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#5534·Dennis HackethalOP revised 4 days agoWhen variations are given for both competing explanations, the user is none the wiser which variation of the ‘better’ explanation he should adopt. There’s no clear preference:
Whenever a wide range of variant theories can account equally well for the phenomenon they are trying to explain, there is no reason to prefer one of them over the others, so advocating a particular one in preference to the others is irrational.
#5526 is an example. Even ignoring the obviously false outcome, which I caused for illustrative purposes, we don’t know which variation of the better explanation to prefer.
This is out of scope for the bounty. The bounty merely says the program must “Return a ranking indicating which explanation is better, worse, or equal.” It doesn’t say the program has to specify which variation.
#5572·Jad Elmourad, 3 days agoI think the program does expose it, given inputs that reflect the user's genuine understanding of the explanations.
If I genuinely regard “axial tilt while I wear one green hat,” “axial tilt while I wear two green hats,” etc. as distinct working variations of the axial-tilt explanation, then I've told the program that the hat count is part of the explanation and can be varied freely. In that case, I think it's completely fair for HTV to judge the explanation easier to vary.
If I instead understand the hat as an irrelevant fact that has nothing to do with the axial-tilt explanation, then I shouldn't submit changes in my hat count as variations of that explanation in the first place.
The program can't accept my judgment that these are genuine variations and then independently override that judgment because it “knows” they're actually irrelevant. Doing that would require the program itself to understand what is doing explanatory work. That's precisely the part I'm outsourcing to the user.
So I don't think this example shows that the program fails to expose easy-to-varyness. It shows that the result depends on which changes the user genuinely judges to be variations of the explanation—which is the same point I made in #5553 and #5555.
The program can't accept my judgment that these are genuine variations and then independently override that judgment because it “knows” they're actually irrelevant. Doing that would require the program itself to understand what is doing explanatory work. That's precisely the part I'm outsourcing to the user.
Fair enough.
#5592·Dennis HackethalOP, 3 days agoRevision 12 says:
Isn’t the assignment of positive scores, of positive reasons to prefer one theory over another, a kind of justificationism? Deutsch criticizes justificationism throughout The Beginning of Infinity, but isn’t an endorsement of a theory as ‘good’ a kind of justification?
I should know better since I recently wrote about how justifying a preference for a theory is fine (as opposed to justifying the claim that a theory is true).
As of 2026-09-02, I’ve removed that part from the blog post.
#3069·Dennis HackethalOP revised 10 months agoMy critique of David Deutsch’s The Beginning of Infinity as a programmer. In short, his ‘hard to vary’ criterion at the core of his epistemology is fatally underspecified and impossible to apply.
Deutsch says that one should adopt explanations based on how hard they are to change without impacting their ability to explain what they claim to explain. The hardest-to-change explanation is the best and should be adopted. But he doesn’t say how to figure out which is hardest to change.
A decision-making method is a computational task. He says you haven’t understood a computational task if you can’t program it. He can’t program the steps for finding out how ‘hard to vary’ an explanation is, if only because those steps are underspecified. There are too many open questions.
So by his own yardstick, he hasn’t understood his epistemology.
You will find that and many more criticisms here: https://blog.dennishackethal.com/posts/hard-to-vary-or-hardly-usable
Revision 12 says:
Isn’t the assignment of positive scores, of positive reasons to prefer one theory over another, a kind of justificationism? Deutsch criticizes justificationism throughout The Beginning of Infinity, but isn’t an endorsement of a theory as ‘good’ a kind of justification?
I should know better since I recently wrote about how justifying a preference for a theory is fine (as opposed to justifying the claim that a theory is true).
#5588·Jad Elmourad, 3 days agoOne 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.
I think this is fair. You can treat new knowledge and criticism as changing the problem situation within which HTV operates, or more narrowly as filtering which explanations still work before applying HTV. I think those are functionally equivalent; if you want to call the latter preference formation outside HTV, I'm fine with that.
It sounds like you’re agreeing, in which case this shouldn’t be marked as a criticism.
#5586·Jad Elmourad, 3 days agoHow does this show that HTV is unrelated to finding truth?
You say:
But guess 1 and 2 are plausible and I see no reason to prefer one over the other.
That's exactly how I see it. Before looking up the historical evidence, both seem like good explanations given what we know. So HTV giving us no preference between them seems like the right result at that point.
Once we acquire new knowledge that distinguishes them, the problem situation changes, as I explained in #5562.
I don't see why HTV failing to distinguish two good explanations before we have the knowledge that distinguishes them means it's unrelated to truth.
I don't see why HTV failing to distinguish two good explanations before we have the knowledge that distinguishes them means it's unrelated to truth.
Because it doesn’t help us form a preference in a factual matter like the Pop-Tart question. HTV is not involved.
#5585·Dennis HackethalOP, 3 days agoSo 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.
HTV could still be part of the process, but DD’s claim was that all rationality boils down to HTV.
I'm not defending DD's claim. My claim is that HTV can be implemented.
