I think playing around with ideas like this in detail is underrated. Noting that I'm only criticizing the strong version because I like it overall. Both 'study' and your named variables here are serving as aether variables. If you have a flexible enough representation then you can use it to represent anything, unfortunately you've also gutted it of predictive power (vs post hoc explanation).
Secondly and more constructively: I'm reminded of Donell Meadow's Leverage Points.
If you have a flexible enough representation then you can use it to represent anything, unfortunately you've also gutted it of predictive power (vs post hoc explanation).
I think this can be wrong:
Can you expand on the connection with Leverage Points? Seems like 12 Leverage Points is an extremely specific and complicated idea (doesn't mean it can't be good in its own field, though).
I see the 12 points as possible trailheads for analyzing D when the person is new to the type of analysis and needs examples to chain off of.
There are two interpretations of this post, weak and strong.
Weak interpretation:
I describe a framework about "three levels of exploration". I use the framework to introduce some of my ideas. I hope that the framework will give more context to my ideas, making them more understandable. I simply want to find people who are interested in exploring ideas. Exploring just for the sake of exploring or for a specific goal.
Strong interpretation:
I use the framework as a model of intelligence. I claim that any property of intelligence boils down to the "three levels of exploration". Any talent, any skill. The model is supposed to be "self-evident" because of its simplicity, it's not based on direct analysis of famous smart people.
Take the strong interpretation with a lot of grains of salt, of course, because I'm not an established thinker and I haven't achieved anything intellectual. I just thought "hey, this is a funny little simple idea, what if all intelligence works like this?", that's all.
That said, I'll need to make a couple of extraordinary claims "from inside the framework" (i.e. assuming it's 100% correct and 100% useful). Just because that's in the spirit of the idea. Just because it allows to explore the idea to its logical conclusion. Definitely not because I'm a crazy man. You can treat the most outlandish claims as sci-fi ideas.
A formula of thinking?
Can you "reduce" thinking to a single formula?
Can you show a single path of the best and fastest thinking?
Well, there's an entire class of ideas which attempt to do this in different fields, especially the first idea: (the first two ideas are well-known to everyone here)
My idea is just another attempt at reduction. You don't have to treat such attempts 100% seriously in order to find value in them. You don't have to agree with them.
Three levels of exploration
Let's introduce my framework.
In any topic, there are three levels of exploration:
The point is that at the 2nd level you study similarities between different X directly, but at the 3rd level you study similarities indirectly through new concepts Y and D. The letter "D" means "dynamics".
I claim that any property of intelligence can be boiled down to your "exploration level". Any talent, any skill and even more vague things such as "level of intentionality". I claim that the best and most likely ideas come from the 3rd level. That 3rd level defines the absolute limit of currently conceivable ideas. So, it also indirectly defines the limit of possible/conceivable properties of reality.
You don't need to trust those extraordinary claims. If the 3rd level simply sounds interesting enough to you and you're ready to explore it, that's good enough. I'll discuss some "core questions" about the framework at the end of the post.
Three levels simplified
A vague description of the three levels:
Or:
Or:
So yeah, it's a Hegelian dialectic rip-off. Down below are examples of applying my framework to different topics. You don't need to read them all to join the discussion, of course.
Exploring debates
1. Argumentation
I think there are three levels of exploring arguments:
If you want to get a real insight about argumentation, you need to study how (D) arguments change/get changed by some new thing Y. D and Y need to be important even outside of the context of explicit argumentation.
For example, Y can be "concepts". And D can be "connecting/separating" (a fundamental process which is important in a ton of contexts). You can study in what ways arguments connect and separate concepts.
A simplified political example: a capitalist can tend to separate concepts ("bad things are caused by mistakes and bad actors"), while a socialist can tend to connect concepts ("bad things are caused by systemic problems"). Conflict Vs. Mistake is just a very particular version of this dynamic[1]. Different manipulations with concepts create different arguments and different points of view. You can study all such dynamics. You can trace arguments back to fundamental concept manipulations. It's such a basic idea and yet nobody has done it[2]. Aristotle has done it 2400 years ago, but for formal logic.
Arguments: conclusion
I think most of us are at the level 1 in argumentation: we throw arguments at each other like angry cavemen without studying what an "argument" is and/or what dynamics it creates. If you completely unironically think that "stupid arguments" exist, then you're probably on the 1st level. Professional philosophers are at the level 2 at best, but usually lower (they are surprisingly judgemental). At least they are somewhat forced to be tolerant to the most diverse types of arguments due to their profession.
On what level are you? Have you studied arguments without judgement?
