Bayesian probability theory fully answers this question from a philosophical point of view, and answers a lot of it from the practical point of view (doing calculations on probability distributions is computationally intensive and can get intractable pretty quick, so it’s not a magic bullet in practice).
It extends logic to handle be able to uniformly handle both probabilistic statements and statements made with complete certainty.
I recommend Jaynes’s “Probability Theory: The Logic of Science” as a good guide to the subject in case you are interested.
There’s more than one problem of induction. Bayesian theory doesn’t tell you anything about the ontological question, what makes the future resemble the past, and it only answers the epistemological question probablistically.
Yeah, exactly. Bayesian theory is built on top of an assumption of regularity, not the other way around. If some malicious genie purposefully screwed with your observations, Bayesian theory would crash and burn. Heck, the classic “inductivist turkey” would have very high Bayesian belief in his chances of living past Christmas.
I find the questions of “how and when can you apply induction” vastly more interesting than the “why it works” question. I am more of a “this is a weird trick which works sometimes, how and when does it apply?” kind of guy.
Bayesianism is probably the strongest argument for the “it works” part I can provide: here are the rules you can use to predict future events. Easily falsifiable by applying the rules, making a prediction and observing the outcomes. All wrapped up in an elegant axiomatic framework.
[The answer is probabilistic because the nature of the problem is (unless you possess complete information about the universe, which coincidentally makes induction redundant).]
I find the questions of “how and when can you apply induction” vastly more interesting than the “why it works” question.
Maybe you are personally not interested in the philosophical aspects, …but then why say that Bayes fully answers them, when it doesn’t and you don’t care anyway?
Bayesian probability theory fully answers this question from a philosophical point of view
The answer is probabilistic because the nature of the problem is
Says who? For a long time, knowledge was associated with certainty.
The post I commented on is about a justification of induction (unless I have commited some egregious misreading, which is a surprisingly common error mode of mine, feel free to correct me on this part).
It seemed natural for me that I would respond with linking the the strongest justification I know—although again, might have misread myself into understanding this differently from what words were written.
[This is basically the extent to which I mean that the question is resolved; I am conceding on ~everything else.]
It sounds like they are simply suggesting I accept the principle of uniformity of nature as an axiom.
Although I agree that this is the crux of the issue, as it has been discussed for decades, it doesn’t really address the points I aim to urge the reader to consider.
If the reader values having solutions to the philosophical issues as well as the practical ones, how are you going to change their mind? It’s just a personal preference.
Why would I want to change a person’s belief if they already value philosophical solutions? I think people should value philosophical solutions. I value them.
Maybe I’m misunderstanding your question.
It seemed like the poster above stated they do not value philosophical solutions. The paper isn’t really aimed at converting a person that doesn’t value ‘the why’ into a person that does. It is aimed at people which already do care about ‘the why’ and are looking to further reinforce/challenge their beliefs about what induction is capable of doing.
The principle of uniformity of nature is something we need to assume if we are going to declare we have evidence that the tenth swan to come out of the box would be white (in the situation where we have a box of ten swans and have observed 9 of them come out of the box and be white). Hume successfully convinced me that this can’t be done without assuming the principle of uniformity in nature.
What I am claiming though, is that although we have no evidence to support the assertion ‘The 10th swan will be white.’ we do have evidence to support the assertion ‘All ten swans in the box will be white.’ (an assertion made before we opened the box.). This justification is not dependent upon assuming the principle of uniformity of nature.
In general, it is a clarification specifically about what induction is capable of producing justification for.
Future observation instances? No.
But general statements? I think this is plausible.
It’s really just an inquiry into what counts as justification.
It just pushes the question further. The essential issue with inference is “why should the universe be so nicely well-behaved and have regular properties?”. Bayesian probability theory assumes it makes sense to e.g. assign a fixed probability to the belief that swans are white based on a certain amount of swans that we’ve seen being white, which already bakes in assumptions like e.g. that the swans don’t suddenly change colour, or that there is a finite amount of them and you’re sampling them in a reasonably random manner. Basically, “the universe does not fuck with us”. If the universe did fuck with us, empirical inquiry would be a hopeless endeavour. And you can’t really prove for sure that it doesn’t.
The strongest argument in favour of the universe really being so nice IMO is an anthropic/evolutionary one. Intelligence is the ability to pattern-match and perform inference. This ability only confers a survival advantage in a world that is reasonably well-behaved (e.g. constant rules in space and time). Hence the existence of intelligent beings at all in a world is in itself an update towards that world having sane rules. If the rules did not exist or were too chaotic to be understood and exploited, intelligence would only be a burden.
I might have an unusual preference here, but I find the “why” question uninteresting.
It’s fundamentally non-exploitable, in a sense that I do not see any advantage to be gained from knowing the answer (not a straightforward /empirical way of finding which one out of the variants I should pay attention to).
