the process and therefore have a proof “object”. But with quantum computer calculations lots of stuff is happening in other universes so you can’t record all that stuff. And this shows that the old traditional mathematical method of trying to have totally certain stuff by stripping away every source of ambiguity and error isn’t viable.

In the next part I’ll try and sum up.

Justin Attempts to Understand Part of “The Fabric of Reality”, Part 1

This post is part of my attempt to understand the discussion of Godel’s incompleteness theorem presented in The Fabric of Reality by David Deutsch (DD).

See part 2 here

In Chapter 10 of The Fabric of Reality, DD says:

Godel proved that if a set of rules of inference in some (sufficiently rich) branch of mathematics is consistent (whether provably so or not), then within that branch of mathematics there must exist valid methods of proof that those rules fail to designate as valid. This is called Godel’s incompleteness theorem. To prove his theorems, Godel used a remarkable extension of the Cantor ‘diagonal argument’ that I mentioned in Chapter 6. He began by considering any consistent set of rules of inference. Then he showed how to construct a proposition which could neither be proved nor disproved under those rules. Then he proved that that proposition would be true.

So my attempt to understand DD’s discussion of Godel’s incompleteness theorem will begin with a review of the relevant portion of Chapter 6, presented below:

DD opens the chapter with the question of whether we will be able to build a fully universal virtual reality generator which can render any environment the human mind is capable of experiencing.

DD clarifies that he’s talking about a virtual reality generator which could be programmed to generate all logically possible environments, and not something that would already contain within itself the specific instructions for generating the environment.

DD says we can imagine a virtual reality generator as having an effectively unlimited memory capacity for storing a given VR environment by imagining that it can read any number of disks.

DD says we can’t imagine unlimited computation speed like we can unlimited memory capacity. So what happens if the VR generator can’t render stuff fast enough??

DD says the answer is basically the VR generator would need to be able to control the equivalent of the brain’s “CPU clock” to keep it in sync with what the VR generator can generate. DD notes that this slowing down would be invisible from the user’s perspective within the simulation, though if their brain needs to be slowed down a bunch to make complex environments, more time will elapse in reality.

DD asks if there is anything outside the repertoire of a VR generator.

Would its repertoire be the set of all logically possible environments? It would not. Even this futuristic machine’s repertoire is drastically circumscribed by the mere fact of its being a physical object. It does not even scratch the surface of what is logically possible, as I shall now show.

DD says the basic idea of the argument he will use, which is called the diagonal argument, has had various other applications, like proving that there are infinite quantities greater than the infinity of natural numbers, and to prove Godel’s Incompleteness Theorem.

DD says that each program for the VR generator has to have some particular, quantized set of values for any variables, and therefore “the set of possible programs must be discrete.”

Question: What’s the alternative here? Like what would a non-discrete set of possible programs mean?

DD says each program has to be expressible as a finite sequence of symbols in a computer language.

There are infinitely many such programs, but each one can contain only a finite number of symbols. That is because symbols are physical objects, made of matter in recognizable configurations, and one could not manufacture an infinite number of them.

Question: Is this similar to how there’s an infinite number of books that could be written but a finite length to any given book, cuz books are made up of sequences of letters represented in some physical objects (in ink on pages, or in a hard drive and then displayed on a screen) and you can’t have infinite actual letters?

DD says the requirements he’s been talking about — “that the programs must be quantized, and that each of them must consist of a finite number of symbols and can be executed in a sequence of steps” — are a big deal that “impose drastic restrictions on the repertoire of any physically possible machine.”

DD asks us to imagine the infinite possible programs in an infinitely long list, numbered Program 1, Program 2, etc. You could also list them by VR environment they generate, so it’d be like Environment 1, Environment 2, etc.

DD says programs could vary a lot in how long they run for but let’s “consider only programs that continue to run for ever” to keep his proof simple.

DD says we can call the class of logically possible environments Cantgotu environments. He defines Cantgotu environments in the following way:

For the first subjective minute, a Cantgotu environment behaves differently from Environment 1 (generated by Program 1 of our generator). It does not matter how it does behave, so long as it is, to the user, recognizably different from Environment i. During the second minute it behaves differently from Environment 2 (though it is now allowed to resemble Environment i again). During the third minute, it behaves differently from Environment 3, and so on.

The “and so on” means that it behaves differently than all the Environments on our infinite list of programs the VR generator can run at some point.