2. Understanding/empathy
I think there are three levels in understanding your opponent:
For example, Y can be "copies of the same thing" and D can be "transformations of copies into each other". Such Y and D are important even outside of debates.
So, on the 3rd level you may be able to describe the opponent's position as a weaker version/copy of your own position (Y) and clearly imagine how your position could turn out to be "the weaker version/copy" of the opponent's views. You can imagine how opponent's opinion transforms into truth and your opinion transforms into a falsehood (D).
Other interesting choices of Y and D are possible. For example, Y can be "complexity of the opinion [in a given context]"; D can be "choice of the context" and "increasing/decreasing of complexity". You can run the opinion of your opponent through different contexts and see how much it reacts to/accommodates the complexity of the world.
Empathy: conclusion
I think people very rarely do the 3rd level of empathy.
Doing it systematically would lead to a new political/epistemological paradigm.
Exploring philosophy
1. Beliefs and ontology
I think there are three levels of studying the connection between beliefs and ontology:
What can D and Y be? Both things need to be important even outside of the context of explicit beliefs. A couple of versions:
Thinking at the level of semantic connections should be natural to people, because they use natural language and... neural nets in their brains! (Berkeley makes a similar argument: "hey, folks, this is just common sense!") And yet this idea is extremely alien to people epistemology-wise and ontology-wise. I think the true potential of the 3rd level remains unexplored.
Beliefs: conclusion
I think most rationalists (Bayesians, LessWrong people) "oscillate" between the 2nd level and the 1st level, even though they have some 3rd level tools.
Eliezer Yudkowsky "oscillates"[3] between the 1st level and the 3rd level: he likes level 1 ideas (e.g. "map is not the territory"), but has a bunch of level 3 ideas ("some maps are the territory") about
2. Ontology and reality
I think there are three level of exploring the relationship between ontologies and reality:
Y can be "human minds" or simply "objects". D can be "matching/not matching" or "creating a structure" (two very basic, but generally important processes). You get Kant's "Copernican revolution" (reality needs to match your basic ontology, otherwise information won't reach your mind: but there are different types of "matching" and transcendental idealism defines one of the most complicated ones) and Ontic Structural Realism (ontology is not about things, it's about structures created by things) respectively.
On what level are you? Have you studied ontologies/epistemologies without judgement? What are the most interesting ontologies/epistemologies you can think of?
3. Philosophy overall
I think there are three levels of doing philosophy in general:
To give a bunch of examples, Y can be:
I think people did a lot of 3rd level philosophy, but we haven't fully committed to the 3rd level yet. We are used to treating philosophy as a closed system, even when we make significant steps outside of that paradigm.
Exploring ethics
1. Commitment to values
I think there are three levels of values:
Example of a semantic value: you care about your friendship with someone. You will try to preserve the friendship. But in a limited way: you're ready that one day the relationship may end naturally (your value may "die" a natural death). Semantic values are temporal and path-dependent. Semantic values are like games embedded in reality: you want to win the game without breaking the rules.
2. Ethics
I think there are three levels of analyzing ethics:
Ethics: tasks and games
For example, Y can be "tasks, games, activities" and D can be "breaking/creating symmetries". You can study how norms and desires affect properties of particular activities.
Let's imagine an Artificial Intelligence or a genie who fulfills our requests (it's a "game" between us). We can analyze how bad actions of the genie can break important symmetries of the game. Let's say we asked it to make us a cup of coffee:
Those are all "symmetry breaks". And such symmetry breaks are bad in most of the tasks.
Ethics: Categorical Imperative
With Categorical Imperative, Kant explored a different choice of Y and D. Now Y is "roles of people", "society" and "concepts"; D is "universalization" and "becoming incoherent/coherent" and other things. Examples of Kant's analysis.
Ethics: Preferences
If Y is "preferences" and D is "averaging", we get Preference utilitarianism. (Preferences are important even outside of ethics and "averaging" is important everywhere.) But this idea is too "low-level" to use in analysis of ethics.
However, if Y is "versions of an abstract preference" and D is "splitting a preference into versions" and "averaging", then we get a high-level analog of preference utilitarianism. For example, you can take an abstract value such as Bodily autonomy and try to analyze the entirety of human ethics as an average of versions (specifications) of this abstract value.
Preference utilitarianism reduces ethics to an average of micro-values, the idea above reduces ethics to an average of a macro-value.
Ethics: conclusion
So, what's the point of the 3rd level of analyzing ethics? The point is to find objective sub-structures in ethics where you can apply deduction to exclude the most "obviously awful" and "maximally controversial and irreversible" actions. The point is to "derive" ethics from much more broad topics, such as "meaningful games" and "meaningful tasks" and "coherence of concepts".
