I have been thinking anew about the problem of induction recently, and wished to explain and contrast two proposed solutions. One of these solutions is Popper’s falsificationism; the other solution is what I believe has been implicitly accepted and taught by other philosophers. It seems to me that both are genuine solutions, and critical rationalists would do well to recognise that, even though we may nonetheless prefer one solution to the other. I also want to briefly comment on how best to discuss and compare these solutions, because they each satisfy the demands of different people.
Let me begin with a brief explanation of the problem of induction as I understand it. The matter will be somewhat simplified for brevity, and I trust the reader to read qualifications and footnotes between the lines.
The problem of induction arises where sense observation is asserted as the only legitimate source of synthetic knowledge. Such knowledge is “based on” sense observation, i.e. scientific theories ought to be reducible to reports of sense observation. A scientific theory that cannot be derived from such reports cannot be part of knowledge.
A problem emerged when it was noticed that mankind’s most successful and celebrated theories cannot be reduced to any finite set of sense observations. The classic illustration of the matter involves the universal proposition “all swans are white.” Because no finite set of sense observations of white swans entails that there are no black swans, the universal proposition “all swans are white” must forever remain beyond legitimate knowledge. The imposition that synthetic knowledge be reducible to reports of sense observation appeared to banish from science its best theories.
The traditional response to this problem has been to propose a special form of derivation called “induction”–a mode of inference that proceeds from a finite set of sense observation reports to a universal theory. Sense observation is retained as the only legitimate source of synthetic knowledge, but augmented with induction it could now justify the universal theories of science.
Induction introduces the possibility that justified yet false theories may enter into scientific knowledge, and so a logical justification for its use was sought. If a “principle of induction” (i.e. the future will resemble the past) could be proved by the application of pure reason, then the use of induction might be justified. But attempts to prove such a principle failed. The only means of justifying a principle of induction seemed to be an appeal to sense observation–if the future has always resembled the past before, then it will continue to do so in the future. However, such an argument must employ the mode of inference it is intended to justify and so begs the question.
The most common solution to the problem of induction is to unshackle it from deduction. In this view, induction was mistakenly jury-rigged into a system of deductive inference where it did not belong, i.e. induction was considered subordinate to the apparatus of basic logic.
Induction could be liberated from the constraints of deduction by positing it as an alternative logic of equal standing. The traditional problems of induction were thereby dissolved: induction is valid on its own terms. Evaluating induction by deductive standards was something like a category error. Sense observation remains the only legitimate source of synthetic knowledge, and science had its own special logic to derive universal theories.
Although the problem remains that induction may produce justified yet false theories, the gradual accumulation of sense observations over time may nonetheless make a scientific theories more or less probable, even though it may never prove such theories true or false. In any case, the need to provide a logical justification for the use of induction was solved.
The solution to the problem of induction proposed by Popper was quite different. He abandoned the notion that sense observation was the only legitimate source of any kind of knowledge. All sources were welcome–the issue legitimacy was moot. In his new paradigm, sense observation was relegated from the only legitimate source of synthetic knowledge to a regulator among competing scientific theories.
The universal theories of science were in no need of justification by sense observation or anything else. In Popper’s estimation, the important issue was not the source of theories, but their critical examination and testing–a theory is wrong because it is false and not because of where it came from. Induction was “superfluous,” and the justification of a principle of induction therefore unecessary.
Popper’s solution to the problem of induction is far more radical than its more common alternative. In fact, Popper’s solution is such a radical reorganisation of how one thinks about epistemology, that many philosophers appear incapable of comprehending it, e.g. accusations that Popper “smuggles induction in through the back door” tacitly assume that Popper’s goal is to justify knowledge by sense observation. Meanwhile, for critical rationalists, the common solution to the problem of induction is a crude fix to a fundamentally broken philosophy. Popper’s solution, in contrast, dispenses not only with the problem of induction, but also quickly unravels many other “perennial” problems of philosophy.
To those inculcated in the conventional rules and problems of philosophy, Popper is simply not playing by the rules of the game, i.e. Popper cheats. The majority of challenges to critical rationalism tacitly attempt to reassert the authority of the traditional rules and goals of philosophical inquiry. These goals are assumed to be non-optional, out there like material objects. The real point of contention–betwen values and goals–is merely disguised as a disagreement of logic, history, or science.
I can quite understand why many people are reluctant to accept Popper’s ideas or even hostile to them. It seems to me that critical rationalists too often get drawn into the apparent debate of logic, history, or science, and fail to address the underlying alteration of meaning and purpose inherent in the critical rationalist view. The debates revolving around the problem of induction may be a prime example of such confusion. It seems to me that there really are (at least) two solutions to the problem of induction; which solution is chosen is more a matter of one’s purpose than anything else.
The “alternative solution” to induction isn’t even close to a solution.