Questions: How can we reason about these Cantgotu environments at all? What makes them logically possible? Do they necessarily contradict one or more of the requirements DD mentioned about programs being quantized in a finite number of symbols, etc? So the idea is these are programs which are physically impossible but which we don’t have any criticism of on logical grounds?

DD says that there’s a ton of Cantgotu environments possible, because the only constraint is that during some minute they behave differently than something in the list of programs the VR Generator can run.

DD says his argument shows that we can only run an infinitesimal fraction of the set of all logically possible environments.

Comments on Paths Forward Part 3

Comments on this essay, continued

See part 1 here

See part 2 here

Summary So Far

Human knowledge can make progress in ongoing, public, written discussions which reuse answers where appropriate and never ignore any issues without answering them. Anyone can contribute to these discussions. For topics that are well understood, most bad ideas will already have answers written down.

Being open to discussion is necessary to being a rational person. You can tell if you’re limiting discussion irrationally by whether you personally have paths forward which you take responsibility for. Your paths forward can cover all relevant topics because you can be open to discussion about what is relevant. And this won’t take too much time because any issue either already has an answer or else is worth the time to answer.

To help apply the idea of a path forward in real life situations, let’s consider some examples.

• Suppose I give a vague answer. That’s bad because I have’t really answered the issue. There’s no way for that to lead to progress. All you can do is say it’s vague, say it’s unclear how my answer answers the issue, and ask me to give a better answer. If my statement is bad enough all you can do is ask for a better one, but the discussion doesn’t actually make forward progress, then that isn’t a good path forward.

It’s important to be really forgiving though. If I say something vague, maybe I just don’t know better. Maybe I thought it wasn’t vague for some mistaken reason that I could be corrected about. Or you could even be mistaken that it’s vague.


Something that comes up very frequently is that in making some statement, people assume some context in their head which they don’t actually write down or communicate. And so it comes across as pretty vague if you just read what they wrote and don’t supply your own context for it. And you could imagine two or three different contexts which the person could have in mind regarding their statement, and some answers to those. But its a lot of work to try and cover the waterfront of possible meanings instead of just following up and asking them to specify their context more.

Like if someone on FI said “I dislike capitalism cuz there’s a ton of people that it hurts”, there’s lots of stuff they could mean. They could mean anything from “exploitation of low wage workers” to “encouraging a materialistic consumer culture that harms traditional values and personal happiness” to like 10 million other things. Its uselessly vague as written and you’re not obligated to write a treatise in response to someone’s vagueness. But if they are new to trying to do high quality rational discussions, you should have a default assumption that they are proceeding in good faith and are just not very good at discussing things yet. Which is fine, since that’s a skill they can learn 😀👍

Don’t give up on people just because they make a mistake. Give them the benefit of the doubt.

Yeah 😀

Tell them that being vague (or whatever else) is a problem, and ask if they’d like to try again. Offer them a reference to read that can help them learn to discuss better. Give them a path forward even though they messed up. And by approaching it that way, there’s also a path forward in case actually you’re misjudging the situation.

Good advice.

• Suppose you write a long argument and I reply pointing out one issue, and I don’t read the whole thing. Good or bad?

It’s fine cuz if I address the issue, you can continue engaging with what I wrote with that issue addressed. Here I’m assuming I don’t have to totally rewrite it cuz I made some fundamental mistake. And if I do have to rewrite it over one issue, maybe it wasn’t very good and you have better things to do than read my current mistaken draft.

It’s fine because there’s a path forward. It may be a bad idea to go through all your points in order. If you have good stuff, answer the issue I brought up, then we’ll continue. A path forward can work fine with many small steps, one by one.


Some readers will be objecting that you have to read a whole argument to understand any part of it. But usually you don’t. In the cases where someone reads too little, tell them that the issue they’re raising is answered later. Give them a quote or page number. That’s not very hard. If you do that you’ve answered what they said; if you don’t then you haven’t.

After the issue I point out is resolved, what next? That depends. If you made a big mistake, you may need to revise your whole argument, or even change your conclusion. If I made a mistake, I could continue reading and better understand what it’s saying now that I’ve learned something. If you made a small mistake, like having a confusing sentence, you could just fix that one part, and then I could continue reading to answer other issues you bring up.

If I point out one issue with your ideas, that’s a good test. If you react irrationally, now I know a rational discussion isn’t available.

This is a reason to be direct/blunt/not concerned with politeness rules, as well. People who are easily offended don’t really offer rational discussion. If you violate politeness rules you’ll find this out more quickly.

