[META: To be fully honest, I don’t think the comments section of this post is the best place to be having this discussion. That I am posting this comment regardless is due to the fact that I have seen you posting about your hobby-horse—the so-called “problem of the criterion”—well in excess of both the number of times and places I think it should be mentioned—including on this post whose comments section I just said I don’t think is suited to this discussion. I am sufficiently annoyed by this that it has provoked a response from me; nonetheless, I will remove this comment should the author of the post request it.]
Worth saying, I think, that this is fully generally true that there’s no observer-independent fact of the matter about whether X “is” Y.
The linked post does not establish what it claims to establish. The claim in question is that “knowledge” cannot be grounded, because “knowledge” requires “justification”, which in turn depends on other knowledge, which requires justification of its own, ad infinitum. Thus no “true” knowledge can ever be had, throwing the whole project of epistemology into disarray. (This is then sometimes used as a basis to make extravagantly provocative-sounding claims like “there is no fact of the matter about anything”.)
Of course, the obvious response to this is to point out that in fact, humans have been accumulating knowledge for quite some time; or at the very least, humans have been accumulating something that very much looks like “knowledge” (and indeed many people are happy to call it “knowledge”). This obvious objection is mainly “addressed” in the linked post by giving it the name of “pragmatism”, and behaving as though the act of labeling an objection thereby relieves that objection of its force.
However, I will not simply reassert the obvious objection here. Instead, I will give two principled arguments, each of which I believe suffices to reject the claims offered in the linked post. (The two arguments in question are mostly independent of each other, so I will present them separately.)
First, there is the question of whether epistemological limitations have significant ontological implications. There is a tendency for “problem of the criterion” adherents to emit sentences that imply they believe this, but—so far as I can tell—they offer no justification for this belief.
Suppose it is the case that I cannot ever know for sure that the sky is blue. (We could substitute any other true fact here, but “the sky is blue” seems to be something of a canonical example.) Does it then follow that there is no objective fact about the color of the sky? If so, why? Through what series of entanglements—causal, logical, or otherwise—does knowing some fact about my brain permit you to draw a conclusion about the sky (especially a conclusion as seemingly far-fetched as “the sky doesn’t have a color”)?
(Perhaps pedants will be tempted to object here that “color” is a property of visual experiences, not of physical entities, so it is in fact true that the sky has no “color” if no one is there to see it. This is where the substitution clause above enters: you may replace “the sky is blue” with any true claim you wish, at any desired level of specificity, e.g. “the majority of light rays emitted from the Sun whose pathway through the atmosphere undergoes sufficient scattering to reach ground level will have an average wavelength between 440-470 nm”.)
If you bite this particular bullet—meaning, you believe that my brain’s (in)ability to know something with certainty implies that that something in fact does not exist—then I would have you reconcile the myriad of issues this creates with respect to physics, logic, and epistemology. (Starter questions include: do I then possess the ability to alter facts as I see fit, merely by strategically choosing what I do and do not find out? By what mechanism does this seemingly miraculous ability operate? Why does it not violate known physical principles such as locality, or known statistical principles such as d-separation?)
And—conversely—if you do not bite the bullet in question, then I would have you either (a) find some alternative way to justify the (apparent) ontological commitments implied by claims such as “there’s no observer-independent fact of the matter about whether X is Y”, or (b) explain why such claims actually don’t carry the ontological commitments they very obviously seem to carry.
(Or (c): explain why you find it useful, when making such claims, to employ language in a way that creates such unnecessary—and untrue—ontological commitments.)
In any of the above cases, however, it seems to me that the original argument has been refuted: regardless of which prong of the 4-lemma you choose, you cannot maintain your initial assertion that “there is no objective fact of the matter about anything”.
The first argument attacked the idea that fundamental epistemological limitations have broader ontological implications; in doing so, it undermines the wild phrasing I often see thrown around in claims associated with such limitations (e.g. the “problem of the criterion”), and also calls into question the degree to which such limitations are important (e.g. if they don’t have hugely significant implications for the nature of reality, why does “pragmatism” not suffice as an answer?).
The second argument, however, attacks the underlying claim more directly. Recall the claim in question:
[...] that “knowledge” cannot be grounded, because “knowledge” requires “justification”, which in turn depends on other knowledge, which requires justification of its own, ad infinitum.
Is this actually the case, however? Let’s do a case analysis; we’ll (once again) use “the sky is blue” as an example:
Suppose I believe that the sky is blue. How might I have arrived at such a belief? There are multiple possible options (e.g. perhaps someone I trust told me that it’s blue, or perhaps I’ve observed it to be blue on every past occasion, so I believe it to be blue right now as well), but for simplicity’s sake we’ll suppose the most direct method possible: I’m looking at it, right now, and it’s blue.
However (says the problemist of the criterion) this is not good enough. For what evidence do you have that your eyes, specifically, are trustworthy? How do you know that your senses are not deceiving you at this very moment? The reliability of one’s senses is, in and of itself, a belief that needs further justification—and so, the problemist triumphantly proclaims, the ladder of infinite descent continues.
But hold on: there is something very strange about this line of reasoning. Humans do not, as a rule, ordinarily take their senses to be in doubt. Yes, there are exceptional circumstances (optical illusions, inebriation, etc.) under which we have learned to trust our senses less than we usually do—but the presence of the word “usually” in that sentence already hints at the fact that, by default, we take our senses as a given: trustworthy, not because of some preexisting chain of reasoning that “justifies” it by tying it to some other belief(s), but simply… trustworthy. Full stop.
Is this an illegal move, according to the problemist? After all, the problemist seems to be very adamant that one cannot believe anything without justification, and in taking our senses as a given, we certainly seem to be in violation of this rule...
...and yet, most of the time things seem to work out fine for us in real life. Is this a mere coincidence? If it’s true that we are actually engaging in systematically incorrect reasoning—committing an error of epistemology, an illegal move according to the rules that govern proper thought—and moreover, doing so constantly throughout every moment of our lives—one might expect us to have run into some problems by now. Yet by and large, the vast majority of humanity is able to get away with trusting their senses in their day-to-day lives; the universe, for whatever reason, does not conspire to punish our collective irrationality. Is this a coincidence, akin to the coincidences that sometimes reward, say, an irrational lottery ticket buyer? If so, there sure do seem to be quite a few repeat lottery winners on this planet of ours...
Of course, it isn’t a coincidence: the reason we can get away with trusting our senses is because our senses actually are trustworthy. And it’s also no coincidence that we believe this implicitly, from the very moment we are born, well before any of us had an opportunity to learn about epistemology or the “problem of the criterion”. The reliability of our senses, as well as the corresponding trust we have in those senses, are both examples of properties hardcoded into us by evolution—the result of billions upon billions of years of natural selection on genetic fitness.
There were, perhaps, organisms on whom the problemist’s argument would have been effective, in the ancient history of the Earth—organisms who did not have reliable senses, and who, if they had chosen to rely unconditionally on whatever senses they possessed, would have been consistently met with trouble. (And if such organisms did not exist, we can still imagine that they did.) But if such organisms did exist back then, they no longer do today: natural selection has weeded them out, excised them from the collective genetic pool for being insufficiently fit. The harsh realities of competition permit no room for organisms to whom the “problem of the criterion” poses a real issue.
And as for the problemist’s recursive ladder of justification? It runs straight into the hard brick wall called “evolutionary hardcoding”, and proceeds no further than that: the buck stops immediately. Evolution neither needs nor provides justification for the things it does; it merely optimizes for inclusive genetic fitness. Even attempting to apply the problemist’s tried-and-true techniques to the alien god produces naught but type and category errors; the genre of analysis preferred by the problemist finds no traction whatsoever. Thus, the problemist of the criterion is defeated, and with him so too vanishes his problem.
Incidentally, what genre of analysis does work on evolution? Since evolution is an optimization process, the answer should be obvious enough: the mathematical study of optimization, with all of the various fields and subfields associated with it. But that is quite beyond the scope of this comment, which is more than long enough as it is. So I leave you with this, and sincerely request that you stop beating your hobby-horse to death: it is, as it were, already dead.