For example, all finite sets of observations are consistent with INFINITELY MANY theories. So how do you induce ONE theory? How do you pick which one? Completely arbitrarily? According to your biases or intuition? This is one of several issues any theory of induction has to address, but which is not addressed.
Elliot,
What you describe is a different problem. In any case, although all finite sets of observations are consistent with infinitely many theories, it doesn’t follow that any such theory can be induced from a particular set of observation reports. As a matter of logic this isn’t an issue. However, a problem may arise when an inductivist is confronted with the issue of what observation reports correspond to what observations, since all such reports are theory-laden. In this sense the issue you describe is important, but when considering the logical matter we need not be concerned with the actual truth of the reports.
As a matter of pure philosophy and logic, induction has to offer a method of choosing which theory to induce from a set of observations. NO SUCH METHOD IS OFFERED. Therefore, there is no procedure of doing induction that anyone could ever do. No one has ever induced a theory, since induction isn’t a well-defined method of coming up with a theory; it’s an incomplete set of instructions and therefore logically impossible to follow it to completion.
The reason no procedure is ever offered is because they don’t have one that isn’t ARBITRARY.
This is a very serious problem, and you can’t just ignore it and say the inductivist view partially works. It doesn’t. The inductivist “solution” offered comes no where near being a solution. It just plain doesn’t answer (or even acknowledge) the basic questions.
Elliot,
Insofar as we are discussing purely formal transformations, I do not believe your objection holds. I used to believe as you do, but not anymore. Only when substituting propositional variables for actual propositions can such arbitrarity by elicited, because otherwise one predicate cannot be defined in terms of others. Even then, the result is merely something like the “grue” problem of induction.
But let me be clear, I believe the “grue” problem of induction is a linguistic counterpart to a more serious epistemological issue: any report of an observation is theory-laden. The proposition supposedly verified by an observation is entirely a result of which particular theories are used to interpret an experience, and therefore any induction from observation reports is, as you so forcefully state, arbitrary. In fact, that anything is being “observed” in the first place is an interpretation, as any solipsist will tell yo … himself.
By the way, notice that even with infinite observation reports, the issue of theory-ladenness causes problems for those seeking more than conjectural knowledge.
Induction purports to be a method which a person can do in order to get a theory.
But one of the steps in the “recipe” is vague and can’t be followed.
You are telling me something is wrong with this objection that induction can’t be performed? What?
You speak of substituting propositional variables, but I didn’t say anything about that. You speak of “purely formal”, but in purely formal terms a method consisting of “Do X, then do something, then do Y” is no good because the “do something” part is undefined.
It’s like:
step 1: steal underpants
step 2: ???
step 3: profit
Methods with missing steps are just plain nonsense.
As to theory laden, I agree that makes a good criticism too.
Elliot,
I do not see any problem with defining a rule of inference which proceeds from a finite conjunction of existential formulas to universal formula. For example,
What is it that you object to? Can you induce another conclusion from these premises that contradicts “every x is y“? I can see one means of doing so, but it depends upon defining a new predicate in terms of another, and I think doing so would put us in new territory.
In a sense, we can “get a theory” by induction, in that a induction may have a theory as a conclusion, though most people who make such claims have something much stronger in mind. Often, inductivists do not just see themselves as believers in a particular kind of logic, but believe themselves to be describing how the mind actually works. Popper called this “psychologism” a confusion of logic and psychology, and I do not mean to defend it.
The evidence always looks like this:
a is x or y or z or w …
b is x or y or z or w …
and so on. In order for induction to be a method of creating knowledge people can do, it has to offer a way to pick between x, y, z, etc. It has to offer guidance for that step of the process.
Elliot,
That is a sound objection, but not against induction per se. It is often assumed that induction is a “method of creating knowledge,” but here I am talking about its logic. When exploring the deductive consequences of a set of premises, whether the premises are actually true or a report of sense observation is irrelevent. When exploring the purely formal consequences of a set of formulas, we just assign the formulas truth values and are not concerned with sense observation. I do not understand why the situation should be different with regard to induction, and so your point about people interpreting their sense observations incorrectly is irrelevent.
As a critical rationalist, you should recognise that your objection applies as much to falsification as it does for verification, and you should also recognise why that problem is irrelevent to the logical analysis of either.
So you’re saying that inductivists allege there is an alternative non-deductive thing called inductive inference. They say that inductive inference is valid by its own standards. I agree that they say that, but there are two large problems with this position.
First, the methodological problem: they do no explain what inductive inference consists of or how it is supposed to be used or anything like that.
Second, inductive inference contradicts deductive inference because it says we can get theories from data and deductive inference says we can’t. So we could take the conclusion of a deductive argument and the contradictory conclusion of an inductive argument and feed them into a deductive argument and then deduction explodes in our faces because from x and NOT-x we can deductively derive any statement.
