Philosophy of Science 101: What is the problem of induction?
thecollector.com
thecollector.com
Since we're talking about induction as the basis of science, I'm surprised the concept of "falsification" wasn't mentioned, which has been the "workhorse" of most science during the past two hundred years. See https://en.wikipedia.org/wiki/Falsifiability
Specifically in the context of classical statistics methods (frequentist statistics), the idea of using p-values for scientific discovery only makes sense as part of repeated studies (induction over multiple tests of a theory). It's easy for any one study to observe some pattern by chance (one black raven), but if repeated studies all show this pattern exists, then we kind of start to believe the pattern might be true.
Bayesian statisticians don't use the falsification paradigm directly, but instead focus on estimation, and combining the evidence from multiple experiments to obtain "tighter bounds" on the estimated quantities of interest. The conceptual machinery is very different, but the idea of induction is still kind of present in the form of "more data reduces uncertainty".
Another benefit of a Bayesian approach is that you stop trying to "prove" things.
We use scientific experimentations not to prove but to rule out alternative theories.
I can explain why a given thing will act a certain way. I don't need probabilities for that.
If I need probability it's because I am just guessing and nothing else.
If I need them I am just dressing up guessing in fancy words. But I am just that.
> I think that we shall have to get accustomed to the idea that we must not look upon science as a ‘body of knowledge’, but rather as a system of hypotheses; that is to say, as a system of guesses or anticipations which in principle cannot be justified, but with which we work as long as they stand up to tests, and of which we are never justified in saying that we know that they are ‘true’ or ‘more or less certain’ or even ‘probable’.
The most common realist arguments are probably variations on the "miracle argument": our scientific practices work, and the only plausible explanation is that they have at least some ability to find the truth.
Paying attention to falsification also performs the useful task of pushing hypotheses into saying something definitive.
Science is much more than falsification, of course: for one thing, a falsificationist stance does not generate hypotheses on its own.
I'm not suggesting that all of philosophy should adopt falsification as a principle (and much less that it should be ignored if it cannot): ethics, for example, is a field which I think is important beyond what is falsifiable.
You probably won't survive that encounter.
If Popper can be boiled down to science = falsification then Kuhn can be boiled down to Science progresses one funeral at a time.
I don’t know about the two others, but after reading about them briefly they seem as antirational as any philosophers subscribing to Hegel and/or Marx. When it comes to Lakatos specifically, I can say with certainty that his philosophy of mathematics has so little to do with mathematics that it’s not worth any paper (I studied maths and know many professional mathematicians personally).
Can you elaborate on this?
"Popper’s demarcation criterion has been criticized both for excluding legitimate science (Hansson 2006) and for giving some pseudosciences the status of being scientific (Agassi 1991; Mahner 2007, 518–519). Strictly speaking, his criterion excludes the possibility that there can be a pseudoscientific claim that is refutable. According to Larry Laudan (1983, 121), it “has the untoward consequence of countenancing as ‘scientific’ every crank claim which makes ascertainably false assertions”"
From the citation on Hansson, the abstract[1] reads:
"...Furthermore, an empirical study of falsification in science is reported, based on the 70 scientific contributions that were published as articles in Nature in 2000. Only one of these articles conformed to the falsificationist recipe for successful science, namely the falsification of a hypothesis that is more accessible to falsification than to verification."
Read Popper's Ch. 1. Conjectural Knowledge: My Solution of the Problem of Induction https://roamresearch.com/#/app/infinitedays/page/tGbhrzsPK
Kuhn frames it as "anything goes", which is supposed to be what the horrified scientist utters to themself as they peruse the historical record of their field. Scientists tend to go with "whatever works best" (and whatever secures more funding), rather than following a strictly falsificationist paradigm.
More and better context here: https://www.nature.com/nature-index/news/the-idea-that-a-sci...
Similarly the problem of induction is a problem for philosophers, not scientists: scientists have a method of doing science that works, and has created a modern world, with all sorts of popular things like televisions and smartphones. However, despite the fact that we’re next door neighbors to philosophy, sometimes borrow their tools, and even have some roots in “natural philosophy,” the best tool we have—the one that makes it all useful to society at large—seems to be the one that their framework says can’t be justified.
When your framework with a long history and lots of proponents seems to indicate that a single little project is not well grounded, that project has a problem. When it seems to indicate that the grand project which underpins all of modern society is not well grounded, the framework has a problem.