For discussion to be thoroughly rational, it has to be open-ended, and not have “taboo” topics. And one of the things that “politeness” takes off the table is making certain moral indictments of people you are talking to which people consider to be TOO OFFENSIVE (by saying e.g. that an implication of their worldview is evil and so they have evil views).

Even one issue is important because one issue can potentially ruin the whole thing. If you address the issue or explain why it’s an isolated issue, then your other ideas become issues for me again, and I should continue.

• Suppose I bring up an issue and you don’t answer. You’re silent. That’s bad. There’s no path forward.

You might think you have an answer. But if you don’t give the answer, then no one is going to learn anything. If your answer is so great, write it down once and then provide it when it comes up. Then it will be exposed to public criticism and maybe one day someone will tell you a problem with it. Or people can learn about it and maybe tell you a way to make it even better.

Silence blocks off all the good paths forward like you learning something, me learning something, or both. It’s irrational.

I think that one thing people do is only count stuff as “silence” if they have a intentional, conscious policy to not reply to something the other person said.

If they instead have a vague intent to reply that never gets acted on, they consider that being “busy” instead of being silent.

They could also reply but at such a slow rate and with such low attention that it impedes the discussion from ever reaching a resolution. The fact that they aren’t technically being silent doesn’t stop this approach from sabotaging the discussion all the same.

Or if they lack the knowledge to have an effective discussion for other reasons (like cuz they struggle with understanding English or they lack a ton of common background knowledge) and they continue trying to muddle through badly instead of actually learn the skills they need to have the discussion, that’s another way of sabotaging progress. But hey at least they’re trying, right?! 🙄

• When I read something, often part of it is confusing. This may be my fault or the writer’s fault. It doesn’t really matter. Anyone who is using this as one of their answers is responsible for clarifying. They shouldn’t be using something unclear as an answer. If I ask a clarifying question, that is a path forward. If no one answers, then everyone who uses that material is blocking the path forward and is irrational.

Clarifying questions should be welcomed. They help make answers better. The answer can be updated to be clearer. Then in the future this particular clarifying question won’t be asked. Rather than complaining that clarifying is a lot of work, fix things. If your answer isn’t clear, it’s not very good and you should be happy to improve it. Don’t have low standards for the quality of ideas you’re satisfied with.

A bit of a tangent: it seems like it’d be good if book-writing was more iterative. Before ebooks, putting out a book was kind of a big deal. You had to do a printing and stuff. And people would update books sometimes, correct errors etc, but it’d be years in between updates.

But now ebooks are fairly widely used and it’d be much easier to just push updates to correct errors and clarify stuff. I don’t think that’s super common though. Its interesting. I have apps that seem to get updated every week, but books get updated maybe once a decade…

• Some people say they’re too busy to answer things. But why aren’t there high quality prewritten answers they can refer to and take responsibility for? If you’re too busy to write new answers, so what? Use existing answers. If there aren’t existing answers written down and you’re too busy to write an answer, don’t claim to have an answer. Don’t think, “I know the answer. It’s just not written anywhere and I’m too busy to write it”. If you do that, there’s no path forward, and you’re an irrational person who isn’t open to discussion.

People might already have a refutation of your idea that you haven’t written down. If you were open to discussion, they could tell you. Blocking people from correcting you is incompatible with progress and learning. It’s not a path forward.

• Sometimes I might say, “What you’re talking about conflicts with theme X I read in book Y that I thought was good. What do you think?” Is that a good answer? It doesn’t answer everything and it’s short. But it does provide a path forward. The person can say whether they agree or disagree with X, and why. The discussion can make progress.

It’s fine to have big picture concerns. It’s fine to wonder how an idea connects with some other idea you think matters. It’s fine to bring up ideas that are in books. If the other guy already knows about this issue, he can answer immediately, no problem. If he doesn’t know about this, maybe he should. He should either investigate the issue or explain why he thinks it’s irrelevant. All of these are good outcomes.

How ideas connect with each other is really important.


OTOH one mistake people make is what I’d call an academic approach to ideas, where they look for connections or conflicts between ideas kind of for its own sake, without having a specific problem which they are trying to solve in mind.

So they ask fake questions in which they kind of cargo cult the sort of questions they think someone with a genuine interest/problem might ask.

Some ideas I advocate seem to contradict what people already think they know. I should explain why either it doesn’t actually contradict, or why their thinking is mistaken.