Oh, I mean, I agree. I’m not asking “why” really. I think in the end “I will assume empiricism works because if it doesn’t then the fuck am I gonna do about it” is as respectable a reason to just shrug off the induction problem as they come. It is in fact the reason why I get so annoyed when certain philosophers faff about how ignorant scientists are for not asking the questions in the first place. We asked the questions, we found as useful an answer as you can hope for, now we’re asking more interesting questions. Thinking harder won’t make answers to unsolvable questions pop out of nowhere, and in practice, every human being lives accordingly to an implicit belief in empiricism anyway. You couldn’t do anything if you couldn’t rely on some basic constant functionality of the universe. So there’s only people who accept this condition and move on and people who believe they can somehow think it away and have failed one way or another for the last 2500 years at least. At some point, you gotta admit you likely won’t do much better than the previous fellows.
Do you have any examples of the “certain philosophers” that you mentioned? I’ve often heard of such people described that way, but I can’t think of anyone who’s insulted scientists for assuming e.g. causality is real.
For example there’s recently been a controversy adjacent to this topic on Twitter involving one Philip Goff (philosopher) who started feuding over it with Sabine Hossenfelder (physicist, albeit with some controversial opinions). Basically Hossenfelder took up an instrumentalist position of “I don’t need to assume that things described in the models we use are real in whatever sense you care to give to the word, I only need to know that those models’ predictions fit reality” and Goff took issue with how she was brushing away the ontological aspects. Several days of extremely silly arguments about whether electrons exist followed. To me Hossenfelder’s position seemed entirely reasonable, and yes, a philosophical one, but she never claimed otherwise. But Goff and other philosophers’ position seemed to be “the scientists are ignorant of philosophy of science, if only they knew more about it, they would be far less certain about their intuitions on this stuff!” and I can’t understand how they can be so confident about that or in what way would that precisely impact the scientists’ actual work. Whether electrons “exist” in some sense or they are just a convenient mathematical fiction doesn’t really matter a lot to a physicist’s work (after all, electrons are nothing but quantized fluctuations of a quantum field, just like phonons are quantized fluctuations of an elastic deformation field; yet people probably feel intuitively that electrons “exist” a lot more than phonons, despite them being essentially the same sort of mathematical object. So maybe our intuitions about existence are just crude and don’t well describe the stuff that goes on at the very edge of matter).
I see. Yes, “philosophy” often refers to particular academic subcultures, with people who do their philosophy for a living as “philosophers” (Plato had a better name for these people). I misread your comment at first and thought it was the “philosopher” who was arguing for the instrumentalist view, since that seems like their more stereotypical way of thinking and deconstructing things (whereas the more grounded physicist would just say “yes, you moron, electrons exist. next question.”).
From the discussion it seemed that most physicists do take the realist view on electrons, but in general the agreement was that either view works and there’s not a lot to say about it past acknowledging what everyone’s favorite interpretation is. A question that can have no definite answer isn’t terribly interesting.
Bayesian probability theory fully answers this question from a philosophical point of view, and answers a lot of it from the practical point of view (doing calculations on probability distributions is computationally intensive and can get intractable pretty quick, so it’s not a magic bullet in practice).
It extends logic to handle be able to uniformly handle both probabilistic statements and statements made with complete certainty. I recommend Jaynes’s “Probability Theory: The Logic of Science” as a good guide to the subject in case you are interested.
There’s more than one problem of induction. Bayesian theory doesn’t tell you anything about the ontological question, what makes the future resemble the past, and it only answers the epistemological question probablistically.
Yeah, exactly. Bayesian theory is built on top of an assumption of regularity, not the other way around. If some malicious genie purposefully screwed with your observations, Bayesian theory would crash and burn. Heck, the classic “inductivist turkey” would have very high Bayesian belief in his chances of living past Christmas.
I find the questions of “how and when can you apply induction” vastly more interesting than the “why it works” question. I am more of a “this is a weird trick which works sometimes, how and when does it apply?” kind of guy.
Bayesianism is probably the strongest argument for the “it works” part I can provide: here are the rules you can use to predict future events. Easily falsifiable by applying the rules, making a prediction and observing the outcomes. All wrapped up in an elegant axiomatic framework.
[The answer is probabilistic because the nature of the problem is (unless you possess complete information about the universe, which coincidentally makes induction redundant).]
Maybe you are personally not interested in the philosophical aspects, …but then why say that Bayes fully answers them, when it doesn’t and you don’t care anyway?
Says who? For a long time, knowledge was associated with certainty.
The post I commented on is about a justification of induction (unless I have commited some egregious misreading, which is a surprisingly common error mode of mine, feel free to correct me on this part). It seemed natural for me that I would respond with linking the the strongest justification I know—although again, might have misread myself into understanding this differently from what words were written.
[This is basically the extent to which I mean that the question is resolved; I am conceding on ~everything else.]
It sounds like they are simply suggesting I accept the principle of uniformity of nature as an axiom.
Although I agree that this is the crux of the issue, as it has been discussed for decades, it doesn’t really address the points I aim to urge the reader to consider.
If the reader values having solutions to the philosophical issues as well as the practical ones, how are you going to change their mind? It’s just a personal preference.
Why would I want to change a person’s belief if they already value philosophical solutions? I think people should value philosophical solutions. I value them.
Maybe I’m misunderstanding your question.