And as for the problemist’s recursive ladder of justification? It runs straight into the hard brick wall called “evolutionary hardcoding”, and proceeds no further than that: the buck stops immediately. Evolution neither needs nor provides justification for the things it does; it merely optimizes for inclusive genetic fitness. Even attempting to apply the problemist’s tried-and-true techniques to the alien god produces naught but type and category errors; the genre of analysis preferred by the problemist finds no traction whatsoever. Thus, the problemist of the criterion is defeated, and with him so too vanishes his problem.
This feels like violent agreement with my arguments in the linked post, so I think you’re arguing against some different reading of the implications of the problem of the criterion than what it does imply. It doesn’t imply there is literally no way to ground knowledge, but that ground is not something especially connected to traditional notions of truth or facts, but rather in usefulness to the purpose of living.
This mostly comes up when we try to assess things like what does it mean for something to “be” an “agent”. We then run headlong into the grounding problem and this becomes relevant, because what it means for something to “be” an “agent” ends up connected to what end we need to categorize the world, rather than how the world actually “is”, since the whole point is that there is no fact of the matter about what “is”, only a best effort assessment of what’s useful (and one of the things that’s really useful is predicting the future, which generally requires building models that correlate to past evidence).
This feels like violent agreement with my arguments in the linked post, so I think you’re arguing against some different reading of the implications of the problem of the criterion than what it does imply.
Perhaps I am! But if so, I would submit that your chosen phrasings of your claims carry unnecessary baggage with them, and that you would do better to phrase your claims in ways that require fewer ontological commitments (even if they become less provocative-sounding thereby).
It doesn’t imply there is literally no way to ground knowledge, but that ground is not something especially connected to traditional notions of truth or facts, but rather in usefulness to the purpose of living.
In a certain sense, yes. However, I assert that “traditional notions of truths or facts” (at least if you mean by that phrase what I think you do) are in fact “useful to the purpose of living”, in the following sense:
It is useful to have senses that tell you the truth about reality (as opposed to deceiving you about reality). It is useful to have a brain that is capable of performing logical reasoning (as opposed to a brain that is not capable of performing logical reasoning). It is useful to have a brain that is capable of performing probabilistic reasoning (as opposed to a brain that is not, etc. etc).
To the extent that we expect such properties to be useful, we ought also to expect that we possess those properties by default. Otherwise we would not exist in the form we do today; some superior organism would be here in our place, with properties more suited to living in this universe than ours. Thus, “traditional notions of truths and facts” remain grounded; there are no excess degrees of freedom available here.
To what extent do you find the above explanation unsatisfying? And if you do not find it unsatisfying, then (I repeat): what is the use of talking about the “problem of the criterion”, beyond (perhaps) the fact that it allows you to assert fun and quirky and unintuitive (and false) things like “facts don’t exist”?
This mostly comes up when we try to assess things like what does it mean for something to “be” an “agent”. We then run headlong into the grounding problem and this becomes relevant, because what it means for something to “be” an “agent” ends up connected to what end we need to categorize the world, rather than how the world actually “is”, since the whole point is that there is no fact of the matter about what “is”, only a best effort assessment of what’s useful (and one of the things that’s really useful is predicting the future, which generally requires building models that correlate to past evidence).
I agree that this is a real difficulty that people run into. I disagree with [what I see as] your [implicit] claim that the “problem of the criterion” framing provides any particular tools for addressing this problem, or that it’s a useful framing in general. (Indeed, the sequence I just linked constitutes what I would characterize as a “real” attempt to confront the issue, and you will note the complete absence of claims like “there is no such thing as knowledge” in any of the posts in question; in the absence of such claims, you will instead see plenty of diagrams and mathematical notation.)
It should probably be obvious by now that I view the latter approach as far superior to the former. To the extent that you think I’m not seeing some merits to the former approach, I would be thrilled to have those merits explained to me; right now, however, I don’t see anything.
To what extent do you find the above explanation unsatisfying? And if you do not find it unsatisfying, then (I repeat): what is the use of talking about the “problem of the criterion”, beyond (perhaps) the fact that it allows you to assert fun and quirky and unintuitive (and false) things like “facts don’t exist”?
To me this is like asking what’s the point in talking about a Theory of Everything when trying to talk about physics. You might complain you can do a lot of physics without it, yet we still find it useful to have a theory that unifies physics at a fundamental level (even if we keep failing to find one). I argue that the problem of the criterion fills a conceptually similar niche in epistemology: it’s the fundamental thing to be understood in order to be able to say anything else meaningful and not inconsistent about how we know or what we know, which is itself fundamental to most activity. Thus it is often quite useful to appeal to because lots of deconfusion research, like this post, are ultimately consequences of the problem of the criterion, and so I find most object-level arguments, like those found in this post, a certain kind of wasted motion that could be avoided if only the problem of the criterion were better understood.
I agree that this is a real difficulty that people run into. I disagree with [what I see as] your [implicit] claim that the “problem of the criterion” framing provides any particular tools for addressing this problem, or that it’s a useful framing in general. (Indeed, the sequence I just linked constitutes what I would characterize as a “real” attempt to confront the issue, and you will note the complete absence of claims like “there is no such thing as knowledge” in any of the posts in question; in the absence of such claims, you will instead see plenty of diagrams and mathematical notation.)
I think the thing the framing of the sequence you link and the way most people approach this is missing something fundamental about epistemology that lets one get confused, specifically by easily forgetting that one’s knowledge is always contingent on some assumption that one may not even be able to see, and so mistakes one’s own perspective for objectivity. As for what tools understanding the problem of the criterion provides, I’d say it’s more like a mindset of correctly calibrated epistemic humility. Not to say that grokking the problem of the criterion makes you perfectly calibrated in making predictions, but to say it requires adopting a mindset that is sufficient to achieve the level of epistemic humility/update fluidity necessary to become well calibrated or, dare we say, Bayesian rational.
(Note: I realize my claim about grokking the problem of the criterion sets up a potential “no true Scotsman” situation where anyone who claims to grok the problem of the criterion and then seems to lack this capacity for update fluidity can be dismissed as not really grokking it. I’m not really looking to go that far, but I want to say that this claim is, I believe, predictive enough to make useful inferences.)
It should probably be obvious by now that I view the latter approach as far superior to the former.
Maybe it is for some people (you wouldn’t be the first person to make this claim). Others do seem to find my approach useful. Perhaps the whole point of this should be that not everyone is necessarily reasoning from the same base assumptions, and thus the ground of truth is unstable enough that what seem like reasonable explanations cannot be sure to be arbitrarily convincing. To be fair, Eliezer doesn’t miss this point, but it seems poorly enough appreciated that I often find cause to remind people of it.
If I really wanted to be pointed about it, I think you’d be less annoyed with me if you grokked the point both Eliezer and I are trying to make in different ways about how epistemology grounds out, since taken to its extreme we must accept that the same lines of reasoning don’t work for everyone on a practical level, by which I mean that even if you show someone correct math, they may yet not be convinced by it, and this is epistemically relevant and not to be dismissed since we are each performing our own reckoning of what to accept as true, no matter how much we may share in common (which, for what it’s worth, brings us right back to the core of the intentional stance and the object level concerns of the OP!).
That I am posting this comment regardless is due to the fact that I have seen you posting about your hobby-horse—the so-called “problem of the criterion”—well in excess of both the number of times and places I think it should be mentioned
It’s not been mentioned enough, since the point has not generally sunk in.
The first argument attacked the idea that fundamental epistemological limitations have broader ontological implications; in doing so, it undermines the wild phrasing I often see thrown around in claims associated with such limitations (e.g. the “problem of the criterion”), and also calls into question the degree to which such limitations are important (e.g. if they don’t have hugely significant implications for the nature of reality, why does “pragmatism” not suffice as an answer?).
