By the way Knut, when I go straight into ‘criticism mode’, that can sound cold or harsh. But don’t let that discourage you from exploring your idea further. Maybe you’re onto something! A working implementation of hard to vary would be useful and vindicating.

We can redefine ‘hard to vary’, but we’d need still a working implementation in the form of computer code.

… Demeter scores 25% and axial tilt scores 100%.

Now do this universally, for any given theory.

When you say it's 100% true that it's raining, "the facts" you correspond to are already facts within that framework, and not reality.

I think of them as facts of reality. I don’t think about ‘frameworks’. I think the idea of frameworks invites relativism.

We don’t need the molecular level for this. Truth is a very simple concept. No need to complicate it.

[W]e have no way of verifying that our conceptual carvings track or pick out entities and relations in reality. … [This] definitely rules out absolute truth.

I don’t see how it does. That we have no way to verify our theories (“conceptual carvings”) doesn’t rule out absolute truth. It does sound like we have different notions of ‘absolute truth’ in mind. For mine, see #4894.

Ironically, your idea that theories can be “more true than others” rules out absolute truth in the sense that truth leaves absolutely no room for deviation. Absolute truth is a binary: true or false. Nothing in between.

If you agree that truth is correspondence with reality, and not with the facts within our conceptual framework, the problem reemerges.

I disagree because I think this sets up a false dichotomy.

When I wrote “Truth means correspondence with the facts”, that means with the facts of reality.

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 which is hard to detect. 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 might give 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 turned into a function, or just 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 measuring the "hard-to-vary" 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%.

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%.

Would you agree that this notion of truth amounts to truth relative to our conceptual framework? When you say it's 100% true that it's raining, "the facts" you correspond to are already facts within that framework, and not reality.

At the molecular level there are no discrete raindrops, only a continuous distribution of H2O molecules constantly evaporating and condensing, and some of those very molecules are diffusing through the roof into the house, since no material is 100% impermeable to water vapor.

You might disagree. But when we search for truth, I think most of us are trying to understand the causal structure of the universe, not just predict it with our own fitted models. This is just a criticism of this notion of truth, which waters the concept down from what I at least think of as truth. Many incompatible theories can fit the same facts without capturing any causality. If you agree that truth is correspondence with reality, and not with the facts within our conceptual framework, the problem reemerges.

A statement carves the world into concepts standing in relations. For it to correspond with reality, those concepts must pick out genuine entities and relations in reality. But we have no way of verifying that our conceptual carvings track or pick out entities and relations in reality. This might not imply that some theories can't be more true than others. But it definitely rules out absolute truth.

When we search for truth, I think most of us are trying to understand the causal structure of the universe, not just predict it with our own fitted models. This is just a criticism of this notion of truth, which waters the concept down from what I at least think of as truth. Many incompatible theories can fit the same facts without capturing any causality. If you agree that truth is correspondence with reality, and not with the facts within our conceptual framework, the problem reemerges.

A statement carves the world into concepts standing in relations. For it to correspond with reality, those concepts must pick out genuine entities and relations in reality. But we have no way of verifying that our conceptual carvings track or pick out entities and relations in reality.

When we search for truth, I think most of us are trying to understand the causal structure of the universe, not just predict it with our own fitted models. This is just a criticism of this notion of truth, which waters the concept down from what I at least think of as truth. Many incompatible theories can fit the same facts without capturing any causality. If you agree that truth is correspondence with reality, and not with the facts within our conceptual framework, the problem reemerges.

A statement carves the world into concepts standing in relations. For it to correspond with reality, those concepts must pick out genuine entities and relations in reality. But we have no way of verifying that our conceptual carvings track the world's entities and relations. And therefore we can't know if a statement is true, or if it merely corresponds with the facts (our ideas/perceptions of the world)

If you take an idea from me and produce a derivative work you may change the value of my copy.

It need not necessarily be a decrease in value. For example, a novel derivative work created by you may increase purchases of my works. Alternatively, your work may tarnish the brand associated with my work, or even directly compete with me, and reduce my sales.

I may not want to take this risk. I ask you not to take such actions in exchange for me sharing a copy with you (with agreed restrictions). If you accept and breach the agreed restrictions, you have violated our contract.

I see, thank you.

Hi Ed, welcome to Veritula. If this idea is meant as a criticism (it sounds like one), be sure to revise it and check the criticism checkbox. See also ‘How Does Veritula Work?’

Risk adversity is widespread enough that restrictive terms may be implicit.

If you take an idea from me and produce a derivative work you may change the value of my copy.

It need not necessarily be a decrease in value. For example, a novel derivative work created by you may increase purchases of my works. Alternatively, your work may tarnish the brand associated with my work, or even directly compete with me, and reduce my sales.

I may not want to take this risk. I ask you not to take such actions in exchange for me sharing a copy with you (with agreed restrictions). If you accept and breach the agreed restrictions, you have violated our contract.

If you take an idea from me and produce a derivative work you may change the value of my copy.

It need not necessarily be a decrease in value. For example, a novel derivative work created by you may increase purchases of my works. Alternatively, your work may tarnish the brand associated with my work, or even directly compete with me, and reduce my sales.

I may not want to take this risk. I ask you not to take such actions in exchange for me sharing a copy with you (with agreed restrictions). If you accept and breach the agreed restrictions, you have violated our contract.

Risk adversity is widespread enough that the contract is implicit.

A contradiction in The Beginning of Infinity by David Deutsch? 🤔
https://www.youtube.com/shorts/xmngAmZMEuo

Steve Jobs was a good writer.
He wrote clearly and simply.
Anyone can understand him.

From https://x.com/WebDesignMuseum/status/2049544240213196807

In that case, I'm unclear what "100% true" means.

Perfect correspondence with the facts.

For example, if it’s currently raining, and you say it is, then your statement is 100% true.

In that case, I'm unclear what "100% true" means. If your definitions have wiggle room, then the truth is not your idea. The truth is within the bounds of your idea, but it is not identical to your idea.