I think:
Exploring perception
1. Properties
There are three levels of looking at properties of objects:
2. Commitment to experiences and knowledge
I think there are three levels of commitment to experiences:
So, on the 3rd level you care about interesting ways (D) in which experiences correspond to reality (Y).
3. Experience and morality
I think there are three levels of investigating the connection between experience and morality:
For example, Y can be "[basic] properties of concepts" and D can be "matches / mismatches [between concepts and actions towards them]". You can study how experience affects properties of concepts which in turn bias actions. An example of such analysis: "loving a sentient being feels fundamentally different from eating a sandwich. food taste is something short and intense, but love can be eternal and calm. this difference helps to not treat other sentient beings as something disposable"
I think the existence of the 3rd level isn't acknowledged much. Most versions of moral sentimentalism are 2nd level at best. Epistemic Sentimentalism can be 3rd level in the best case.
Exploring cognition
1. Patterns
I think there are three levels of [studying] patterns:
For example, Y can be "pieces of information" or "contexts": you can study how patterns get discarded or redefined (D) when new information gets revealed/new contexts get considered.
You can study patterns which are "objective", but exist only in a limited context. For example, think about your friend's bright personality (personality = a pattern). It's an "objective" pattern, and yet it exists only in a limited context: the pattern would dissolve if you compared your friend to all possible people. Or if you saw your friend in all possible situations they could end up in. Your friend's personality has some basis in reality (X), has a limited domain of existence (Y) and the potential for change (D).
2. Patterns and causality
I think there are three levels in the relationship between patterns and causality. I'm going to give examples about visual patterns:
Y can be "basic properties of images" and "basic properties of patterns"; D can be "sharing properties" and "keeping the complexity the same". In simpler words:
On the 3rd level you learn patterns which have strong connections to other patterns and basic properties of images. You could say such patterns are created/prevented by "global" causal processes. For example: "I'm unlikely to see a place fully filled with dogs. dogs are not people or birds or insects, they don't create such crowds or hordes". This is very abstract, connects to other patterns and basic properties of images.
Causality: implications for Machine Learning
I think...
3. Cognitive processes
Suppose you want to study different cognitive processes, skills, types of knowledge. There are three levels:
For example, Y can be "fundamental[4] configurations / fundamental objects" and D can be "finding a fundamental configuration/object in a given domain". You can "reduce" different cognitive process to those Y and D: (names of the processes below shouldn't be taken 100% literally)
I know, this looks "funny", but I think all this could be easily enough formalized. Isn't that a natural way to study types of reasoning? Just ask what knowledge a certain type of reasoning learns!
Exploring theories
2/3 of this part is just an overview of popular mathematical and physical ideas. The purpose of this part is to train you to look at things in terms of Y and D.
1. Science
I think there are three ways of doing science:
Imagine you want to explain combustion (why/how things burn):
So, I think phlogiston theory was a step in the right direction, but it failed because the choice of Y and D wasn't abstract enough.
I think most significant scientific breakthroughs require level 3 ideas. Partially "by definition": if a breakthrough is not "level 3", then it means it's contained in a (very) specific part of reality.
2. Math
I think there are three ways of doing math:
Mathematico-philosophical insights
Let's look at math through the lens of the 3rd level:
All concepts above are "3rd level". But we can classify them, creating new three levels of exploration (yes, this is recursion!). Let's do this. I think there are three levels of mathematico-philosophical concepts:
So, Calculus is really "the king of kings" and "the insight of insights". 3rd level of the 3rd level.
3. Physico-philosophical insights
I would classify physico-philosophical concepts as follows:
Exploring meta ideas
To define "meta ideas" we need to think about many pairs of "Y, D" simultaneously. This is the most speculative part of the post. Remember, you can treat those speculations simply as sci-fi ideas.
Each pair of abstract concepts (Y, D) defines a "language"[5] for describing reality. And there's a meta-language which connects all those languages. Or rather there's many meta-languages. Each meta-language can be described by a pair of abstract concepts too (Y, D).
I think the idea of "meta-languages" can be used to analyze:
According to the framework, ideas about "meta-languages" define the limit of conceivable ideas.
If you think about it, it's actually a quite trivial statement: "meta-models" (consisting of many normal models) is the limit of conceivable models. Your entire conscious mind is such "meta-model". If no model works for describing something, then a "meta-model" is your last resort. On one hand "meta-models" is a very trivial idea[6], on another hand nobody ever cared to explore the full potential of the idea.
Nature of percepts
I talked about qualia in general. Now I just want to throw out my idea about the nature of particular percepts.