Pragmatism isn’t a sufficient answer, because it can show that we are accumulating certain kinds of knowledge, namely the ability to predict things and make things, but does not show that we are accumulating other kinds , specifically ontological knowledge, ie. successful correspondence to reality.
You can objectively show that a theory succeeds or fails at predicting observations, and at the closely related problem of achieving practical results . It is is less clear whether an explanation succeeds in explaining, and less clear still whether a model succeeds in corresponding to the territory. The lack of a test for correspondence per se, ie. the lack of an independent “standpoint” from which the map and the territory can be compared, is the is the major problem in scientific epistemology. Its the main thing that keeps non-materialist ontology going. And the lack of direct testability is one of the things that characterises philosophical problems as opposed to scientific ones—you can’t test ethics for correctness,you can’t test personal identity, you can’t test correspondence-to-reality separately from prediction-of-observation—so the “winning” or pragmatic approach is a particularly bad fit for philosophy.
The thing scientific realists care about is having an accurate model of reality, knowing what things are. If you want that, then instrumentalism is giving up something of value to you. So long as it s possible. If realistic knowledge is impossible , then ther’es no loss of value.
Far from having no ontological implications, the problem of the criterion has mainly ontological implications, since the pragmatic response works in other areas.
Of course, it isn’t a coincidence: the reason we can get away with trusting our senses is because our senses actually are trustworthy
Trustworthy or reliable at what?
You cannot ascertain an ontologicaly correct model of reality just by looking at things. A model is a theoretical structure. Multiple models can be compatible with the same sense data, so a a further criterion is needed. Of course, you can still do predictive, instrumental stuff with empiricism.
And as for the problemist’s recursive ladder of justification? It runs straight into the hard brick wall called “evolutionary hardcoding”, and proceeds no further than that: the buck stops immediately. Evolution neither needs nor provides justification for the things it does; it merely optimizes for inclusive genetic fitness.
That’s part of the problem, not part of the solution. If evolution is optimising for genetic fitness, then it is not optimising for the ability to achieve a correct ontology … after all , a wrong but predictive model is good enough for survival.
So I leave you with this, and sincerely request that you stop beating your hobby-horse to death: it is, as it were, already dead.
It’s not been mentioned enough, since the point has not generally sunk in.
I find this response particularly ironic, given that I will now proceed to answer almost every one of your points simply by reiterating one of the two arguments I provided above. (Perhaps it’s generally a good idea to make sure the point of someone’s comment has “sunk in” before replying to them.)
Pragmatism isn’t a sufficient answer, because it can show that we are accumulating certain kinds of knowledge, namely the ability to predict things and make things, but does not show that we are accumulating other kinds , specifically ontological knowledge, ie. successful correspondence to reality.
Suppose this is true (i.e. suppose we have no means of accumulating “ontological knowledge”). I repeat the first of my two arguments: by what mechanism does this thereby imply that no ontological facts of any kind exist? Is it not possible both that (a) the sky exists and has a color, and (b) I don’t know about it? If you claim this is not possible, I should like to see you defend this very strong positive claim; conversely, if you do not make such a claim, the idea that the “problem of the criterion” has any ontological implications whatsoever is immediately dismissed.
The thing scientific realists care about is having an accurate model of reality, knowing what things are. If you want that, then instrumentalism is giving up something of value to you. So long as it s possible. If realistic knowledge is impossible , then ther’es no loss of value.
I repeat the second of my two arguments: to build an accurate model of reality requires taking some assumptions to be foundational; mathematicians might call these “axioms”, whereas Bayesians might call them “the prior”. As long as you have such a foundation, it is possible to build models that are at least as trustworthy as the foundation itself; the limiting factor, therefore, on the accumulation of scientific knowledge—or, indeed, any other kind of knowledge—is the reliability of our foundations.
And what are our foundations? They are the sense and reasoning organs provided to us by natural selection; to the extent that they our trustworthy, the theories and edifices we build atop them will be similarly trustworthy. (Assuming, of course, that we do not make any mistakes in our construction.)
So the “problem of the criterion” reduces to the question of how reliable natural selection is at building organisms with trustworthy senses; to this question I answer “very reliable indeed.” Should you claim otherwise, I should like to see you defend this very strong positive claim; if you do not claim otherwise, then the “problem of the criterion” immediately ceases to exist.
Far from having no ontological implications, the problem of the criterion has mainly ontological implications, since the pragmatic response works in other areas.
I repeat the first of my two arguments: what ontological implications, and why? I should like to see you defend the (very strong) positive claim that such implications exist; or, alternatively, relinquish the notion that they do.
Of course, it isn’t a coincidence: the reason we can get away with trusting our senses is because our senses actually are trustworthy
Trustworthy or reliable at what?
Per my second argument: at doing whatever they need to do in order for us not to have been selected out of existence—in other words, at providing an effective correspondence between our beliefs and reality. (Why yes, this is the thing the “problem of the criterion” claims to be impossible; why yes, this philosophical rigmarole does seem to have had precisely zero impact on evolution’s ability to build such organisms.)
Should you deny that evolution has successfully built organisms with trustworthy senses, I should like to see you defend this very strong positive claim, etc. etc.
You cannot ascertain an ontologicaly correct model of reality just by looking at things. A model is a theoretical structure. Multiple models can be compatible with the same sense data, so a a further criterion is needed. Of course, you can still do predictive, instrumental stuff with empiricism.
The problem of selecting between multiple compatible models is not something I often see packaged with the “problem of the criterion” and others of its genre; it lacks the ladder of infinite descent that those interested in the genre seem to find so attractive, and so is generally omitted from such discussions. But since you bring it up: there is, of course, a principled way to resolve questions of this type as well; the heuristic version (which humans actually implement) is called Occam’s razor, whereas the ideal version is called Solomonoff induction.
This is an immensely powerful theoretical tool, mind you: since Solomonoff induction contains (by definition) every computable hypothesis, that means that every possible [way-that-things-could-be] is contained somewhere in its hypothesis space, including what you refer to as “the ontologically correct model of reality”; moreover, one of the theoretical guarantees of Solomonoff induction is that said “correct model” will become the predictor’s dominant hypothesis after a finite (and generally, quite short) amount of time.
For you to deny this would require that you claim the universe is not describable by any computable process; and I should like to see you defend this very strong positive claim, etc. etc.
That’s part of the problem, not part of the solution. If evolution is optimising for genetic fitness, then it is not optimising for the ability to achieve a correct ontology … after all , a wrong but predictive model is good enough for survival.
Per my second argument: evolution does not select over models; it selects over priors. A prior is a tool for constructing models; if your prior is non-stupid, i.e. if it doesn’t rule out some large class of hypotheses a priori, you will in general be capable of figuring out what the correct model is and promoting it to attention. For you to deny this would require that you claim non-stupid priors confer no survival advantage over stupid priors; and I should like to see you defend this very strong positive claim, etc. etc.
I repeat the first of my two arguments: by what mechanism does this thereby imply that no ontological facts of any kind exist
If “fact” means “statement known to be true” , then it follows directly.
If “fact” means “component of reality, whether know or not”, it does not follow...but that is irrelevant, since I did not deny the existence of some kind of reality.
I repeat the second of my two arguments: to build an accurate model of reality requires taking some assumptions to be foundational;
In which case, I will repeat that the only testable accuracy we have is predictive accuracy, and we do not know whether our ontological claims are accurate, because we have no direct test.
As long as you have such a foundation, it is possible to build models that are at least as trustworthy as the foundation itself;
That is a major part of the problem. Since our most fundamental assumptions aren’t based on anything else, how do we know how good they are? The only solution anyone has is to judge by results, but that just goes back to the original problem of being able to test predictiveness but not ontological correspondence.
But maybe “no worse than your assumptions” is supposed to be a triumphant refutation of my claim that everything is false...but, again, I didn’t say that.
And what are our foundations? They are the sense and reasoning organs provided to us by natural selection;
To reword my previous argument, sense data are not a sufficient foundation, because you cannot appeal to them to choose between two models that explain the same sense data.
