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So I don't see acquiring new knowledge as something that sits outside the process and simply overrides the HTV result.

One would reject some explanations for reasons unrelated to HTV. It’s not that one would override a specific HTV result – one wouldn’t even get to that result because one would first make other choices leading to different inputs.

If I gather new info and the problem situation changes to where I already know Pop-Tarts aren’t tart but sweet (eg because I taste test them), then I simply won’t include that guess in the inputs to the program, and I won’t bother varying that guess.

HTV could still be part of the process, but DD’s claim was that all rationality boils down to HTV.

#5585​·​Dennis HackethalOP, about 3 hours ago

So I don't see acquiring new knowledge as something that sits outside the process and simply overrides the HTV result.

One would reject some explanations for reasons unrelated to HTV. It’s not that one would override a specific HTV result – one wouldn’t even get to that result because one would first make other choices leading to different inputs.

If I gather new info and the problem situation changes to where I already know Pop-Tarts aren’t tart but sweet (eg because I taste test them), then I simply won’t include that guess in the inputs to the program, and I won’t bother varying that guess.

HTV could still be part of the process, but DD’s claim was that all rationality boils down to HTV.

#5585​·​Dennis HackethalOP, about 3 hours ago

But suppose grass really did cure the disease and we actually understood how. Maybe a particular compound in the grass interacts with some biological mechanism, and a certain concentration is required for the effect. The explanation might allow a whole range of effective dosages rather than one exact number, but that range would itself be explained and constrained by the mechanism.

That assumes the cure works: then I agree there’s a reason for the specific range, and that range will be part of the one working variant. Your program would then accurately prefer it over a rival.

But the program also needs to account for cases where the cure doesn’t work. Then we can’t refer to a range anymore because there’s no reason to constrain the explanation to that range. And then we’re left with the situation described in #5549.

#5571​·​Dennis HackethalOP, about 4 hours ago

Being hard to vary also doesn't guarantee that an explanation is true.

Agreed, but I’m not asking for a guarantee. I’m basically saying preference formation using HTV should help us find truth. The Pop-Tart example seems to be a case where HTV is unrelated to finding truth.

#5580​·​Dennis HackethalOP, about 3 hours ago

I think the Pop-Tarts example mixes together two different things: acquiring new knowledge and forming a preference between explanations. Looking up why Pop-Tarts were actually given their name gives us new knowledge; it doesn't by itself show that the preference formation between explanations isn't HTV.

As I argued in #5553, the program operates on the user's current understanding of the problem and explanations. The user is comparing explanations and variations they currently judge to work. So everything they already know, including criticisms they're aware of, is part of that judgment.

In the Pop-Tarts example, say the three explanations are equally hard to vary given what I currently know. That's fine. I currently have no reason to prefer one over another.

Now suppose I look it up and find historical evidence saying the name was chosen for reason X. I've gained new knowledge, and that changes the problem situation. I'm no longer just asking why they're called Pop-Tarts; I'm asking why they're called Pop-Tarts given that I also know this historical evidence says X.

I could still maintain that the real reason was something else. Maybe the company was lying or the historical source was wrong. But then I have to explain that too. If I just say “the real reason is that they pop out of the toaster, and for some unrelated reason the company says X,” I've added another arbitrary factor to preserve my explanation. That seems like exactly the kind of thing that would expose it as easy to vary.

So I don't see acquiring new knowledge as something that sits outside the process and simply overrides the HTV result. New knowledge changes the problem situation and therefore changes what a working explanation now has to account for. We can then compare the explanations again in light of that new problem situation.

Being hard to vary also doesn't guarantee that an explanation is true. Newton's theory of gravity was a good explanation and remains good enough for many engineering problem situations, even though we later learned that it isn't the full story. As new problems and observations came up that Newton couldn't adequately account for, the problem situation changed and we needed a better explanation.

So I don't think every act of acquiring knowledge or finding a criticism itself needs to take the form of thinking about variants. Those things change the problem situation and affect which explanations and variations we consider to still work.

But that's different from saying the preference formation itself isn't HTV. Once our current knowledge and criticisms are taken into account, HTV can still operate on the explanations that still work and give us a preference—or sometimes tell us that, given what we currently know, they're equally good.

#5562​·​Jad Elmourad, about 7 hours ago

I don't think the program needs to choose one of the surviving variants if our current knowledge gives us no reason to choose.

It does. Preference formation is the point of the program.