I think science and philosophy of science would both improve if there was less separation between the fields. Many, if not most, practicing scientists have a Doctorate of Philosophy in a scientific field, yet none of the graduate programs that I'm aware of require a single course in philosophy of science. Equally problematic, I'm not sure how many philosophers of science have actually taken the time to empirically discover anything.
Lakatos is interesting because his philosophy tried to rescue Popper's philosophy in light of Kuhn's arguments, but mutated it considerably in the process.
"The classical or frequentist approach to statistics (in which inference is centered on significance testing), is associated with a philosophy in which science is deductive and follows Popper’s doctrine of falsification. In contrast, Bayesian inference is commonly associated with inductive reasoning and the idea that a model can be dethroned by a competing model but can never be directly falsified by a significance test. The purpose of this article is to break these associations, which I think are incorrect and have been detrimen- tal to statistical practice, in that they have steered falsificationists away from the very useful tools of Bayesian inference and have discouraged Bayesians from checking the fit of their models."
An article on the subject of falsifiability and Popper was also published on the site (and posted on HN by me within minutes of this one):
Popper would agree that Bayesian techniques are useful (and even powerful) tools in statistics and practical problem-solving. But he would say that Bayesian ideas are insufficient to understand how knowledge grows and progresses. From a critical rationalism viewpoint, knowledge grows through conjecture and refutation - the proposal and testing of new explanatory theories. Bayesian statistical approaches can be part of the toolkit to falsify those theories, but they can’t explain how they come about, so they aren’t adequate as an epistemology. Popper’s critical rationalism may not be entirely complete, but it seems far better as a starting point for explaining how we get knowledge (which is what an epistemological framework needs to do) than Bayesian ideas about measuring truth statistically. Major breakthroughs like relativity and quantum entanglement are evidence for this: they required conjectures that at first seemed at odds with what we had observed. Physicists had to follow rational theories down very strange paths before any empirical confirmation, eventually to create new explanations that allowed us to model and predict distant cosmological events that had previously appeared random to us.
If anyone is interested in these ideas (which are still fairly new to me; sorry for anything I’m expressing poorly), I highly recommend reading The Beginning of Infinity. It is an exciting, wide-ranging study of Popper’s epistemology by the guy who ‘invented’ quantum computing. It also discusses the ‘many universes’ theory, which is fascinating.
"Problem of induction" - https://en.wikipedia.org/wiki/Problem_of_induction
"...First formulated by David Hume, the problem of induction questions our reasons for believing that the future will resemble the past, or more broadly it questions predictions about unobserved things based on previous observations. This inference from the observed to the unobserved is known as "inductive inferences", and Hume, while acknowledging that everyone does and must make such inferences, argued that there is no non-circular way to justify them, thereby undermining one of the Enlightenment pillars of rationality..."
I think it is this disparity that makes us intuitively dismissive of the idea that seeing green apples helps us in any way with the color of ravens. And we might maybe also have some bias in our way of thinking - do you first see that a thing is a apple and then that it is red, or do you first see that it is a red thing and then that it is an apple? Ad hoc I would say that color usually comes second especially as we can essentially paint any object in any color we like, for example a blue apple. Color seems to only be the primary attribute if one can not clearly identify something, than it becomes just a red thing in the distance.
[1] Also note that in both variants we ignore black non-ravens, in the first variant because they are not ravens, in the second one because they are not non-black.
[0] https://einsteinpapers.press.princeton.edu/vol7-trans/124
We first posit a universal, and then each subsequent data point is taken to confirm or delimit the universal. With a clear counter-example, the universal is dropped.
As soon as the child touches the fire once, the conclusion "fire is always dangerous" is reached.
This is impart why all ML (etc.) approaches based on conditional probability break: they are subject to the problem of induction.
You cannot do science with statistics: there is nothing in the data that generalises. The generality is the hypothetical properties of the data generating process itself.
ie., the shadows on the wall of Plato's cave cannot be averaged to produce the vases on the outside. It is the properties of the vases (the universals) that produce the shadows -- there are an infinite number of possible shadows, and no statistical operation on any amount of them reverses to "clay pot"
The entire team at CERN would beg to differ.
So would all of the field of cosmology.
So would the entire medical profession, researchers and practitioners - although I do agree that calling medicine a science is a stretch.
You reasoning may be sound, but as in the example you give of child and the fire, your theory has the minor problem that it doesn't fit reality.
The way that (actual,) scientists use statistics is to "choose between possible vases". Suppose we're in plato's cave: we notice strange shadows. We then build pots inside the cave to match those shadows. different pots produce indistinguishable ones; and some pots produce impossible shadows.
Here we can statistically analyses all the shadow data to select the best possible pot model.