Neither Gordon not myself are appealing to the unreliability if sense data. Even if sense data are completely reliable, the above problem holds.
So the “problem of the criterion” reduces to the question of how reliable natural selection is at building organisms with trustworthy senses;
Of course not. There are lots of animals have better senses than humans, and none of them have a clue about ontology.
But since you bring it up: there is, of course, a principled way to resolve questions of this type as well; the heuristic version (which humans actually implement) is called Occam’s razor, whereas the ideal version is called Solomonoff induction.
I know. Its completely standard to put forward simplicity criteria as the missing factor that allows you to choose between empirically adequate models .
The problem is that, while simplicity criteria allow you to select models , you need to know that they are selecting models that are more likely to correspond to reality, rather than on some other basis. SI fares particularly badly, because there is no obvious reason why a short programme should be true, or even that it is a description of reality at all .
For you to deny this would require that you claim the universe is not describable by any computable process
I see no strength to that claim at all. The universe is partly predictable by computational processes, and that’s all for we know.
It is the claim that a programme is ipso facto a description that us extraordinary.
Per my second argument: evolution does not select over models; it selects over priors. A prior is a tool for constructing models; if your prior is non-stupid, i.e. if it doesn’t rule out some large class of hypotheses a priori, you will in general be capable of figuring out what the correct model is and promoting it to attention. For you to deny this would require that you claim non-stupid priors confer no survival advantage over stupid priors; and I should like to see you defend this very strong positive claim, etc. etc
To repeat my argument yet again, evolution only needs to keep you alive and reproducing , and merely predictivene correctness is good enough for that.
you will in general be capable of figuring out what the correct model
Correct in what sense ?
The basis of my argument is the distinction between predictive accuracy and ontological correctness. Your responses keep ignoring that distinction in favour of a single notion of correctness/truth/accuracy. If you could show that the two are the same , it the one implies the other, you would be on to something.
Well, it’s a hard habit to break. Everything you are saying to me now is something I used to believe for many years, until I awoke from my dogmatic slumbers.
If “fact” means “component of reality, whether know or not”, it does not follow...but that is irrelevant, since I did not deny the existence of some kind of reality.
Well, good! It’s heartening to see we agree on this; I would ask then why it is that so many subscribers to epistemological minimalism (or some variant thereof) seem to enjoy phrasing their claims in such a way as to sound as though they are denying the existence of external reality; but I recognize that this question is not necessarily yours to answer, since you may not be one of those people.
I repeat the second of my two arguments: to build an accurate model of reality requires taking some assumptions to be foundational;
In which case, I will repeat that the only testable accuracy we have is predictive accuracy, and we do not know whether our ontological claims are accurate, because we have no direct test.
For predictive accuracy and “ontological accuracy” to fail to correspond [for some finite period of time] would require the universe to possess some very interesting structure; the longer the failure of correspondence persists, the more complex the structure in question must be; if (by hypothesis) the failure of correspondence persists indefinitely, the structure in question must be uncomputable.
Is it your belief that one of the above possibilities is the case? If so, what is your reason for this belief, and how does it contend with the (rather significant) problem that the postulated complexity must grow exponentially in the amount of time it takes for the “best” (most predictive) model to line up with the “true” model?
[The above argument seems to address the majority of what I would characterize as your “true” rejection; your comment contained other responses to me concerning sense data, natural selection, the reliability of animal senses, etc. but those seem to me mostly like minutiae unrelated to your main point. If you believe I’m mistaken about this, let me know which of those points you would like a specific response to; in the interim, however, I’m going to ignore them and jump straight to the points I think are relevant.]
The problem is that, while simplicity criteria allow you to select models , you need to know that they are selecting models that are more likely to correspond to reality, rather than on some other basis. SI fares particularly badly, because there is no obvious reason why a short programme should be true, or even that it is a description of reality at all .
The simplicity criterion does not come out of nowhere; it arises from the fact that description complexity is bounded below, but unbounded above. In other words, you can make a hypothesis as complex as you like, adding additional epicycles such that the description complexity of your hypothesis increases without bound; but you cannotdecrease the complexity of your hypothesis without bound, since for any choice of computational model there exists a minimally complex hypothesis with description length 0, beneath which no simpler hypotheses exist.
This means that for any hypothesis in your ensemble—any computable [way-that-things-could-be]—there are only finitely many hypotheses with complexity less than that of the hypothesis in question, but infinitely many hypotheses with complexity equal or greater. It follows that for any ordering whatsoever on your hypothesis space, there will exist some number n such that the complexity of the kth hypothesis H_k exceeds some fixed complexity C for any k > n… the upshot of which is that every possible ordering of your hypothesis space corresponds, in the limit, to a simplicity prior.
Does it then follow that the universe we live in must be a simple one? Of course not—but as long as the universe is computable, the hypothesis corresponding to the “true” model of the universe will live only finitely far down our list—and each additional bit of evidence we receive will, on average, halve that distance. This is what I meant when I said that the (postulated) complexity of the universe must grow exponentially in the amount of time any “correspondence failure” can persist: each additional millisecond (or however long it takes to receive one bit of evidence) that the “correspondence failure” persists corresponds to a doubling of the true hypothesis’ position number in our list.
So the universe need not be simple a priori for Solomonoff induction to work. All that is required is that the true description complexity of the universe does not exceed 2^b, where b represents the sum total of all knowledge we have accumulated thus far, in bits. That this is a truly gigantic number goes without saying; and if you wish to defend the notion that the “true” model of the universe boasts a complexity in excess of this value, you had better be prepared to come up with some truly extraordinary evidence.
For you to deny this would require that you claim the universe is not describable by any computable process
I see no strength to that claim at all. The universe is partly predictable by computational processes, and that’s all for we know.
It is the claim that a programme is ipso facto a description that us extraordinary.
This is the final alternative: the claim, not that the universe’s true description complexity is some large but finite value, but that it is actually infinite, i.e. that the universe is uncomputable.
I earlier (in my previous comment) said that “I should like to see” you defend this claim, but of course this was rhetorical; you cannot defend this claim, because no finite amount of evidence you could bring to bear would suffice to establish anything close. The only option, therefore, is for you to attempt to flip the burden of proof, claiming that the universe should be assumed uncomputable by default; and indeed, this is exactly what you did: “It is the claim that a program is ipso facto a description that is extraordinary.”
But of course, this doesn’t work. “The claim that a program can function as a description” is not an extraordinary claim at all; it is merely a restatement of how programs work: they take some input, perform some internal manipulations on that input, and produce an output. If the input in question happens to be the observation history of some observer, then it is entirely natural to treat the output of the program as a prediction of the next observation; there is nothing extraordinary about this at all!
So the attempted reversal of the burden of proof fails; the “extraordinary” claim remains the claim that the universe cannot be described by any possible program, regardless of length, and the burden of justifying such an impossible-to-justify claim is, thankfully, not my problem.
But of course, this doesn’t work. “The claim that a program can function as a description” is not an extraordinary claim at all; it is merely a restatement of how programs work: they take some input, perform some internal manipulations on that input, and produce an output. If the input in question happens to be the observation history of some observer, then it is entirely natural to treat the output of the program as a prediction of the next observation; there is nothing extraordinary about this at all!
Emphasis added. You haven’t explained how a programme functions as a description. You mentioned description, and then you started talking prediction, but you didn’t explain how they relate.
So the attempted reversal of the burden of proof fails; the “extraordinary” claim remains the claim that the universe cannot be described by any possible program, regardless of length,
The length has nothing to do with it—the fact it is a programme at all is the problem.
On the face of it, Solomonoff Inductors contain computer programmes, not explanations, not hypotheses and not descriptions. (I am grouping explanations, hypotheses and beliefs as things which have a semantic interpretation, which say something about reality . In particular, physics has a semantic interpretation in a way that maths does not.)