Sometimes the rational state really is that we don't yet know which variant is right. We can continue developing and testing them until we find something that differentiates them.

Then we’d need to find a way to feed the results of the tests back into the program. Tests would somehow need to be formally tied to HTV. The program has to at least be able to tell the user which preference to form (short of the user not typing in the variant he’s already decided he doesn’t want, eg because of a negative test case).

#5573​·​Dennis HackethalOP, about 3 hours ago

I don't think the program needs to choose one of the surviving variants if our current knowledge gives us no reason to choose.

It does. Preference formation is the point of the program.

Sometimes the rational state really is that we don't yet know which variant is right. We can continue developing and testing them until we find something that differentiates them.

Then we’d need to find a way to feed the results of the tests back into the program. Tests would somehow need to be formally tied to HTV. The program has to at least be able to tell the user which preference to form (short of the user not typing in the variant he’s already decided he doesn’t want, eg because of a negative test case).

#5573​·​Dennis HackethalOP, about 3 hours ago

So I don't think different people getting different results is necessarily a problem.

#5531 doesn’t say that.

#5569​·​Dennis HackethalOP, about 4 hours ago

I don’t think this response addresses the part from #5531 that says “nor is the user given an opportunity to correct any mistakes to that effect.”

#5570​·​Dennis HackethalOP, about 4 hours ago

I think the Pop-Tarts example mixes together two different things: acquiring new knowledge and forming a preference between explanations. Looking up why Pop-Tarts were actually given their name gives us new knowledge; it doesn't by itself show that the preference formation between explanations isn't HTV.

As I argued in #5553, the program operates on the user's current understanding of the problem and explanations. The user is comparing explanations and variations they currently judge to work. So everything they already know, including criticisms they're aware of, is part of that judgment.

In the Pop-Tarts example, say the three explanations are equally hard to vary given what I currently know. That's fine. I currently have no reason to prefer one over another.

Now suppose I look it up and find historical evidence saying the name was chosen for reason X. I've gained new knowledge, and that changes the problem situation. I'm no longer just asking why they're called Pop-Tarts; I'm asking why they're called Pop-Tarts given that I also know this historical evidence says X.

I could still maintain that the real reason was something else. Maybe the company was lying or the historical source was wrong. But then I have to explain that too. If I just say “the real reason is that they pop out of the toaster, and for some unrelated reason the company says X,” I've added another arbitrary factor to preserve my explanation. That seems like exactly the kind of thing that would expose it as easy to vary.

So I don't see acquiring new knowledge as something that sits outside the process and simply overrides the HTV result. New knowledge changes the problem situation and therefore changes what a working explanation now has to account for. We can then compare the explanations again in light of that new problem situation.

Being hard to vary also doesn't guarantee that an explanation is true. Newton's theory of gravity was a good explanation and remains good enough for many engineering problem situations, even though we later learned that it isn't the full story. As new problems and observations came up that Newton couldn't adequately account for, the problem situation changed and we needed a better explanation.

So I don't think every act of acquiring knowledge or finding a criticism itself needs to take the form of thinking about variants. Those things change the problem situation and affect which explanations and variations we consider to still work.

But that's different from saying the preference formation itself isn't HTV. Once our current knowledge and criticisms are taken into account, HTV can still operate on the explanations that still work and give us a preference—or sometimes tell us that, given what we currently know, they're equally good.

#5562​·​Jad Elmourad, about 7 hours ago

I think #5567 applies here, too.

#5568​·​Dennis HackethalOP, about 4 hours ago

One could run the program again with corrected inputs but as I noted in #5533, that approach won’t scale.

Jad originally replied in #5559. I’ve extracted his reply to avoid bulk criticism:

If the user later changes their mind about one of those judgments, then yes, the current minimal CLI requires them to run it again with the corrected input. I agree that wouldn't be good UX for a full application, but that's not what I'm trying to build here. Adding the ability to add, edit, or delete variations and immediately recalculate the ranking is straightforward and doesn't change the decision procedure being demonstrated.

#5576​·​Dennis HackethalOP, about 3 hours ago

But I don't think adding “while I wear one green hat,” “while I wear two green hats,” etc. to the axial-tilt explanation necessarily varies the explanation at all.

If you don’t think those are genuine variations, the program should either reject them or, in light of #5553, it should give users a way to resolve disagreement about what makes a genuine variation, because such a resolution would presumably itself involve some measure of HTV and so is part of the problem of making HTV work.