There are theories and concepts which link percepts to "possible actions" and "intentions": see Affordance. I like such ideas, because I like to think about types of actions.
So I have a variation of this idea: I think that any percept gets created by an abstract dynamic (Y, D) or many abstract dynamics. Any (important) percept corresponds to a unique dynamic. I think abstract dynamics bind concepts. But this is an "unfinished" idea.
A criticism of Bayesian reasoning?
I haven't got much here, but I thought I'd share. You can use my framework to come up with a criticism of Bayesianism. It doesn't have to be a criticism, though.
You can classify types of reasoning as follows:
So, you update only on particular type of information (1st level) or on any type of information (2nd level) or on a changing type of information (3rd level).
According to the classification, Bayesianism is only 2nd level and there should exist some other type of reasoning. Does it actually exist and does it matter? It's up to your intuitions.
I think that 2nd type of reasoning is infeasible for humans and there are some subtle hints that humans don't think like this: see the Raven paradox, Sunrise problem, reference class problem and Pascal's Mugging (which may require a non-Bayesian update for a solution). The first two "paradoxes" have a Bayesian solution, but they can make you question inductive reasoning anyway.
For David Deutsch Y is "memes", "good explanations" and "invariants": new information is meaningful only to the extent that it leads to new hard-to-vary memes ("good explanations"). So, in a way observing a new sunrise gives absolutely zero new information about the sun, because we already have a good explanation of the way the sun works. You can read this review/summary of "The Beginning of Infinity" to get more familiar with David Deutsch's ideas.
Discussion
This part of the post discusses some questions about my framework. I mostly answer "from inside the framework" and my own opinion (which may be unjustified to you).
Q: Isn't the choice of possible "Y" and "D" too large?
A:
I think in practice it doesn't matter:
Q: Why should we explore?
Q: Why should I explore ideas if I think I already discovered the best idea? Do you think that exploration is an unconditional virtue? A:
I just think that:
So, I think that "level of exploration" can be an important measure of intelligence/progress in a given topic even if the best idea is known beforehand.
Q: What about modeling and predicting?
Q: It's extremely important for intelligence to create models and specific predictions of reality. This seems completely missing from your idea. What's the deal? A:
At every step of the thinking process you have a choice "what should I think about next?", the post describes how to make the correct choice. The post doesn't mention specific models with specific predictions: that's because I think good models and good predictions follow from making the correct choices. I think it's an unexpected/counterintuitive/interesting property of my idea that it doesn't explicitly discuss predicting reality.
I think "three levels of exploration" can be turned into a probabilistic inference rule. But it's a very exotic one.
Q: Do you overestimate the importance of the 3rd level?
A:
To answer this I'll need to introduce another way to describe the "three levels of exploration". It goes like this:
First, I think that all types of reasoning are important.
Second, I think that "dynamical" reasoning is underestimated. Partially because it can be confused with pure meta-level or pure object-level reasoning.
Third, I think that we need to "try" overestimating the 3rd level. As a thought experiment, in order to explore the 3rd level, we need to imagine a world where 3rd level is the most important one.
So I think "yes", it's likely that I'm overestimating the 3rd level, especially in this post.
P.S.
Thank you for reading this.
If you want to discuss the idea, please focus on the idea itself and its particular applications. Or on exploring particular topics!
I want to thank JustisMills for feedback and a couple of specific ideas.
I don't agree too much with Scott Alexander's specific framing, by the way.
What do I mean by "nobody had done it"? I wear my "confidence hat" saying it. Not counting the confidence hat, my reasoning goes somewhat as follows:
1) Rationalists are rare people who worry about not having a (general) theory of reasoning. Yet they don't study informal argumentation much. Scott Alexander seems more interested in informal arguments and intentions behind them (e.g. Conflict Vs. Mistake, Noncentral Fallacy, Weak Men), but he doesn't try to build any theory of informal argumentation.
2) Progressive left are rare people who try to deconstruct almost any concept (Social constructionism). Yet they are not too focused on deconstructing argumentation itself.
3) Philosophers are rare people who question everything... but they are not very focused on questioning "philosophical debates" in general.
So, people thinking about fundamental stuff related to argumentation is a priori rare, but people focusing on argumentation itself (in a fundamental way) is even more rare. If they exist, they are pretty removed from any popular discourse.
This doesn't have to be a criticism. Even though I think that community as a whole should explore 3rd level more.
"fundamental" here means "VERY widespread in a certain domain"
Instead of "language" I could use the word "model". But I wanted to highlight that those "models" don't have to be formal in any way.
For example, we have a "meta-model" of physics: a combination of two 'wrong' theories, General Relativity and Quantum Mechanics.