The Yukdowskian version of Solomonoff switches from talking about programs to talking about hypotheses as if they are obviously equivalent. Is it obvious? There’s a vague and loose sense in which physical theories “are” maths, and computer programs “are” maths, and so on. But there are many difficulties in the details. Neither mathematical equations not computer programmes contain straightforward ontological assertions like “electrons exist”. The question of how to interpret physical equations is difficult and vexed. And a Solomonoff inductor contains programmes, not typical physics equations. whatever problems there are in interpreting maths ontologically are compounded when you have the additional stage of inferring maths from programmes.
In physics, the meanings of the symbols are taught to students, rather than being discovered in the maths. Students are taught the in f=ma, f is force, is mass and a is acceleration. The equation itself , as ours maths, does not determine the meaning. For instance it has the same mathematical form as P=IV, which “means” something different. Physics and maths are not the same subject, and the fact that physics has a real-world semantics is one of the differences.
Similarly, the instructions in a programme have semantics related to programme operations, but not to the outside world. The issue is obscured by thinking in terms of source code. Source code often has meaningful symbol names , such as MASS or GRAVITY...but that’s to make it comprehensible to other programmers. The symbol names have no effect on the function and could be mangled into something meaningless but unique. And a SI executes machine code anyway..otherwise , you can’t meaningfully compare programne lengths. Note how the process of backtracking from machine code to meaningful source code is a difficult one. Programmers use meaningful symbols because you can’t easily figure out what real world problem a piece of machine code is solving from its function. One number is added to another..what does that mean? What do the quantifies represent?
Well, maybe programmes-as-descriptions doesn’t work on the basis that individual Al symbols or instructions have meanings in the way that natural language words do. Maybe the programme as a whole expresses a mathematician structure as a whole. But that makes the whole situation worse because it adds an extra step , the step of going from code to maths, to the existing problem of going from maths to ontology.
The process of reading ontological models from maths is not formal or algorithmic. It can’t be asserted that SI is the best formal epistemology we have and also that it is capable of automating scientific realism. Inasmuch as it is realistic , the step from formalism to realistic interpretation depends on human interpretation, and so is not formal. And if it SI is purely formal, it is not realistic.
But code already is maths, surely? In physics the fundamental equations are on a higher abstraction level than a calculation: generally need to be ” solved” for some set of circumstances, to obtain a more concrete equation you can calculate with. To get back to what would normally be considered a mathematical structure, you would have to reverse the original process. If you succeed in doing that, then SI is as good or bad as physics...remember, that physics still needs ontological interpretation. If you don’t succeed in doing that.. which you you might not, since there is no algorithm reliable method for doing so...then SI is strictly worse that ordinary science, since it has an extra step of translation from calculation to mathematical structure, in addition to the standard step of translation from mathematical structure to ontology.
That’s part of the problem, not part of the solution. If evolution is optimising for genetic fitness, then it is not optimising for the ability to achieve a correct ontology … after all , a wrong but predictive model is good enough for survival.
In many ways this is the crux of things. The problem of the criterion does mean that we can’t ground knowledge in the ways we had hoped to, and that we can still ground knowledge, just in something quite a bit different from the objective: namely, in some practical purpose to which we use knowledge.
It’s not been mentioned enough, since the point has not generally sunk in.
For what it’s worth, I feel exactly the same way about the robustness of Goodhart and I’ll keep beating that drum as long as I have to. Luckily no one much objects that Goodharting is a problem, whereas everyone seems to be annoyed with epistemology that makes a fairly simple point that is counterintuitive to the experience of being able to make use of knowledge to do useful things, and thinking this is somehow contrary to the epistemological point being made that becomes relevant when you try to ground concepts rather than just use them as you find them.
[META: To be fully honest, I don’t think the comments section of this post is the best place to be having this discussion. That I am posting this comment regardless is due to the fact that I have seen you posting about your hobby-horse—the so-called “problem of the criterion”—well in excess of both the number of times and places I think it should be mentioned—including on this post whose comments section I just said I don’t think is suited to this discussion. I am sufficiently annoyed by this that it has provoked a response from me; nonetheless, I will remove this comment should the author of the post request it.]
The linked post does not establish what it claims to establish. The claim in question is that “knowledge” cannot be grounded, because “knowledge” requires “justification”, which in turn depends on other knowledge, which requires justification of its own, ad infinitum. Thus no “true” knowledge can ever be had, throwing the whole project of epistemology into disarray. (This is then sometimes used as a basis to make extravagantly provocative-sounding claims like “there is no fact of the matter about anything”.)
Of course, the obvious response to this is to point out that in fact, humans have been accumulating knowledge for quite some time; or at the very least, humans have been accumulating something that very much looks like “knowledge” (and indeed many people are happy to call it “knowledge”). This obvious objection is mainly “addressed” in the linked post by giving it the name of “pragmatism”, and behaving as though the act of labeling an objection thereby relieves that objection of its force.
However, I will not simply reassert the obvious objection here. Instead, I will give two principled arguments, each of which I believe suffices to reject the claims offered in the linked post. (The two arguments in question are mostly independent of each other, so I will present them separately.)
First, there is the question of whether epistemological limitations have significant ontological implications. There is a tendency for “problem of the criterion” adherents to emit sentences that imply they believe this, but—so far as I can tell—they offer no justification for this belief.
Suppose it is the case that I cannot ever know for sure that the sky is blue. (We could substitute any other true fact here, but “the sky is blue” seems to be something of a canonical example.) Does it then follow that there is no objective fact about the color of the sky? If so, why? Through what series of entanglements—causal, logical, or otherwise—does knowing some fact about my brain permit you to draw a conclusion about the sky (especially a conclusion as seemingly far-fetched as “the sky doesn’t have a color”)?
(Perhaps pedants will be tempted to object here that “color” is a property of visual experiences, not of physical entities, so it is in fact true that the sky has no “color” if no one is there to see it. This is where the substitution clause above enters: you may replace “the sky is blue” with any true claim you wish, at any desired level of specificity, e.g. “the majority of light rays emitted from the Sun whose pathway through the atmosphere undergoes sufficient scattering to reach ground level will have an average wavelength between 440-470 nm”.)
If you bite this particular bullet—meaning, you believe that my brain’s (in)ability to know something with certainty implies that that something in fact does not exist—then I would have you reconcile the myriad of issues this creates with respect to physics, logic, and epistemology. (Starter questions include: do I then possess the ability to alter facts as I see fit, merely by strategically choosing what I do and do not find out? By what mechanism does this seemingly miraculous ability operate? Why does it not violate known physical principles such as locality, or known statistical principles such as d-separation?)
And—conversely—if you do not bite the bullet in question, then I would have you either (a) find some alternative way to justify the (apparent) ontological commitments implied by claims such as “there’s no observer-independent fact of the matter about whether X is Y”, or (b) explain why such claims actually don’t carry the ontological commitments they very obviously seem to carry.
(Or (c): explain why you find it useful, when making such claims, to employ language in a way that creates such unnecessary—and untrue—ontological commitments.)
In any of the above cases, however, it seems to me that the original argument has been refuted: regardless of which prong of the 4-lemma you choose, you cannot maintain your initial assertion that “there is no objective fact of the matter about anything”.
The first argument attacked the idea that fundamental epistemological limitations have broader ontological implications; in doing so, it undermines the wild phrasing I often see thrown around in claims associated with such limitations (e.g. the “problem of the criterion”), and also calls into question the degree to which such limitations are important (e.g. if they don’t have hugely significant implications for the nature of reality, why does “pragmatism” not suffice as an answer?).
The second argument, however, attacks the underlying claim more directly. Recall the claim in question:
Is this actually the case, however? Let’s do a case analysis; we’ll (once again) use “the sky is blue” as an example:
Suppose I believe that the sky is blue. How might I have arrived at such a belief? There are multiple possible options (e.g. perhaps someone I trust told me that it’s blue, or perhaps I’ve observed it to be blue on every past occasion, so I believe it to be blue right now as well), but for simplicity’s sake we’ll suppose the most direct method possible: I’m looking at it, right now, and it’s blue.