As the bounty states, human input is fine within reason. It’s beginning to look like your program does relatively little compared to the amount of work it expects its users to do.

#5567​·​Dennis HackethalOP, about 4 hours ago

There are still all the normal problems of human knowledge: maybe I missed a variation, maybe I accepted a bad one, maybe someone else would judge things differently. But those same problems exist when we come up with and judge criticisms.

That’s true, but it isn’t clear how criticisms fit into the program as proposed. The BoI chapter 1 glossary (p. 31) defines:

Good/bad explanation    An explanation that is hard/easy to vary while
still accounting for what it purports to account for.

The program currently has no way to tell, neither automatically nor through human input, whether a variation of an explanation still accounts for what it purports to account for. One could run the program again with corrected inputs but as I noted in #5533, that approach won’t scale.

#5536​·​Dennis HackethalOP, 1 day ago

I don't think the program needs to choose one of the surviving variants if our current knowledge gives us no reason to choose.

If several variants of the better explanation still work and we currently have nothing that differentiates them, then I think it's fine for them to remain competing possibilities. In fact, my guess is that this is exactly how different research programs can get started: people can follow the different explanatory threads until further criticism, experiments, observations, or other new knowledge gives us a reason to distinguish them.

So I don't think the program should invent a preference between variants when our current problem situation and knowledge don't provide one. Sometimes the rational state really is that we don't yet know which variant is right. We can continue developing and testing them until we find something that differentiates them.

#5558​·​Jad Elmourad, about 10 hours ago

I would consider that a problem with the explanation, not with the HTV comparison. It's exactly the kind of arbitrariness that HTV is supposed to expose.

Yes but if the program is an accurate representation/use of HTV, then the program should expose it. The program asks the user for variations in service of exposing it. But that doesn’t work in this case. I think that’s a problem.

#5566​·​Dennis HackethalOP, about 4 hours ago

I don't think it follows that a competing explanation would also have uncountably many working variants just because it involves continuous quantities.

The grass example is easy to vary precisely because there's no explanation for why the amount should be 1kg rather than 0.9kg, 0.95kg, etc. If 1kg doesn't work, I can just keep changing the number. Nothing in the explanatory argument constrains it.

But suppose grass really did cure the disease and we actually understood how. Maybe a particular compound in the grass interacts with some biological mechanism, and a certain concentration is required for the effect. The explanation might allow a whole range of effective dosages rather than one exact number, but that range would itself be explained and constrained by the mechanism.

I wouldn't consider every possible dosage within that range a different variation of the explanation. They're different cases covered by the same explanation. Saying “this mechanism works within this dosage range” is one explanatory claim, even if there are infinitely many numerical values inside the range.

So I think there's a difference between an explanation containing a continuous variable and an explanation whose parameters can be changed arbitrarily without explanatory reason. The first can be perfectly constrained by the explanatory structure. The second is exactly what I understand easy-to-vary to mean.

This also comes back to the point I made in #5553: the program relies on the user's understanding of the explanatory argument. A knowledgeable user wouldn't enter 0.9kg, 0.9001kg, 0.90001kg, etc. as infinitely many distinct explanatory variations if they understand them as instances of one explained dosage range.

#5561​·​Jad Elmourad, about 8 hours ago

I agree that people can disagree about what counts as a variation versus a completely different explanation. I don't agree that the program itself needs to recognize the difference.

The program isn't intended to distinguish a variation from a completely different explanation. That's something the user has to decide. In fact, I don't see how a program could make that distinction in general without being a general intelligence that actually comprehends the problem situation and the explanations involved.

And people themselves can disagree about what counts as a variation. That's unavoidable because it depends on how they understand the underlying explanatory argument. What looks like a harmless change to me might look to someone with a deeper understanding like a change that completely breaks the explanation.

So I don't think different people getting different results is necessarily a problem. If I understand an explanation poorly, I may think lots of its details can be changed independently. Once I understand more of the connections between those details, I may realize that many of those variations don't actually work. On the other hand, an expert might also know valid ways of varying an explanation that I would never have thought of. The result reflects our current understanding, and that can change as our knowledge changes.

This is also part of the broader point I made in #5553: the program operates on the user's current understanding of the problem and explanations rather than independently understanding them for the user.

#5557​·​Jad Elmourad, about 10 hours ago

I agree that people can disagree about what counts as a variation versus a completely different explanation. I don't agree that the program itself needs to recognize the difference.

