That's true. This wasn't meant as an argument against realist truth, and it's probably beside the point I'm making anyway. I was just drawing a distinction: an absolute truth can exist, but without a god's eye view we can never know whether our theories correspond to it.

Have some thoughts, which might be way off. But interested in your response. It seems to me that "hard-to-vary" is itself the criterion that a theory should be as programmable as possible. As you note, the goal of a theory should be to make it as explicit as possible, and a program is explicitness in its most complete form. Any theory with ambiguous components automatically has a breaking point that is changeable without detection. A programmable theory has strict causal relations all the way from the axioms to the prediction, which makes any change to the components detectable. In other words: a theory is hard to vary to the extent that its components and the couplings between them can be specified as a program. If a theory is vague, you cannot tell when it has been varied.

This gives a concrete operationalization. A breaking point is any place in the formalization where the chain stops being programmable: a primitive with no implementable type, a coupling between components that cannot be specified, or a step that requires implicit theories to fill the explanatory gaps. A mathematical theory with no remaining gaps has zero breaking points and is maximally hard to vary. A theory in natural language is already worse, because words carry ambiguity and vary from mind to mind. This does not rule out better and worse theories in natural language, since we can use more or less ambiguous words and relations. But it does create a hierarchy of hard-to-vary explanations, where the share of the explanation that is programmable, or at least unambiguous, forms the basis for the criterion.

This is probably too crude a formalization. But evaluating the two theories of Demeter's emotions and axial tilt as explanations, you could check how much of each is programmable. Detecting seasons is programmable in both cases through temperature and changes in weather. Demeter's emotions and the causal link from them to the weather, which is the entire explanation, are not programmable. In the axial tilt theory, every component is. So on this measure Demeter scores 25% and axial tilt scores 100%.

If we normalize a theory into the parts that can be put on a computer, the types it uses, the nodes (specific values) it commits to, and the functions between them, we can score the theory by how many of those parts run.

The program goes through each item in a theory, counts how many are marked True, and divides by the total. That fraction is the score of how hard the theory is to vary.

An item is True if it can be put on a computer, either by reusing an existing type (Float, Int) or by defining a new one that compiles. It is False if no working type system can express it. The user fills in the labels; the program just counts.

Demeter: 2 of 8 items program (Latitude and Temperature). Demeter, her emotions, and the functions linking them to weather can't. So the score is 25%.

Axial tilt: 9 of 9 items program. Standard types, measured constants, and functions from standard physics. So the score is 100%.

I'm not a programmer, so the code below is 100% AI-generated. But here is an attempt. If we normalize a theory into the parts that can be put on a computer, the types it uses, the nodes (specific values) it commits to, and the functions between them, we can score the theory by how many of those parts run.

from dataclasses import dataclass

@dataclass
class Item:
name: str
kind: str # "type", "node", or "function"
programmable: bool # does it compile and run?

@dataclass
class Theory:
name: str
items: list[Item]

1
2
3
4
5

def score(self) -> float:
    if not self.items:
        return 0.0
    ok = sum(1 for i in self.items if i.programmable)
    return ok / len(self.items)

def compare(a: Theory, b: Theory) -> None:
print(f"{a.name:<20} {a.score():.0%}")
print(f"{b.name:<20} {b.score():.0%}")

Demeter theory

demeter = Theory("Demeter", [
Item("Latitude", "type", True),
Item("Temperature", "type", True),
Item("Goddess", "type", False),
Item("Emotion", "type", False),
Item("Demeter", "node", False),
Item("emotionstate", "node", False),
Item("emotionat", "function", False),
Item("emotion_weather", "function", False),
])

Axial tilt theory

axialtilt = Theory("Axial tilt", [
Item("Latitude", "type", True),
Item("Temperature", "type", True),
Item("Angle", "type", True),
Item("Insolation", "type", True),
Item("axialtilt", "node", True),
Item("solarconstant", "node", True),
Item("solarangle", "function", True),
Item("insolation_at", "function", True),
Item("temperature", "function", True),
])

compare(demeter, axial_tilt)

Output metrics:
Demeter 25%
Axial tilt 100%

If we normalize a theory into the parts that can be put on a computer, the types it uses, the nodes (specific values) it commits to, and the functions between them, we can score the theory by how many of those parts actually run.

from dataclasses import dataclass

@dataclass
class Item:
name: str
kind: str # "type", "node", or "function"
programmable: bool # does it compile and run?

