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.
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.