The program isn't intended to distinguish a variation from a completely different explanation. That's something the user has to decide. In fact, I don't see how a program could make that distinction in general without being a general intelligence that actually comprehends the problem situation and the explanations involved.

And people themselves can disagree about what counts as a variation. That's unavoidable because it depends on how they understand the underlying explanatory argument. What looks like a harmless change to me might look to someone with a deeper understanding like a change that completely breaks the explanation.

So I don't think different people getting different results is necessarily a problem. If I understand an explanation poorly, I may think lots of its details can be changed independently. Once I understand more of the connections between those details, I may realize that many of those variations don't actually work. On the other hand, an expert might also know valid ways of varying an explanation that I would never have thought of. The result reflects our current understanding, and that can change as our knowledge changes.

This is also part of the broader point I made in #5553: the program operates on the user's current understanding of the problem and explanations rather than independently understanding them for the user.

#5557​·​Jad Elmourad, about 10 hours ago

I think this is where the problem/question given to the program matters.

If the problem I'm trying to answer is “Why does Earth have seasons?”, then replacing Earth with Mars doesn't give me another working variation of the explanation of Earth's seasons. I've changed the phenomenon I'm trying to explain. Applying the same underlying theory to explain seasons on Mars seems to me like an example of its reach, not a variation of its explanation of Earth's seasons.

This is one reason the program asks for the question first. Whether a proposed variation still works can't be judged independently of what we're trying to explain.

As I explained in #5553, the program relies on the user's understanding of both the problem situation and the explanation. So I agree that reach and easy-to-vary shouldn't be confused, but I don't think the program requires us to confuse them. The user has to judge whether they've varied an explanation while preserving what it was supposed to explain, or instead applied the explanation to a different problem.

And of course people can disagree about that distinction, because they can understand the problem situation and explanatory argument differently. That's part of the human judgment the program deliberately leaves to the user.

#5556​·​Jad Elmourad, about 10 hours ago

As I argued in #5554, if the number of green hats is genuinely part of an explanation and can be changed arbitrarily without affecting anything, then I think that really does expose an easy-to-vary part of the explanation.

But I don't think adding “while I wear one green hat,” “while I wear two green hats,” etc. to the axial-tilt explanation necessarily varies the explanation at all.

If my explanation is that Earth's seasons result from its axial tilt and the resulting relationship between Earth and the Sun, whether I happen to be wearing one green hat or a thousand isn't part of that explanatory argument. Appending an unrelated fact to the English sentence doesn't change the explanation it expresses.

If, on the other hand, I genuinely claim that my hat is part of the explanation—say, that Earth's seasons occur because of axial tilt and because I'm wearing exactly one green hat—then changing the number of hats would be a genuine variation. But in that case I really have made the explanation worse by adding an arbitrary component that isn't constrained by what I'm trying to explain.

So I think there's a difference between varying an explanation and varying the string of English used to express it. The program relies on the user to understand that distinction, for the same reason I described in #5553: it operates on the user's understanding of the explanatory argument, not on arbitrary syntactic changes to its wording.

On that understanding, I don't think both explanations become equally easy to vary merely because infinitely many irrelevant statements can be appended to the sentences expressing them.

#5555​·​Jad Elmourad, about 11 hours ago

As I explained in #5553, the program operates on the user's current understanding of the explanation.

In this case, though, I think the green-hat example actually illustrates what it means for an explanation to be easy to vary.

Suppose my explanation really is “God causes the seasons while wearing one green hat,” and I genuinely think I can change that to two hats, three hats, a thousand hats, etc. without affecting the explanation at all. Then the number of hats is completely unconstrained by what I'm trying to explain. Nothing in the explanation tells me why it should be one rather than two or a thousand.

I would consider that a problem with the explanation, not with the HTV comparison. It's exactly the kind of arbitrariness that HTV is supposed to expose.

Of course, the program isn't going to enumerate infinitely many hats. It only works with the variations the user actually comes up with. But if I can keep producing arbitrary variations without affecting the explanatory argument, that seems like evidence that the explanation is easy to vary, not a reason to reject the method.

#5554​·​Jad Elmourad, about 11 hours ago

Take the question: Why do seasons occur?

Should credit Deutsch for the example. Reference BoI chapter 1.

#5525​·​Dennis HackethalOP, 1 day ago

She spends part of the year in Hades…

Hades is god the underworld, not a place.

#5524​·​Dennis HackethalOP, 1 day ago