It seemed like the poster above stated they do not value philosophical solutions. The paper isn’t really aimed at converting a person that doesn’t value ‘the why’ into a person that does. It is aimed at people which already do care about ‘the why’ and are looking to further reinforce/challenge their beliefs about what induction is capable of doing.
The principle of uniformity of nature is something we need to assume if we are going to declare we have evidence that the tenth swan to come out of the box would be white (in the situation where we have a box of ten swans and have observed 9 of them come out of the box and be white). Hume successfully convinced me that this can’t be done without assuming the principle of uniformity in nature.
What I am claiming though, is that although we have no evidence to support the assertion ‘The 10th swan will be white.’ we do have evidence to support the assertion ‘All ten swans in the box will be white.’ (an assertion made before we opened the box.). This justification is not dependent upon assuming the principle of uniformity of nature.
In general, it is a clarification specifically about what induction is capable of producing justification for.
Future observation instances? No.
But general statements? I think this is plausible.
It’s really just an inquiry into what counts as justification.
Necessary or sufficient evidence.
It just pushes the question further. The essential issue with inference is “why should the universe be so nicely well-behaved and have regular properties?”. Bayesian probability theory assumes it makes sense to e.g. assign a fixed probability to the belief that swans are white based on a certain amount of swans that we’ve seen being white, which already bakes in assumptions like e.g. that the swans don’t suddenly change colour, or that there is a finite amount of them and you’re sampling them in a reasonably random manner. Basically, “the universe does not fuck with us”. If the universe did fuck with us, empirical inquiry would be a hopeless endeavour. And you can’t really prove for sure that it doesn’t.
The strongest argument in favour of the universe really being so nice IMO is an anthropic/evolutionary one. Intelligence is the ability to pattern-match and perform inference. This ability only confers a survival advantage in a world that is reasonably well-behaved (e.g. constant rules in space and time). Hence the existence of intelligent beings at all in a world is in itself an update towards that world having sane rules. If the rules did not exist or were too chaotic to be understood and exploited, intelligence would only be a burden.
I might have an unusual preference here, but I find the “why” question uninteresting.
It’s fundamentally non-exploitable, in a sense that I do not see any advantage to be gained from knowing the answer (not a straightforward /empirical way of finding which one out of the variants I should pay attention to).
Oh, I mean, I agree. I’m not asking “why” really. I think in the end “I will assume empiricism works because if it doesn’t then the fuck am I gonna do about it” is as respectable a reason to just shrug off the induction problem as they come. It is in fact the reason why I get so annoyed when certain philosophers faff about how ignorant scientists are for not asking the questions in the first place. We asked the questions, we found as useful an answer as you can hope for, now we’re asking more interesting questions. Thinking harder won’t make answers to unsolvable questions pop out of nowhere, and in practice, every human being lives accordingly to an implicit belief in empiricism anyway. You couldn’t do anything if you couldn’t rely on some basic constant functionality of the universe. So there’s only people who accept this condition and move on and people who believe they can somehow think it away and have failed one way or another for the last 2500 years at least. At some point, you gotta admit you likely won’t do much better than the previous fellows.
Do you have any examples of the “certain philosophers” that you mentioned? I’ve often heard of such people described that way, but I can’t think of anyone who’s insulted scientists for assuming e.g. causality is real.
For example there’s recently been a controversy adjacent to this topic on Twitter involving one Philip Goff (philosopher) who started feuding over it with Sabine Hossenfelder (physicist, albeit with some controversial opinions). Basically Hossenfelder took up an instrumentalist position of “I don’t need to assume that things described in the models we use are real in whatever sense you care to give to the word, I only need to know that those models’ predictions fit reality” and Goff took issue with how she was brushing away the ontological aspects. Several days of extremely silly arguments about whether electrons exist followed. To me Hossenfelder’s position seemed entirely reasonable, and yes, a philosophical one, but she never claimed otherwise. But Goff and other philosophers’ position seemed to be “the scientists are ignorant of philosophy of science, if only they knew more about it, they would be far less certain about their intuitions on this stuff!” and I can’t understand how they can be so confident about that or in what way would that precisely impact the scientists’ actual work. Whether electrons “exist” in some sense or they are just a convenient mathematical fiction doesn’t really matter a lot to a physicist’s work (after all, electrons are nothing but quantized fluctuations of a quantum field, just like phonons are quantized fluctuations of an elastic deformation field; yet people probably feel intuitively that electrons “exist” a lot more than phonons, despite them being essentially the same sort of mathematical object. So maybe our intuitions about existence are just crude and don’t well describe the stuff that goes on at the very edge of matter).
I see. Yes, “philosophy” often refers to particular academic subcultures, with people who do their philosophy for a living as “philosophers” (Plato had a better name for these people). I misread your comment at first and thought it was the “philosopher” who was arguing for the instrumentalist view, since that seems like their more stereotypical way of thinking and deconstructing things (whereas the more grounded physicist would just say “yes, you moron, electrons exist. next question.”).
From the discussion it seemed that most physicists do take the realist view on electrons, but in general the agreement was that either view works and there’s not a lot to say about it past acknowledging what everyone’s favorite interpretation is. A question that can have no definite answer isn’t terribly interesting.