# Has the Problem of Induction been solved?

The problem as to acquiring knowledge about times where we cannot experiment/observe. For e.g, you haven't seen the future, so you cannot make any definitive statements, or rather, scientifically definitive statements about the future. But then what stops the laws of physics from being non-valid in the future?

For centuries, we have seen basic principles of science remaining consistent in our world, but that isn't reason enough to know that they'll hold up even in the next second.

So, is there any way through which you can either validate or invalidate induction?

• I believe the reliability of inductive principles has been more than amply validated. It was proved by induction. Mar 21, 2014 at 20:26
• Don't be misled by the word 'problem'. That's not an appropriate question to ask. Nothing can prove or disprove it. This is to @DavidH : mathematical induction has nothing to do with this sort of induction. But it's worth realizing, however, that any proposition established by mathematical induction relies on the assumption that mathematical induction is true. Peano assumed it is; set-theoretic models of PA assume the existence of inductive sets; and so on. These principles are also not subject to proof or disproof. We simply assume them and then do math. Mar 21, 2014 at 20:57
• @HunanRostomyan Yes, mathematical induction is completely different, and I was not referring to that kind at all. I was referring to the epistemological concept of inductive reasoning as contrasted to deductive reasoning. Ironically, since mathematical induction falls into the deductive category and doesn't count as a form of inductive reasoning. Mar 21, 2014 at 21:24
• I don't think there is short of time travel.
– Drux
Mar 21, 2014 at 22:20
• Time travel has its problems. Serious problems.. Mar 22, 2014 at 5:42

You can see in SEP The Problem of Induction

Also : Ian Hackintg, An introduction to probability and inductive logic (2001)

Also : Dov Gabbay (editor), Inductive Logic (volume 10 of Handbook of the History of Logic, 2011).

Clearly (for me) the problem of induction has not been solved yet (as all interesting philosophical problems ...).

Human being has a sort of "innate propensity" to believe in regularities and in causal connections.

When the hunter notes the traces in the grass, he assume that they has been produced by a beast.

We build scientific theories and mathematical laws on the assumption that they will describe the machinery "out there".

From Hans Reichenbach, The Direction of Time (1956 - Dover reprint), page 10 :

The physics of Galileo and Newton revealed that many more events can be predicted than are forseeable to common sense; and it showed that prediction can achieve amazing quantitative precision. The use of mathematical models in the physical sciences has brought this kind of success. [...] The steam engine and the airplane bear witness to the determination of future. Who would dare to step into an airplane were he not convinced that the laws of aerodynamics formulate highly reliable predictions ?

Popper is right when he says that refutation is the driving force in the progress of scientific theories. But Popper's critics are also right in saying that the scientific community give up a theory only when it has found a better one.

What the scientific community (and mankind in general) never give up is the metaphysical assumption that regualrities and causal connections are "out there" and that we can describe and explain them.

Yes. Induction is a solid way of getting to know things. Never fear.

First of all, it seems that the laws of physics themselves are in such a way, that they do not change over time. This just plain seems to be a feature built into our particular universe (like for instance, electrons, 2 plus 2 being four, and the speed of light) Do note that assuming the laws of physics are the same tomorrow as they are today have made a lot of people very, very wealthy.

Second, there is an extensive field of applied mathematics, Machine Learning, which works with a certain concept of statistics: The Bayesian Update. In short, every time a learning system gets new information from it's sensory channels, it updates it's internal probability distribution over possible sensory inputs to fit. It is a mathematically well-founded way of building an internal model of the surrounding environment, just by looking. Google made literally all their money by using machine learning.

Lastly, there is a brilliant formalization of Occam's Razor (the simplest explanation, all else being equal, should be favoured) called Solomonoff induction; where a hypothetical prediction machine runs all possible simulations of universes which would explain it's current sensory data, and every time it gains new information it discards the ones that don't fit. Given that it is not computable, it has yet to make people rich, but it has spawned some serious research in AI.

This is just a few name drops of what mathematicians work with when they talk about "inductive reasoning." And, again, there is money to be made with inductive reasoning, so ponder long and well before you argue against induction.

ETA: "Proof by induction" is something very different from inductive reasoning. Such a proof is only relevant when you are proving a property of numbers and works like this: If P is true for 0, and P being true for n implies that P is true for n+1, then P is true for all numbers. Prove P for 0; assumbe P for n and prove for n+1 and you're done.