Understanding relationships between ideas helps us understand them better and is a great issue to raise. Discussing those issues is a good path forward.

• Some people say, “I studied this issue, you don’t know anything”. This provides no path forward. What if you studied it and reached a wrong answer? If you learned so much from your studying, then you should already have a really good answer. Share it.

I don’t care that you studied something. I care if your studies led to actual results that you’re willing to contribute to a discussion. If you don’t do that, your studies don’t have a rational path forward.

• Some people say, “I’m a psychiatrist and you’re a philosopher. Some of what you say is irrelevant to my field, and other stuff is mistaken, which you would know if you learned psychiatry.” This statement doesn’t provide any path forward.

Which points are irrelevant, and why? We could discuss relevance. What would I have learned if I studied psychiatry, specifically? Bring up some ideas, provide answers about the topic. It often works well to explain an idea in your field briefly and what it’s consequences are (such as how it wins the argument for you), and then refer people to a book for the details of why that idea is true.

In the context of stuff like the Real Peer Review twitter account, I’ve seen people saying that maybe if you were familiar with the field of [Insert fake left wing field here] then you’d understand the subtle and sophisticated point some journal article is making.

People are massively deferential to BS fields and “expertise” in such fields. And so a lot of the people in them don’t really ever have to engage in critical discussion.

If my points are wrong because I don’t know your field, show me some writing which explains this. Instead of calling me ignorant, refer me to answers. Then I can learn more, or explain mistakes with your answers, or both.

And if you don’t have any pre-written answers that apply to the specific issues I’m raising, then that’s interesting. Why has no one in your field ever answered these issues (in a reusable way)? Improve your field’s literature instead of making irrational excuses to end discussion.

Extended Example: The Busy Intellectual
Some people are super awesome. They’re so smart they get really popular and everyone wants to discuss with them. They’re so flooded with issues, they don’t even have time to refer everyone to pre-written answers. What can they do?

These amazing people need discussion places. Instead of having individual discussions with everyone, there can be group discussion. At the discussion place, many people can give answers. People who partly understand the busy intellectual’s work, and want to learn more, will answer some issues.

If you’re a busy intellectual, and I have an issue with your work, set things up so that I can get an answer at your discussion place. That is a path forward.

It doesn’t matter if you own or created the discussion place. It doesn’t matter if your work is the only topic discussed there. What matters is that all issues actually get answered, and that you take responsibility for this.

The best discussion places are public, online, and use writing. That makes the discussion open to more people, keeps track of what’s said. A great approach is an email discussion list, which handles nested quoting and notifications well, and can keep long discussions organized over time.

How people use quoting plays a big role in whether a discussion place is good. Without quotes, people forget the context of ideas, talk past each other, reply to things that weren’t said, and discuss vaguely.

(If you’re interested in learning at a good discussion place, you should join the Fallible Ideas Discussion Group.)

Good discussion places also do not moderate (block) contributions for “low quality”, or for much of anything besides being automated non-human spam. Moderation policies are a way to keep some ideas out of the discussion, without answering them, even though those ideas could be correct. Moderation prevents some ideas from being discussed and answered. It’s irrational (and authoritarian).

The stuff that might get blocked as low quality is stuff people thought was worth writing. It’s part of them. If its crap, they should be able to say it and get criticism about it, instead of being forced into a straightjacket of discussion topics + tone which forces them to misrepresent who they are and what they want to talk about.

Now imagine you’re a busy intellectual and some issue is brought up, but no one answers it. You’ve got a nice discussion place that answers some issues, but not this one. Then you need to either answer it (or else consider it an unanswered issue). If your thinking has an unanswered issue, you should reconsider it. Try to fix the problem, but also consider other ideas. There’s only a path forward for your thinking if you take responsibility for every unanswered issue.

The discussion place approach saves a lot of time. Many issues can be answered by others who are trying to learn. In the manageable number of cases where an issue isn’t answered, you can quickly refer people to a pre-written answer. If that happens too much, you should consider writing better material. That way, people can understand your answers better and talk about them with less intervention from you.

Do you think there could be a problem where you write really good material but not enough people really understand it well enough to answer questions effectively?

Like Rand wrote lots of really good stuff. How many people are there who even understand 5% of it?

But I guess if you have a bunch of people who each understand a somewhat different 5%, that starts to be pretty good. They can answer something regarding the 5% they are good on while you do other stuff. Comparative advantage 🙂

On the other hand, if no one is interested in discussing your ideas, then you may have to answer everything yourself. In that case, you aren’t actually a busy intellectual getting flooded with inquiries.