However (says the problemist of the criterion) this is not good enough. For what evidence do you have that your eyes, specifically, are trustworthy? How do you know that your senses are not deceiving you at this very moment? The reliability of one’s senses is, in and of itself, a belief that needs further justification—and so, the problemist triumphantly proclaims, the ladder of infinite descent continues.
But hold on: there is something very strange about this line of reasoning. Humans do not, as a rule, ordinarily take their senses to be in doubt. Yes, there are exceptional circumstances (optical illusions, inebriation, etc.) under which we have learned to trust our senses less than we usually do—but the presence of the word “usually” in that sentence already hints at the fact that, by default, we take our senses as a given: trustworthy, not because of some preexisting chain of reasoning that “justifies” it by tying it to some other belief(s), but simply… trustworthy. Full stop.
Is this an illegal move, according to the problemist? After all, the problemist seems to be very adamant that one cannot believe anything without justification, and in taking our senses as a given, we certainly seem to be in violation of this rule...
...and yet, most of the time things seem to work out fine for us in real life. Is this a mere coincidence? If it’s true that we are actually engaging in systematically incorrect reasoning—committing an error of epistemology, an illegal move according to the rules that govern proper thought—and moreover, doing so constantly throughout every moment of our lives—one might expect us to have run into some problems by now. Yet by and large, the vast majority of humanity is able to get away with trusting their senses in their day-to-day lives; the universe, for whatever reason, does not conspire to punish our collective irrationality. Is this a coincidence, akin to the coincidences that sometimes reward, say, an irrational lottery ticket buyer? If so, there sure do seem to be quite a few repeat lottery winners on this planet of ours...
Of course, it isn’t a coincidence: the reason we can get away with trusting our senses is because our senses actually are trustworthy. And it’s also no coincidence that we believe this implicitly, from the very moment we are born, well before any of us had an opportunity to learn about epistemology or the “problem of the criterion”. The reliability of our senses, as well as the corresponding trust we have in those senses, are both examples of properties hardcoded into us by evolution—the result of billions upon billions of years of natural selection on genetic fitness.
There were, perhaps, organisms on whom the problemist’s argument would have been effective, in the ancient history of the Earth—organisms who did not have reliable senses, and who, if they had chosen to rely unconditionally on whatever senses they possessed, would have been consistently met with trouble. (And if such organisms did not exist, we can still imagine that they did.) But if such organisms did exist back then, they no longer do today: natural selection has weeded them out, excised them from the collective genetic pool for being insufficiently fit. The harsh realities of competition permit no room for organisms to whom the “problem of the criterion” poses a real issue.
And as for the problemist’s recursive ladder of justification? It runs straight into the hard brick wall called “evolutionary hardcoding”, and proceeds no further than that: the buck stops immediately. Evolution neither needs nor provides justification for the things it does; it merely optimizes for inclusive genetic fitness. Even attempting to apply the problemist’s tried-and-true techniques to the alien god produces naught but type and category errors; the genre of analysis preferred by the problemist finds no traction whatsoever. Thus, the problemist of the criterion is defeated, and with him so too vanishes his problem.
Incidentally, what genre of analysis does work on evolution? Since evolution is an optimization process, the answer should be obvious enough: the mathematical study of optimization, with all of the various fields and subfields associated with it. But that is quite beyond the scope of this comment, which is more than long enough as it is. So I leave you with this, and sincerely request that you stop beating your hobby-horse to death: it is, as it were, already dead.
This feels like violent agreement with my arguments in the linked post, so I think you’re arguing against some different reading of the implications of the problem of the criterion than what it does imply. It doesn’t imply there is literally no way to ground knowledge, but that ground is not something especially connected to traditional notions of truth or facts, but rather in usefulness to the purpose of living.
This mostly comes up when we try to assess things like what does it mean for something to “be” an “agent”. We then run headlong into the grounding problem and this becomes relevant, because what it means for something to “be” an “agent” ends up connected to what end we need to categorize the world, rather than how the world actually “is”, since the whole point is that there is no fact of the matter about what “is”, only a best effort assessment of what’s useful (and one of the things that’s really useful is predicting the future, which generally requires building models that correlate to past evidence).
Perhaps I am! But if so, I would submit that your chosen phrasings of your claims carry unnecessary baggage with them, and that you would do better to phrase your claims in ways that require fewer ontological commitments (even if they become less provocative-sounding thereby).
In a certain sense, yes. However, I assert that “traditional notions of truths or facts” (at least if you mean by that phrase what I think you do) are in fact “useful to the purpose of living”, in the following sense:
It is useful to have senses that tell you the truth about reality (as opposed to deceiving you about reality). It is useful to have a brain that is capable of performing logical reasoning (as opposed to a brain that is not capable of performing logical reasoning). It is useful to have a brain that is capable of performing probabilistic reasoning (as opposed to a brain that is not, etc. etc).
To the extent that we expect such properties to be useful, we ought also to expect that we possess those properties by default. Otherwise we would not exist in the form we do today; some superior organism would be here in our place, with properties more suited to living in this universe than ours. Thus, “traditional notions of truths and facts” remain grounded; there are no excess degrees of freedom available here.
To what extent do you find the above explanation unsatisfying? And if you do not find it unsatisfying, then (I repeat): what is the use of talking about the “problem of the criterion”, beyond (perhaps) the fact that it allows you to assert fun and quirky and unintuitive (and false) things like “facts don’t exist”?
I agree that this is a real difficulty that people run into. I disagree with [what I see as] your [implicit] claim that the “problem of the criterion” framing provides any particular tools for addressing this problem, or that it’s a useful framing in general. (Indeed, the sequence I just linked constitutes what I would characterize as a “real” attempt to confront the issue, and you will note the complete absence of claims like “there is no such thing as knowledge” in any of the posts in question; in the absence of such claims, you will instead see plenty of diagrams and mathematical notation.)
It should probably be obvious by now that I view the latter approach as far superior to the former. To the extent that you think I’m not seeing some merits to the former approach, I would be thrilled to have those merits explained to me; right now, however, I don’t see anything.
To me this is like asking what’s the point in talking about a Theory of Everything when trying to talk about physics. You might complain you can do a lot of physics without it, yet we still find it useful to have a theory that unifies physics at a fundamental level (even if we keep failing to find one). I argue that the problem of the criterion fills a conceptually similar niche in epistemology: it’s the fundamental thing to be understood in order to be able to say anything else meaningful and not inconsistent about how we know or what we know, which is itself fundamental to most activity. Thus it is often quite useful to appeal to because lots of deconfusion research, like this post, are ultimately consequences of the problem of the criterion, and so I find most object-level arguments, like those found in this post, a certain kind of wasted motion that could be avoided if only the problem of the criterion were better understood.
I think the thing the framing of the sequence you link and the way most people approach this is missing something fundamental about epistemology that lets one get confused, specifically by easily forgetting that one’s knowledge is always contingent on some assumption that one may not even be able to see, and so mistakes one’s own perspective for objectivity. As for what tools understanding the problem of the criterion provides, I’d say it’s more like a mindset of correctly calibrated epistemic humility. Not to say that grokking the problem of the criterion makes you perfectly calibrated in making predictions, but to say it requires adopting a mindset that is sufficient to achieve the level of epistemic humility/update fluidity necessary to become well calibrated or, dare we say, Bayesian rational.
(Note: I realize my claim about grokking the problem of the criterion sets up a potential “no true Scotsman” situation where anyone who claims to grok the problem of the criterion and then seems to lack this capacity for update fluidity can be dismissed as not really grokking it. I’m not really looking to go that far, but I want to say that this claim is, I believe, predictive enough to make useful inferences.)
Maybe it is for some people (you wouldn’t be the first person to make this claim). Others do seem to find my approach useful. Perhaps the whole point of this should be that not everyone is necessarily reasoning from the same base assumptions, and thus the ground of truth is unstable enough that what seem like reasonable explanations cannot be sure to be arbitrarily convincing. To be fair, Eliezer doesn’t miss this point, but it seems poorly enough appreciated that I often find cause to remind people of it.