You can see that we never get to certainty, because there's always a class of pots producing identical shadows. So we use stats + "theoretical virutes" to select the pot we think most likely.
My point is that in this story stats was never used to build the pots. Such a thing is provably impossible.
This is, essentially, the problem of induction. And it's why the ML approach to pot = "compression of the shadows" breaks. It only works if you never move around the cave, ie., are always sat in exactly the position that the "compressed shadow" looks identical to the real one.
Newton's universal law of gravitation didn't predict huge amounts of stuff in the solar system. Rather than say it's wrong, we supposed there were missing planets.
All models i'm aware of "predict" in the sense that they make existence claims; they don't "predict" observations -- on the latter, they'd basically all 'wrong'.
The body of science we call "gravity, space/time, etc." makes the following existence claims: there is a sun, earth, planets, there are forces, masses,; these have properties that give rise to interactions; etc.
From this body of knowlege, most of what we can predict abotu the observable universe is wrong. simply because, ex hyp., we arent able to observe enough of it.
The models here arent wrong, we just do not have enough data to match them to observations. The world really has forces,masses,planets,etc. and they interact such that F=GMm/r^2 subject to {some constraints}. But if we use that to predict where "everythign should be", nothing is in the right place. We're missing a lot of "Everythign".
This "science predicts observations" is humean problem of induction BS. It's never been true; it's radically sceptical; and is a deeply broken model explaining how we know things.
If we had to literally have models from observations to observations, knowledge would be impossible.
Now you're being entirely unreasonable.
How did NASA put people on the moon?
How did we fly satellites to the outer reaches of the solar system using orbital sling effects?
Clearly because the Newtownian model of gravity is entirely wrong. We only pulled it off by chance.
They do predict data counter-factually: if a rocket were to do X, then Y would happen.
They do this by a model of how the world works.
The actual world is a place of a near infinite number of causes that no one model explains
We correct for telescopic lenses, light shift, atomsspherei optic distortion etc in our scanning the skys.
The skys themselves are unexplained by any of these models
Literally, there is no direct observational data predicted by scientific models
Usually we engineer highly simplified situations where we can use them predicely
that's because they're descriptions of mechanism so can be used to engineer situations
they are /not/ descriptions of observational data
As a matter of fact, IIRC, the Chinese around the 11th century walked the exact same intellectual path, which led them to conclude that trying to model the behavior of the natural world was a waste of time, and made them completely abandon the idea of simplified, yet predictive and therefore useful models.
The net result was: they killed their then budding tech/science endeavors in the egg.
In other words, your take does not seem to be particularly fruitful.
Engineers build "useful models", scientists as a matter of fact, build explanations.
Whether those explanations prove useful is always an open question; newton's took centuries to have much of an engineering use.
Engineering is a kind of pseudoscience justified by its utitility -- if it's undertood to be mere utility, it's fine. But "engineering thinking" has taken over large areas of thinking, and it's a catastrophe.
You cannot build really new things by engineering. Engineering is just "statisticalisation" of new science; a simplification, an eloration, a proceduralisation. The science must come first.
Which came first, man made winged objects that flew, or the equations of winged flight?
So, accidental discoveries -> lenses -> optics -> telescopes -> theory of gravity -> etc.
The full picture is here is very subtle. The idea is that we are in the world as animals engaged in a protoypical science in every action we perform: we interpret causes, take goal-directed actions, refute universals, etc. Our conscious mind is a kind of "local, heuristical science" of our own bodies and how we relate to our environments.
This "native science" gives rise to a "naive engineering" where we play around with possible tools and see what they do. You then bootstrap those tools to do non-naive science.
Science, in the sense I mean of mechanistic explanation involving making claims about stuff that exists, how it works, how it interacts etc.... must necessarily proceed engineering (in the sense of "utility of coincidences").
But it's an incredibly naive science of basic animal intelligence at first -- a science of one's body hurting finding out why, etc. -- you need to supplement this with iterated engineering-science loops to "get to the stars".
The problem with Hume, and the sceptics in this thread, is they either have this backwards; or have no science at all in the picture.
Hume just assumed science is impossible because we were just "engineers of images in our heads", rather than "scientists of our bodies"
This, a 100%.
The "explaining how the world works" is only interesting insofar as it helps produce further and better predictive models (BTW Feynmann had that exact same view [1])
Everything else is intellectual onanism, an unfortunately rather common academic pursuit.