You don’t necessarily have to read everything at your discussion place. You just have to take responsibility for everything. You can monitor discussion and see that issues are getting answered. When a particular topic gets a lot of discussion, take a look. If someone doesn’t get an answer but isn’t persistent about moving the discussion forward, that’s his fault. He should make an effort to resolve disagreements, not just give up immediately. Watch for this if you have time, but you can’t help everyone.

There are ways to monitor your discussion place efficiently. Watch for people who give lots of good answers. When they don’t know the answer to an issue (it doesn’t matter if they thought of the issue or someone else did), pay closer attention. If no one else gives an answer as good as you could have given, answer the issue yourself.

Big picture: If there’s nowhere that people with criticisms, questions or other issues can get answers from you or regarding your ideas, then you aren’t open to discussion. If there is somewhere but it’s not very good, you aren’t open to discussion. If there is somewhere and you take responsibility for its quality and participate as needed, then you’re open to discussion.

When do you personally need to participate? Whenever there won’t be a path forward unless you participate. You need to take responsibility for making sure there are always paths forward for all issues. If you do that you’re rational, and if you don’t you’re irrational.

Extended Example: The Content Guy
Some people are pretty happy. They think their life is pretty good. They don’t really feel the need for a path forward because they’re content with what they already have. Usually they do try to make progress in a few areas like their career or a favorite hobby, but they don’t have a path forward for everything. They don’t really want to be intellectuals. They know they aren’t open to discussion about everything, but so what?

They might be wrong! Maybe their whole lifestyle is a mistake. Maybe they’re suffering and don’t realize it.

Lots of people suffer in some area, but are so defeatist about the inevitability of suffering in that area that they don’t really count it as suffering.

Like they hate their job but think everyone hates their job, its inevitable, so not worth mentioning or trying to improve…

and they’ll tell themselves stories like “having to do something for work ruins everything.” So just totally ignore that there’s people who live and enjoy their work…

Maybe what they think is happiness isn’t very good, and a much better kind of happiness is possible. Maybe they have huge problems which they’re blind to.

It’s important to be intellectual enough to improve your life. There should be a path forward to a better life.

If someone raises an intellectual issue, you can ask how it’s relevant to you. Say you don’t just want knowledge for the sake of knowledge, but improving your life would interest you.

If you’re content with your life, lots of intellectual ideas aren’t relevant to you. Keep doing your thing. But some are relevant. If someone explains how something is relevant, it’s important to discuss it.

You may think something would be relevant if it were true, but you consider it false. But how do you know? You’re not an intellectual. Unless you have rational path forwards to find out about all your mistaken ideas, you shouldn’t trust your judgment about what’s false.

If you aren’t interested in something because you think it’s false, that’s a big mistake. You need to be open to discussion. What if it’s true? If you won’t consider it, there’s no path forward and you’ll be wrong forever. You need to be intellectual enough not to block off progress.

You can point out how majorly wrong people have been in the past (about things like racism or slavery, how to treat women, etc.) and argue that there’s no reason to think that they’re immune to having big blindspots. But I find this isn’t very effective. Everyone kind of thinks they’re at the end of moral progress or something, doesn’t take seriously that they could be making major mistakes. Even people who’ve actually UNDERGONE a big worldview change take this kind of attitude — often they’re MORE SURE they aren’t making big mistakes BECAUSE they’ve made a major world view transition. Instead of learning the lesson of humility, they get more arrogant 🙁

You may think if you aren’t aware of a problem, it can’t be that big a deal. You’re wrong. People actually put a lot of effort into hiding their problems from themselves. People put lots of energy into pretending their problems don’t exist. People refuse to admit problems exist, and make up excuses for why stuff isn’t that bad.

(I’m not giving any examples here on purpose. Short examples of problems people deny won’t be convincing. People will deny the examples are problems, or deny they personally have that problem. If you want examples, read my websites or ask.)

Some people pretend something isn’t a problem if they have an argument (which they aren’t open to discussion about) for why that problem is an inevitable part of life. Rather than solve the problem, they tell themselves a better life isn’t possible. Then, believe it or not, they will claim they’re content with their life. Almost everyone does this sometimes.

Yeah 🙁

Still doubt it? No problem. There are answers already written. The link discusses the issue of your life having big problems you aren’t aware of. That is relevant to you. You should be interested. You should react in a way that has a path forward in case I’m right about this.