@dataclass
class Theory:
name: str
items: list[Item]

1
2
3
4
5

def score(self) -> float:
    if not self.items:
        return 0.0
    ok = sum(1 for i in self.items if i.programmable)
    return ok / len(self.items)

def compare(a: Theory, b: Theory) -> None:
print(f"{a.name:<20} {a.score():.0%}")
print(f"{b.name:<20} {b.score():.0%}")

Demeter theory

demeter = Theory("Demeter", [
Item("Latitude", "type", True),
Item("Temperature", "type", True),
Item("Goddess", "type", False),
Item("Emotion", "type", False),
Item("Demeter", "node", False),
Item("emotionstate", "node", False),
Item("emotionat", "function", False),
Item("emotion_weather", "function", False),
])

Axial tilt theory

axialtilt = Theory("Axial tilt", [
Item("Latitude", "type", True),
Item("Temperature", "type", True),
Item("Angle", "type", True),
Item("Insolation", "type", True),
Item("axialtilt", "node", True),
Item("solarconstant", "node", True),
Item("solarangle", "function", True),
Item("insolation_at", "function", True),
Item("temperature", "function", True),
])

compare(demeter, axial_tilt)

Output metrics:
Demeter 25%
Axial tilt 100%

It seems to me that "hard-to-vary" is itself the criterion that a theory should be as programmable as possible. As you note, the goal of a theory should be to make it as explicit as possible, and a program is explicitness in its most complete form. Any theory with ambiguous components automatically has a breaking point that is changeable without detection. A programmable theory has strict causal relations all the way from the axioms to the prediction, which makes any change to the components detectable. In other words: a theory is hard to vary to the extent that its components and the couplings between them can be specified as a program. If a theory is vague, you cannot tell when it has been varied.

This gives a concrete operationalization. A breaking point is any place in the formalization where the chain stops being programmable: a primitive with no implementable type, a coupling between components that cannot be specified, or a step that requires implicit theories to fill the explanatory gaps. A mathematical theory with no remaining gaps has zero breaking points and is maximally hard to vary. A theory in natural language is already worse, because words carry ambiguity and vary from mind to mind. This does not rule out better and worse theories in natural language, since we can use more or less ambiguous words and relations. But it does create a hierarchy of hard-to-vary explanations, where the share of the explanation that is programmable, or at least unambiguous, forms the basis for the criterion.

This is probably too crude a formalization. But evaluating the two theories of Demeter's emotions and axial tilt as explanations, you could check how much of each is programmable. Detecting seasons is programmable in both cases through temperature and changes in weather. Demeter's emotions and the causal link from them to the weather, which is the entire explanation, are not programmable. In the axial tilt theory, every component is. So on this measure Demeter scores 25% and axial tilt scores 100%.

Thanks! Creativity is one of the most interesting ideas in DD's philosophy. If you come across any articles or resources on it that you've found helpful, I'd love for you to send them over.

I'm actually in the channel, just haven't been very active.

I think tractibility lacks the open-ended capacity to reformulate what counts as a problem, a solution, and relevant data. Creativity is (at least partially) the ability to reformulate the problem space itself, not by ironing out implications of existing theories. An AI and computational systems is already good at ironing out the implications in our language and existing knowledge systems. But that's search within a given space, not the creation of a new one. Creativity seems to work on a higher level. It's operating at the level of problem framing, which requires things like relevance. An AI can't create new relevance, because its weights are a statistical compression of what humans have already found relevant. It inherits a pre-given frame.

I might be confused about what you mean by tractible. But it seems to me that tractability can't do the work the bounty asks. Tractability is formally defined relative to a fixed problem space. But universal creativity is (at least partially) the capacity to restructure the space, to change what counts as a problem, a solution, and relevant data.

An interesting example from cognitive science is the Mutilated Chessboard Problem, which asks whether a board with two same-coloured corners removed can be tiled by dominoes. As a tiling problem the search space is combinatorially explosive. But reframe it as a colour problem and the answer is easy. Every domino covers one black and one white square, and you have unequal numbers of each. The solution came not from searching harder, but from seeing the problem differently.