If I really wanted to be pointed about it, I think you’d be less annoyed with me if you grokked the point both Eliezer and I are trying to make in different ways about how epistemology grounds out, since taken to its extreme we must accept that the same lines of reasoning don’t work for everyone on a practical level, by which I mean that even if you show someone correct math, they may yet not be convinced by it, and this is epistemically relevant and not to be dismissed since we are each performing our own reckoning of what to accept as true, no matter how much we may share in common (which, for what it’s worth, brings us right back to the core of the intentional stance and the object level concerns of the OP!).
It’s not been mentioned enough, since the point has not generally sunk in.
Pragmatism isn’t a sufficient answer, because it can show that we are accumulating certain kinds of knowledge, namely the ability to predict things and make things, but does not show that we are accumulating other kinds , specifically ontological knowledge, ie. successful correspondence to reality.
You can objectively show that a theory succeeds or fails at predicting observations, and at the closely related problem of achieving practical results . It is is less clear whether an explanation succeeds in explaining, and less clear still whether a model succeeds in corresponding to the territory. The lack of a test for correspondence per se, ie. the lack of an independent “standpoint” from which the map and the territory can be compared, is the is the major problem in scientific epistemology. Its the main thing that keeps non-materialist ontology going. And the lack of direct testability is one of the things that characterises philosophical problems as opposed to scientific ones—you can’t test ethics for correctness,you can’t test personal identity, you can’t test correspondence-to-reality separately from prediction-of-observation—so the “winning” or pragmatic approach is a particularly bad fit for philosophy.
The thing scientific realists care about is having an accurate model of reality, knowing what things are. If you want that, then instrumentalism is giving up something of value to you. So long as it s possible. If realistic knowledge is impossible , then ther’es no loss of value.
Far from having no ontological implications, the problem of the criterion has mainly ontological implications, since the pragmatic response works in other areas.
Trustworthy or reliable at what?
You cannot ascertain an ontologicaly correct model of reality just by looking at things. A model is a theoretical structure. Multiple models can be compatible with the same sense data, so a a further criterion is needed. Of course, you can still do predictive, instrumental stuff with empiricism.
That’s part of the problem, not part of the solution. If evolution is optimising for genetic fitness, then it is not optimising for the ability to achieve a correct ontology … after all , a wrong but predictive model is good enough for survival.
The issues I mentioned have not been answered.
I find this response particularly ironic, given that I will now proceed to answer almost every one of your points simply by reiterating one of the two arguments I provided above. (Perhaps it’s generally a good idea to make sure the point of someone’s comment has “sunk in” before replying to them.)
Suppose this is true (i.e. suppose we have no means of accumulating “ontological knowledge”). I repeat the first of my two arguments: by what mechanism does this thereby imply that no ontological facts of any kind exist? Is it not possible both that (a) the sky exists and has a color, and (b) I don’t know about it? If you claim this is not possible, I should like to see you defend this very strong positive claim; conversely, if you do not make such a claim, the idea that the “problem of the criterion” has any ontological implications whatsoever is immediately dismissed.
I repeat the second of my two arguments: to build an accurate model of reality requires taking some assumptions to be foundational; mathematicians might call these “axioms”, whereas Bayesians might call them “the prior”. As long as you have such a foundation, it is possible to build models that are at least as trustworthy as the foundation itself; the limiting factor, therefore, on the accumulation of scientific knowledge—or, indeed, any other kind of knowledge—is the reliability of our foundations.
And what are our foundations? They are the sense and reasoning organs provided to us by natural selection; to the extent that they our trustworthy, the theories and edifices we build atop them will be similarly trustworthy. (Assuming, of course, that we do not make any mistakes in our construction.)
So the “problem of the criterion” reduces to the question of how reliable natural selection is at building organisms with trustworthy senses; to this question I answer “very reliable indeed.” Should you claim otherwise, I should like to see you defend this very strong positive claim; if you do not claim otherwise, then the “problem of the criterion” immediately ceases to exist.
I repeat the first of my two arguments: what ontological implications, and why? I should like to see you defend the (very strong) positive claim that such implications exist; or, alternatively, relinquish the notion that they do.
Per my second argument: at doing whatever they need to do in order for us not to have been selected out of existence—in other words, at providing an effective correspondence between our beliefs and reality. (Why yes, this is the thing the “problem of the criterion” claims to be impossible; why yes, this philosophical rigmarole does seem to have had precisely zero impact on evolution’s ability to build such organisms.)
Should you deny that evolution has successfully built organisms with trustworthy senses, I should like to see you defend this very strong positive claim, etc. etc.
The problem of selecting between multiple compatible models is not something I often see packaged with the “problem of the criterion” and others of its genre; it lacks the ladder of infinite descent that those interested in the genre seem to find so attractive, and so is generally omitted from such discussions. But since you bring it up: there is, of course, a principled way to resolve questions of this type as well; the heuristic version (which humans actually implement) is called Occam’s razor, whereas the ideal version is called Solomonoff induction.
This is an immensely powerful theoretical tool, mind you: since Solomonoff induction contains (by definition) every computable hypothesis, that means that every possible [way-that-things-could-be] is contained somewhere in its hypothesis space, including what you refer to as “the ontologically correct model of reality”; moreover, one of the theoretical guarantees of Solomonoff induction is that said “correct model” will become the predictor’s dominant hypothesis after a finite (and generally, quite short) amount of time.
For you to deny this would require that you claim the universe is not describable by any computable process; and I should like to see you defend this very strong positive claim, etc. etc.
Per my second argument: evolution does not select over models; it selects over priors. A prior is a tool for constructing models; if your prior is non-stupid, i.e. if it doesn’t rule out some large class of hypotheses a priori, you will in general be capable of figuring out what the correct model is and promoting it to attention. For you to deny this would require that you claim non-stupid priors confer no survival advantage over stupid priors; and I should like to see you defend this very strong positive claim, etc. etc.
Yes, well.
If “fact” means “statement known to be true” , then it follows directly.
If “fact” means “component of reality, whether know or not”, it does not follow...but that is irrelevant, since I did not deny the existence of some kind of reality.
In which case, I will repeat that the only testable accuracy we have is predictive accuracy, and we do not know whether our ontological claims are accurate, because we have no direct test.
That is a major part of the problem. Since our most fundamental assumptions aren’t based on anything else, how do we know how good they are? The only solution anyone has is to judge by results, but that just goes back to the original problem of being able to test predictiveness but not ontological correspondence.
But maybe “no worse than your assumptions” is supposed to be a triumphant refutation of my claim that everything is false...but, again, I didn’t say that.
To reword my previous argument, sense data are not a sufficient foundation, because you cannot appeal to them to choose between two models that explain the same sense data.
Neither Gordon not myself are appealing to the unreliability if sense data. Even if sense data are completely reliable, the above problem holds.
Of course not. There are lots of animals have better senses than humans, and none of them have a clue about ontology.
I know. Its completely standard to put forward simplicity criteria as the missing factor that allows you to choose between empirically adequate models .
The problem is that, while simplicity criteria allow you to select models , you need to know that they are selecting models that are more likely to correspond to reality, rather than on some other basis. SI fares particularly badly, because there is no obvious reason why a short programme should be true, or even that it is a description of reality at all .
I see no strength to that claim at all. The universe is partly predictable by computational processes, and that’s all for we know.
It is the claim that a programme is ipso facto a description that us extraordinary.
To repeat my argument yet again, evolution only needs to keep you alive and reproducing , and merely predictivene correctness is good enough for that.
Correct in what sense ?
The basis of my argument is the distinction between predictive accuracy and ontological correctness. Your responses keep ignoring that distinction in favour of a single notion of correctness/truth/accuracy. If you could show that the two are the same , it the one implies the other, you would be on to something.
Well, it’s a hard habit to break. Everything you are saying to me now is something I used to believe for many years, until I awoke from my dogmatic slumbers.