Hume's observations were shocking, precisely because they undermined the most foundational of our assumptions and they have never been satisfactorily countered since; the use here of "ideological" and "misdirection" then seems rather unfair to Hume (though I acknowledge your use of "since") - he flagged our own misdirection in the most un-ideological way imaginable.
Without this premise, hume has nothing to say
He is also the father of quantum computation and his two books Fabric of Reality and Beginning of Infinity the most important books I have ever read.
Here is an interview with him: https://josephnoelwalker.com/139-david-deutsch/
And here is a short lecture he did: https://www.youtube.com/watch?v=cs2n7l7wJow&t
Since our reality is "atoms and void", and since the sun and earth are huge configurations of atoms locked together in a stable pattern, the sun coming up tomorrow has nothing to do with statistics. And bayesian reasoning plays no role in our predictions or certainty. At least not directly. It does indirectly, by asking what perturbation, what intervention, can stop this from happening? And how likely are such events?
Any attempt to debate this point is self-refuting.
There are no stupid determinists; it takes a certain level of intelligence to become so disconnected from literal moment-to-moment lived experience.
Edit: I erred in saying it is false; that is too generous. It is arbitrary.
One framing of determinism is that you can only choose from the options in your head, weighted by your preferences. Both your preferences and those options were acquired through your experience, so how can choose anything other than what your experience already influenced you to do?
It's fine to disagree, but do you find that "incoherent" and "self-evidently false"?
You are relying on my free will: that I will focus my mind, read your argument, incorporate my experience, judge its truth using my reasoning faculty, and choose.
Without free will, reason is impotent. Philosophers can’t agree or disagree because they have no choice in the matter.
Free will is not about being able to choose any random thing at all. That would be like saying I’m not a human because I can’t will myself into becoming a banana peel.
Interesting idea, I'm a bit sceptical but would love to learn more about this argument. Where does it come from?
If we don’t have free will, then we can’t reason. If we can’t reason, then there is no such thing as evidence.
To learn more about this approach, see Rand’s “Introduction to Objectivist Epistemology” and Peikoff’s “Objectivism: The Philosophy of Ayn Rand”.
Entities act in accordance with their nature. Aspects of a man’s nature of man include consciousness, free will, and the character he cultivates. This doesn’t mean they behave randomly.
I cannot imagine a 'free will' that is not founded on randomness, but that may be a personal limit.
The law of causality affirms a necessary connection between entities and their actions. It does not, however, specify any particular kind of entity or of action. The law does not say that only mechanistic relationships can occur, the kind that apply when one billiard ball strikes another; this is one common form of causation, but it does not preempt the field. Similarly, the law does not say that only choices governed by ideas and values are possible; this, too, is merely a form of causation; it is common but not universal within the realm of consciousness. The law of causality does not inventory the universe; it does not tell us what kinds of entities or actions are possible. It tells us only that whatever entities there are, they act in accordance with their nature, and whatever actions there are, they are performed and determined by the entity which acts.
The law of causality by itself, therefore, does not affirm or deny the reality of an irreducible choice. It says only this much: if such a choice does exist, then it, too, as a form of action, is performed and necessitated by an entity of a specific nature.
The content of one’s choice could always have gone in the opposite direction; the choice to focus could have been the choice not to focus, and vice versa. But the action itself, the fact of choosing as such, in one direction or the other, is unavoidable. Since man is an entity of a certain kind, since his brain and consciousness possess a certain identity, he must act in a certain way. He must continuously choose between focus and nonfocus. Given a certain kind of cause, in other words, a certain kind of effect must follow. This is not a violation of the law of causality, but an instance of it.It would really be helpful if you could show your work on this claim, I'm not certain how it is self refuting.
By what means would one even “show their work” on this subject? That would be asking me to prove consciousness using some means outside of consciousness.
For example, in practice the raven problem is not to guess if all ravens are black but to predict the color of the next raven if that color affects a decision.
From that perspective if one knows absolutely nothing about ravens and has seen a single black raven, then it is mathematically sound to guess that the next raven will be black, not white, and make a decision accordingly.
The problem in practice is that accounting for the existing information is hard with guessing of priors etc. But that is the problem of applicability of Bayesian inference, not the problem with the principle itself.
I.e. Bayesian inference is a good answer to the philosophical problem of induction. It is sad that the article has not even touched on that subject.
[0] http://edwardfeser.blogspot.com/2017/04/the-problem-of-humes...
The Truth is a perturbation of Objective Reality (the state resolve of universal potential into manifest form in the moment of now); and the truth is a figment of mind. Integrity is the measure of consistency between.
More mental models should factor in the unreliability of conceptual state in reference to external resolve.