This also admits of the distinction between AI and AGI (and "universal creativity") as being whether the system is capable of creating knowledge ex nihilo, as argued by Deutsch. Only universal creativity could create knowledge from nothing. Bounded creativity must start with something.

Moved the criticism of 4694

By Tractible, do you mean "efficient relative to fixed task"?

Could you elaborare? Is the point that physical experience, metaphors and other things that ground ideas don’t constrain the reach of ideas at all or only partially?

"Understanding" isn't just another way of saying "can explain.". Explaining follows from understanding, but isn't synonymous. An RNG could by chance generate a good explanation, but it doesn't understand it, and therefore can't distinguish it from garbage. Understanding involves recognizing that something is a good explanation. It is conscious understanding that makes conjecture and criticism possible. Without it, you have no criticism, only random selection. What do you think of the suggestion that what's lacking from the explanatory universality definition, is an intelligent selection mechanism. A random program can generate any explanation given infinite time, but it will never select which explanation is good.

Understanding explanatory knowledge seems like a better criterion

Those are just spacial metaphors though. I'm not saying we can't extend our ideas through imagination, creativity etc. Only that the metaphors and concepts we use/have meaning for us, are constrained by the perspectives we can take as humans. Can you think of any ideas that isn't rooted in an experiential perspective?

If this is the case, it would make sense to make AGI as similar to ourselves as possible, so AGI can use our pre-existing knowledge more directly.

One part of my question was whether a formal criterion can be applied universally. If the citerion itself must be chosen, like for instance what brings more fun, meaning, practical utility, then by what criterion do we choose the criterion? Or is the answer simply to apply the same process of critical examination to everything that arises, until a coherent path emerges?

The other part was how you actually critize an implicit or unconcious idea. If you have an unconcious idea that gives rise to a conflicting feeling for instance, how do you critisize a feeling?

That was autocorrect from my cellphone. Mye means alot in Norwegian. Not a good idea to have autocorrect on when you're writing in two languages..

Just referring here to alters as the clinical word for 'the other dissociated personalities

It seems more plausible to me that associative identity disorder actually is more like the division of a mind. They often recall meeting each other in dreams (seeing the other alters from their local perspective within the dream). So it seems that the split goes further, and actually gives rise to different experiences within a mind. They live and experience from different perspectives, and start communicating with each other more like distinct minds. In split-brain patients, the left and right hemispheres can disagree on what clothing to wear in the morning, and physically fight over wearing a tie or not.

Interesting! Getting ideas to jibe/cohere seems like a more and more fundamental idea the more I think about it. Has anyone explored whether the collection of ideas in a person's mind must have a specific structure?

When discussing virtues, you seem to suggest a hierarchical organization of ideas, as opposed to ideas competing horizontally for attention and salience. It appears that ideas organize vertically in a hierarchy, where activating "higher-level" ideas automatically resolves conflicts among lower-level ones. For example, if a snake suddenly appears next to you, all previous internal conflicts dissolve because self-preservation is among the most dominant (highest) ideas in their value structure.

However, individuals can construct even higher-order values that override self-preservation. The structure seems hierarchical: when a top-level idea is activated, there seems to be some alignment in lower level ideas.

Has anyone explored whether the collection of ideas in a person's mind must have a specific structure?

When discussing virtues, you seem to suggest a hierarchical organization of ideas, as opposed to ideas competing horizontally for attention and salience. It appears that ideas organize vertically in a hierarchy, where activating "higher-level" ideas automatically resolves conflicts among lower-level ones. For example, if a snake suddenly appears next to you, all previous internal conflicts dissolve because self-preservation is among the most dominant (highest) ideas in their value structure.

However, individuals can construct even higher-order values that override self-preservation. The structure seems hierarchical: when a top-level idea is activated, there seems to be some alignment in lower level ideas.

Aah, then I agree. I thought you meant AGI would develop the same metaphors independently.

If we view addiction as entrenchment of ideas (in the broad sense), why can't you have conflict between implicit and explicit preferences, which are both short-term preferences? Something in your body is addicted to a substance, but you could simultaneously, consciously, not want to take the substance because you don't like how it feels.

After reading some more about Deutsch's and your definition of reason. Is it accurate to view reason more as a process than a static state? Where the process might be summed up by
1. Being open to criticism
2. Truth-seeking (commitment to getting ideas to jibe)