If you read my answers and think I’m wrong, don’t react with silence. Then there’s no path forward in case actually you misunderstood something. What if I’m right? Want to bet your life on this? Instead of ignoring this disagreement, point out at least one issue with what I’m saying. Contribute a step to the discussion. Then there’s a path forward, step by step. (The best place to discuss is at the Fallible Ideas Discussion Group. You can also email me at elliot@fallibleideas.com.)


Rational people are open to discussion because they recognize they may be wrong about some important things. Many people claim to be open to discussion, but limit it. You can judge whether limits are rational or irrational by whether they keep a path forward open or not.

A path forward is a way progress can happen, a way disagreements can be resolved, a way learning can take place. There should be paths forward so that any improvement can reach you, no matter who thought of it. (As long as it’s relevant to your life. But make sure there are paths forward for improving your understanding of what is relevant to you and what is a good life.)

Don’t make irrational excuses. You’re not too busy to deal with paths forward. Your life is not so problem-free that no progress could help. Never say (or act like), “I’m too busy to proceed in a rational way” or “I’m happy with my life, I don’t need reason”.

Take responsibility for your paths forward. Don’t assume “scientists” or other authorities have it covered for you. Don’t trust someone else to be rational for you. Consider important ideas. Use paths forward involving clear public writing with context.

If you agree, start making changes to become more rational. If you think you already do this perfectly, put that to the test in some discussions at the Fallible Ideas Discussion Group. Or if you disagree, you should be open to discussion about why that is, if nothing else. If you won’t even discuss your reasons for not having paths forward, you’re irrational.

Thinking in terms of paths forward is an opportunity to be more rational. You can have better discussions and a better life.

On an earlier comment post elliot asked:

In addition to commenting on specific passages, I suggest you separately comment on the overall main concept. big picture stuff. how does this fit into life? is it important? what’s the point of it? what problems does it solve? do you like it? are you going to do it? got objections overall? etc etc

such replies could work with various other stuff you read, too.


I liked the essay. It has a big potential audience of people it can help — from regular Joes to busy intellectuals.

I think there’s a nice spirit throughout the essay of treating everybody as a mind worthy of respect by default. Like it says “If there’s nowhere that people with criticisms, questions or other issues can get answers from you or regarding your ideas, then you aren’t open to discussion.” Just regular people should be able to get answers from you — being able to get answers from you isn’t some elite status. The essay is explicitly anti-authority of experts, too: “Don’t use authority, social status, curation, moderation or gatekeepers instead of your own mind. That’s irresponsible.” And it gives the example of people who know some stuff being able to help a busy intellectual answer questions. Lots of people get scared off of intellectual stuff by thinking maybe they aren’t worthy and don’t have the mind for it. But the entire essay is very against that sort of approach. I think that is a nice and rare quality.

I think the Paths Forward essay takes discussions seriously. It treats discussions as something which can and should make progress. It gives lots of specific advice about how to approach discussion and avoid some common pitfalls. It offers explicit criteria for good answers which it argues for. Most people’s approach to discussions is similar to most people’s approach to playing games — its unserious and casual. Paths Forward takes discussions seriously enough to try and avoid systematic mistakes which mess up people’s progress in their individual lives (and progress in all fields of knowledge).

If the ideas in this essay were taken seriously, understood, and applied, it would revolutionize the world.

I think a big part of what would prevent it from being taken seriously and applied is people NOT LIKING IT.

To take one example, Elliot wrote:

An answer can be a good path forward even if it’s mistaken, since the mistake could be pointed out and progress could still be made.

and i commented (in Part 2 of my comments)

Lots of people will throw out a whole valuable system of ideas (like Objectivism) because they spot some mistake in the thinking of one of its advocates (while systematically avoiding any engagement with the mistakes in their own thinking).

An FIer finds excitement in finding mistakes because it provides an opportunity for improvement and doing better.

But there’s another type of mentality which finds mistakes exciting because it lets them throw stuff out wholesale. They’re excited by the prospect of finding an excuse to remain intellectually stagnant. Very sad!!!

(And Alan pointed out this happens in physics re: MWI 😩)

So I think it’s a great essay, but basically lots of people will resent it, because it will threaten some of their excuses for delegitimizing disagreement. And so they’ll turn to one of their standard rationalizations (like dismissing “some guy on the internet”) and it won’t really catch on. Not sure how to address this problem 😔