• Hmm ... "no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white" (Karl Popper)
– Drux
Mar 21, 2014 at 22:12
• "Do note that assuming the laws of physics are the same tomorrow as they are today have made a lot of people very, very wealthy." -- It's made a hell of a lot of poor people too. Of course the laws of physics change. If you take "laws of physics" to be what contemporary physicists believe, then the laws of physics are historically contingent and under constant change and refinement. If you believe there are laws of physics outside of human cognition ... please present some evidence of such! Mar 22, 2014 at 1:19
• Money? Seriously? We are talking about objective issues here.. Maybe you did not read the description I provided. Just because till today you saw something happening, doesn't mean that it'll happen tomorrow too! You can choose to 'believe' that it would happen given that it has happened since documented history, but you cannot say anything objectively (read empirically, here) as you are required to observe the future for that. Mar 22, 2014 at 5:41
• @Drux Karl Popper's innovations in the philosophy of science has since been overtaken by Kuhn and Judea Pearl. Logic is not a sound basis for reasoning on incomplete knowledge; that is literally what we have (bayesian) statistics for. Mar 23, 2014 at 9:21
• @user4894 If there is not laws of physics outside of human condition, pray tell, what do physicists study then? Ponder this: When I make a prediction about my sensory inputs (an "experimental prediction"), sometimes I am wrong. Therefore the thing that makes the predictions (my "brain") and the thing that decides the sensory data I receive (the "outside world") is the probably different systems, are they not? Mar 23, 2014 at 9:24

You can validate Induction by creating a (climate) model and run it.

The only problem I see with induction is that the person doing the induction is part of the thing it induces. So this is like the observer effect. You are affecting the system as you are measuring or inducing it.

That's why we are supposed to live in the now. For that is what only exists. The past and the future and the now we are talking about while we are talking about don't really exist. While you talk about the now it has already passed. You cannot talk about the now. You can only be in the now.

Or in other words you are the now. Now that means now is you and you is now. You would induce yourself which would mean you are no longer you and in the now but creating a simulation of yourself which is born out of you but not identical with you.

So my summary is: Any induction is by definition talking about a smaller group of relations than the relations it tries to describe because it is a new relation itself. Thus it is always imperfect.

It sounds to me like you're looking for a justification for the use of induction. Induction is postulated in many proofs and much reasoning. But has it ever been proven that it is in fact valid?

This has come up in Hume's analysis of causality.

1. In most cases, what persuades us of the reality of some fact, existence or presence is a reasoning based on a cause-and-effect relationship.

2. The cause-effect relationships we thus make such large use of originate exclusively from experience.

3. These cause-effect relationships cannot be inferred by pure reasoning or, in other words, that the validity of induction cannot be established this way. And if we try to justify it by referring to experience, that is, by asserting that since induction worked in many instances it should also work in other instances, we are caught in a vicious circle; for this, obviously, is already an inductive argument. So we are postulating the validity of induction as an element in our very attempt at proving this validity. To put it in a nutshell, there is no justification for induction.

But postulating the validity of induction, even without a proof or justification, has proved to be invaluable.

Source: Veiled Reality, Bernard d'Espanat, Frontiers in Physics series, Westview Press, pp 9-10.

• I know this is a late answer but I was going to ask this same question and then I found your question here. Jun 10, 2016 at 15:36

The problem of induction was solved by Karl Popper. Induction is a myth. People before Popper knew that induction was plagued with logical problems – it doesn't work. But everyone assumed it had to work because they didn't know what else could replace it. Popper recognized that the problem of induction cannot be solved in the standard sense and people should stop trying. Instead he replaced induction with an evolutionary epistemology which explains how we create knowledge and doesn't have the logical holes that induction had. This solves the real underlying problem (how do humans get knowledge), but doesn't solve the problem of saving induction, which is unnecessary.

Here's an example problem with induction that no one has been able to deal with: define whether and how much evidence X supports idea Y, in a clear way that'll give a good answer for any evidence/observation X and any idea Y.

One reason no one can do this is there's no such thing as evidential support. There is evidence X that contradicts idea Y, and there is evidence that does not contradict it. That's it. No one has come up with another relationship (support) other than non-contradiction. And looking only for contradiction and non-contradiction doesn't do what's needed for induction.

One aspect of Popper's epistemology (you have to read and discuss his books to understand it – not secondary sources which are unreliable) is an emphasis on finding problems with our ideas and rejecting mistaken ideas (such as the ones contradicted by evidence).

Epistemology is a big topic. Induction has a very lengthy history of discussion, debate, etc, of which I've brought up a tiny fraction. Please feel free to ask followup questions about whichever parts catch your interest.

There is an experimental approach to resolving the problem of induction via means of pattern recognition and prediction.

There is this particular paper:--

Rathmanner, Samuel, and Marcus Hutter. "A philosophical treatise of universal induction." Entropy 13.6 (2011): 1076-1136.

This is an attempt at solving the problem of induction, but I cannot gurantree that it truly solves the issue.

Best of luck to the OP in your search.

• Interesting. But, essentially, I believe that the basis of scientific induction is simply the premise that “Nature has order”. Therefore, everything transpires NOT HAPHAZARDLY but ACCORDING TO CERTAIN LAWS. Because of this, that things happen not haphazardly but according to certain laws, induction is a justifiable process, and there is no problem of induction. Apr 10, 2019 at 9:37
• What kind of answer do you expect of us, OP? Apr 11, 2019 at 2:41
• I accept all kinds of answers. Your answer is good and interesting. I just express my personal belief because I think it's basically more general. But that's just my personal belief. Apr 11, 2019 at 2:53
• Fair enough. Good luck! :) Apr 12, 2019 at 3:47
• @user287279 I apologize if my tone was a bit harsh. Apr 14, 2019 at 5:41