#5585·Dennis HackethalOP, 3 days agoSo 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.
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.
I think this is fair. You can treat new knowledge and criticism as changing the problem situation within which HTV operates, or more narrowly as filtering which explanations still work before applying HTV. I think those are functionally equivalent; if you want to call the latter preference formation outside HTV, I'm fine with that.
#5571·Dennis HackethalOP, 3 days agoBut 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.
I think this is the same basic point as #5577.
#5580·Dennis HackethalOP, 3 days agoBeing 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.
How does this show that HTV is unrelated to finding truth?
You say:
But guess 1 and 2 are plausible and I see no reason to prefer one over the other.
That's exactly how I see it. Before looking up the historical evidence, both seem like good explanations given what we know. So HTV giving us no preference between them seems like the right result at that point.
Once we acquire new knowledge that distinguishes them, the problem situation changes, as I explained in #5562.
I don't see why HTV failing to distinguish two good explanations before we have the knowledge that distinguishes them means it's unrelated to truth.
#5562·Jad Elmourad, 3 days agoI 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.
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.
#5573·Dennis HackethalOP, 3 days agoI 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).
I don't think test results need some separate formal mechanism for being “fed back” into HTV.
This is the same point I made in #5562. A test result is new knowledge, and new knowledge changes the problem situation and therefore what counts as a working explanation.
#5573·Dennis HackethalOP, 3 days agoI 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).
It does. Preference formation is the point of the program.
I don't think preference formation requires the program to always select exactly one variant.
If several variants are equally hard to vary given everything I currently know, then “equally hard to vary” is itself the result of the comparison. I don't currently have a rational reason from HTV to prefer one over the others.
I don't think the program should invent a preference when the current problem situation doesn't give us one. The variants can remain competing possibilities until we learn something that differentiates them.
#5569·Dennis HackethalOP, 3 days agoSo I don't think different people getting different results is necessarily a problem.
#5531 doesn’t say that.
Fair, I didn't mean to imply that #5531 says different people getting different results is itself a problem. I was explaining why I think disagreement about what counts as a variation is okay, even when that disagreement leads to different results.
#5570·Dennis HackethalOP, 3 days agoI 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.”
#5562·Jad Elmourad, 3 days agoI 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.
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.
#5576·Dennis HackethalOP, 3 days agoOne 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.
@jadelmourad be sure to submit separate criticisms separately. You benefit because it means I need to address each criticism individually, not in ‘bulk’. (See #5546, keyword ‘bulk’.)
#5567·Dennis HackethalOP, 3 days agoBut 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.
I don't think those are genuine variations, so I wouldn't input them when running the program. But someone else might genuinely think they are.
The program can't decide which of us is right without itself understanding the explanation and the problem situation—in other words, without being a general intelligence. That's the point I just made in #5572, and more generally in #5553 and #5557.
At the current stage, without AGI, I think any work that requires that kind of understanding and creative judgment necessarily has to be outsourced to the user. The program then operates on the judgments the user supplies.
#5536·Dennis HackethalOP, 4 days agoThere 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.
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.
Extract out separate criticism to prevent bulk criticism
I think the program already gets this through human input.
The prompt isn't asking the user to enter arbitrary changes. It specifically asks:
“Enter variations of this explanation that would still work to explain the same thing.”
So by entering a variation, the user is making the judgment that it still accounts for what the original explanation was supposed to account for. That's intentionally a human judgment, just like the other judgments I've discussed in #5553.
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.
I think the program already gets this through human input.
The prompt isn't asking the user to enter arbitrary changes. It specifically asks:
“Enter variations of this explanation that would still work to explain the same thing.”
So by entering a variation, the user is making the judgment that it still accounts for what the original explanation was supposed to account for. That's intentionally a human judgment, just like the other judgments I've discussed in #5553.
#5558·Jad Elmourad, 3 days agoI 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.
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).
#5566·Dennis HackethalOP, 3 days agoI 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.
I think the program does expose it, given inputs that reflect the user's genuine understanding of the explanations.
If I genuinely regard “axial tilt while I wear one green hat,” “axial tilt while I wear two green hats,” etc. as distinct working variations of the axial-tilt explanation, then I've told the program that the hat count is part of the explanation and can be varied freely. In that case, I think it's completely fair for HTV to judge the explanation easier to vary.
If I instead understand the hat as an irrelevant fact that has nothing to do with the axial-tilt explanation, then I shouldn't submit changes in my hat count as variations of that explanation in the first place.
The program can't accept my judgment that these are genuine variations and then independently override that judgment because it “knows” they're actually irrelevant. Doing that would require the program itself to understand what is doing explanatory work. That's precisely the part I'm outsourcing to the user.
So I don't think this example shows that the program fails to expose easy-to-varyness. It shows that the result depends on which changes the user genuinely judges to be variations of the explanation—which is the same point I made in #5553 and #5555.
#5561·Jad Elmourad, 3 days agoI 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.
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.
#5557·Jad Elmourad, 3 days agoI 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.
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.”