Well, good! It’s heartening to see we agree on this; I would ask then why it is that so many subscribers to epistemological minimalism (or some variant thereof) seem to enjoy phrasing their claims in such a way as to sound as though they are denying the existence of external reality; but I recognize that this question is not necessarily yours to answer, since you may not be one of those people.
For predictive accuracy and “ontological accuracy” to fail to correspond [for some finite period of time] would require the universe to possess some very interesting structure; the longer the failure of correspondence persists, the more complex the structure in question must be; if (by hypothesis) the failure of correspondence persists indefinitely, the structure in question must be uncomputable.
Is it your belief that one of the above possibilities is the case? If so, what is your reason for this belief, and how does it contend with the (rather significant) problem that the postulated complexity must grow exponentially in the amount of time it takes for the “best” (most predictive) model to line up with the “true” model?
[The above argument seems to address the majority of what I would characterize as your “true” rejection; your comment contained other responses to me concerning sense data, natural selection, the reliability of animal senses, etc. but those seem to me mostly like minutiae unrelated to your main point. If you believe I’m mistaken about this, let me know which of those points you would like a specific response to; in the interim, however, I’m going to ignore them and jump straight to the points I think are relevant.]
The simplicity criterion does not come out of nowhere; it arises from the fact that description complexity is bounded below, but unbounded above. In other words, you can make a hypothesis as complex as you like, adding additional epicycles such that the description complexity of your hypothesis increases without bound; but you cannot decrease the complexity of your hypothesis without bound, since for any choice of computational model there exists a minimally complex hypothesis with description length 0, beneath which no simpler hypotheses exist.
This means that for any hypothesis in your ensemble—any computable [way-that-things-could-be]—there are only finitely many hypotheses with complexity less than that of the hypothesis in question, but infinitely many hypotheses with complexity equal or greater. It follows that for any ordering whatsoever on your hypothesis space, there will exist some number n such that the complexity of the kth hypothesis H_k exceeds some fixed complexity C for any k > n… the upshot of which is that every possible ordering of your hypothesis space corresponds, in the limit, to a simplicity prior.
Does it then follow that the universe we live in must be a simple one? Of course not—but as long as the universe is computable, the hypothesis corresponding to the “true” model of the universe will live only finitely far down our list—and each additional bit of evidence we receive will, on average, halve that distance. This is what I meant when I said that the (postulated) complexity of the universe must grow exponentially in the amount of time any “correspondence failure” can persist: each additional millisecond (or however long it takes to receive one bit of evidence) that the “correspondence failure” persists corresponds to a doubling of the true hypothesis’ position number in our list.
So the universe need not be simple a priori for Solomonoff induction to work. All that is required is that the true description complexity of the universe does not exceed 2^b, where b represents the sum total of all knowledge we have accumulated thus far, in bits. That this is a truly gigantic number goes without saying; and if you wish to defend the notion that the “true” model of the universe boasts a complexity in excess of this value, you had better be prepared to come up with some truly extraordinary evidence.
This is the final alternative: the claim, not that the universe’s true description complexity is some large but finite value, but that it is actually infinite, i.e. that the universe is uncomputable.
I earlier (in my previous comment) said that “I should like to see” you defend this claim, but of course this was rhetorical; you cannot defend this claim, because no finite amount of evidence you could bring to bear would suffice to establish anything close. The only option, therefore, is for you to attempt to flip the burden of proof, claiming that the universe should be assumed uncomputable by default; and indeed, this is exactly what you did: “It is the claim that a program is ipso facto a description that is extraordinary.”
But of course, this doesn’t work. “The claim that a program can function as a description” is not an extraordinary claim at all; it is merely a restatement of how programs work: they take some input, perform some internal manipulations on that input, and produce an output. If the input in question happens to be the observation history of some observer, then it is entirely natural to treat the output of the program as a prediction of the next observation; there is nothing extraordinary about this at all!
So the attempted reversal of the burden of proof fails; the “extraordinary” claim remains the claim that the universe cannot be described by any possible program, regardless of length, and the burden of justifying such an impossible-to-justify claim is, thankfully, not my problem.
:P
Emphasis added. You haven’t explained how a programme functions as a description. You mentioned description, and then you started talking prediction, but you didn’t explain how they relate.
The length has nothing to do with it—the fact it is a programme at all is the problem.
On the face of it, Solomonoff Inductors contain computer programmes, not explanations, not hypotheses and not descriptions. (I am grouping explanations, hypotheses and beliefs as things which have a semantic interpretation, which say something about reality . In particular, physics has a semantic interpretation in a way that maths does not.)
The Yukdowskian version of Solomonoff switches from talking about programs to talking about hypotheses as if they are obviously equivalent. Is it obvious? There’s a vague and loose sense in which physical theories “are” maths, and computer programs “are” maths, and so on. But there are many difficulties in the details. Neither mathematical equations not computer programmes contain straightforward ontological assertions like “electrons exist”. The question of how to interpret physical equations is difficult and vexed. And a Solomonoff inductor contains programmes, not typical physics equations. whatever problems there are in interpreting maths ontologically are compounded when you have the additional stage of inferring maths from programmes.
In physics, the meanings of the symbols are taught to students, rather than being discovered in the maths. Students are taught the in f=ma, f is force, is mass and a is acceleration. The equation itself , as ours maths, does not determine the meaning. For instance it has the same mathematical form as P=IV, which “means” something different. Physics and maths are not the same subject, and the fact that physics has a real-world semantics is one of the differences.
Similarly, the instructions in a programme have semantics related to programme operations, but not to the outside world. The issue is obscured by thinking in terms of source code. Source code often has meaningful symbol names , such as MASS or GRAVITY...but that’s to make it comprehensible to other programmers. The symbol names have no effect on the function and could be mangled into something meaningless but unique. And a SI executes machine code anyway..otherwise , you can’t meaningfully compare programne lengths. Note how the process of backtracking from machine code to meaningful source code is a difficult one. Programmers use meaningful symbols because you can’t easily figure out what real world problem a piece of machine code is solving from its function. One number is added to another..what does that mean? What do the quantifies represent?
Well, maybe programmes-as-descriptions doesn’t work on the basis that individual Al symbols or instructions have meanings in the way that natural language words do. Maybe the programme as a whole expresses a mathematician structure as a whole. But that makes the whole situation worse because it adds an extra step , the step of going from code to maths, to the existing problem of going from maths to ontology.
The process of reading ontological models from maths is not formal or algorithmic. It can’t be asserted that SI is the best formal epistemology we have and also that it is capable of automating scientific realism. Inasmuch as it is realistic , the step from formalism to realistic interpretation depends on human interpretation, and so is not formal. And if it SI is purely formal, it is not realistic.
But code already is maths, surely? In physics the fundamental equations are on a higher abstraction level than a calculation: generally need to be ” solved” for some set of circumstances, to obtain a more concrete equation you can calculate with. To get back to what would normally be considered a mathematical structure, you would have to reverse the original process. If you succeed in doing that, then SI is as good or bad as physics...remember, that physics still needs ontological interpretation. If you don’t succeed in doing that.. which you you might not, since there is no algorithm reliable method for doing so...then SI is strictly worse that ordinary science, since it has an extra step of translation from calculation to mathematical structure, in addition to the standard step of translation from mathematical structure to ontology.
In many ways this is the crux of things. The problem of the criterion does mean that we can’t ground knowledge in the ways we had hoped to, and that we can still ground knowledge, just in something quite a bit different from the objective: namely, in some practical purpose to which we use knowledge.
But that still doesn’t give us ontological knowledge, if we ever wanted it: we have to settle for less.
For what it’s worth, I feel exactly the same way about the robustness of Goodhart and I’ll keep beating that drum as long as I have to. Luckily no one much objects that Goodharting is a problem, whereas everyone seems to be annoyed with epistemology that makes a fairly simple point that is counterintuitive to the experience of being able to make use of knowledge to do useful things, and thinking this is somehow contrary to the epistemological point being made that becomes relevant when you try to ground concepts rather than just use them as you find them.