So the inductivists recommend adopting a type of inference they have never managed to define or explain, that does not solve any problems and whose adoption would require the abandonment of deductive logic, which is well-defined and can be used to solve problems. The inductivists have not solved any of the problems associated with their position, despite their protestations to the contrary. Just saying you have solved a problem is not the same as actually solving it.
> As a critical rationalist, you should recognise that your objection applies as much to falsification as it does for verification
What? When you take a critical approach, you look at the evidence like this:
a is ~i ^ ~j ^ ~k …
b is ~i ^ ~j ^ ~k …
you focus on what evidence is inconsistent with, rather than consistent with.
then, if you tentatively accept the evidence, you can rule out i, j, k, etc… when you focus on criticism instead of support, then you don’t hit major logical roadblocks; it actually works.
As to my previous comments, OK you’re right that if you assume impossible premises you can skirt my objection. But I don’t understand the value of defending induction in cases where we have impossible premises.
But Elliot, that’s the just the point, I am not looking at evidence, but at logical formulas.
Induction is supposed to be the method of science, used in real life, not just a logical construct with no relation to the real world.
Induction is not just a logic, true; many people mean it to be something far more than a type formal logic. But induction is, at least, a type of logic.
I believe induction is entirely superfluous to a scientific method, and I believe attempts to describe the growth of knowledge in terms of induction are very mistaken. However, that does not mean everything is wrong about induction in every context. Certainly, I do not mean to suggest the popular solution to the problem of induction solves all the problems associated with induction. I have spent a great deal of time criticising induction and its applications. I am quite familiar with many ways in which it is inadequate for the purposes that many people wish of it. In the process of such criticism I have realised that not every problem associated with induction is unsolvable with the traditional metacontext, and not everything about induction is mistaken.
Perhaps I should play devils advocate by writing a more thorough defense of induction?
Sure, if you want.
I’m not sure it will be fruitful unless you can offer some claim induction is actually useful to something. Anemic versions of theories, which don’t say enough to be useful for anything, are often fairly easy to defend from most criticism, but that’s not interesting.
Some forms of induction are extremely common in science: for instance,
inferring the characteristics of a population from a sample. Pretty well
every health statistic you have ever read has been arrived at that way.
The objection to treating induction as a form of deduction is that inductions are sometimes wrong. A popular response is to treat it as a form of probablistic induction
Hi, ‘old’ post, but very important.
Forgive me when I am fully wrong as I have no philosophical background.
I see the problem of induction. The white swans are a nice example. Theories should be right. Instead of blaming the problem to induction, why not blaming the wrong definition of theories? If a right theory cannot accept counter examples and induction cannot guarantee the absence of any future counter example, why not changing the definition of a theory? A theory is valid only for the past and the present and highly probable for the future by definition. Also deduction which passes a hypothesis which confirms the theory, cannot rule out another future hypothesis falsifying it. So any logic in defense of a fool proof theory must be presumptuous?
kyrill,
Substituting ‘true’ for ‘probable’ doesn’t solve the problem of induction. If past observations do not imply anything about future observations, then they no more imply they are probable than they are true.
If by probability you just mean to describe your subjective confidence or judgement, then perhaps the predictions of a theory become more probable. However, there would remain no logical connexion between the statements describing past and future events. In other words, you will have just substituted a epistemological theory for a psychological one.
Induction is “that which we have had no experience, must resemble those which we have had experience, and nature continues uniformly the same.”, “We suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery.”, “we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them.”. So induction is only about us going from what is known, observational reports of present and past, which are all particular. We go from what we know to what we do not know which show up when go from particular to particular, general to general, particular to general, or general to particular. Science does this all the time. Not only does science rely on this, it is also the cornerstone of inter-subjective (based on known to unknown) to have Public (known to unknown) repeatability of experiments (known to unknown).
Of course, Popper only cared about justification of scientific hypothesis. How they came about did not matter, even though they did come about by going from the known to the unknown.
I think Hume’s and subsequently Popper’s point is that going from the known to the unknown is a conjecture, in other words, a guess. There is no logical basis to support guessing and there need not be. One can guess any way one likes.
Corroboration comes from surviving attempted refutations, not from mere repeated observations. There is no logic behind “must”.
Hi Kelly
maybe along this line of reasoning the problem can never be solved as the rules are set fixed. The induction problem is intrinsically linked to past and future and needs the existence of time ‘enveloping’ the realm of objects and events. But does time exist apart from being a human construct? (Kant made clear: no) If theories are right that only an ever existing ‘here and now’ exists and past and future as ‘here and now’ human memory (called past) and ‘here and now’ future (called human expectations) what then?
The problem then is, ‘Do I have the right to link in my brain my memory constructions to my expectation constructions bypassing* the ever present here and now as I see fit as ‘scientist’ and expect those links to be real properties of the * here and now objects* out there?
* We cannot catch the here and now, it goes too fast
“In his new paradigm, sense observation was relegated from the only legitimate source of synthetic knowledge to a regulator among competing scientific theories”
I’m not sure I understood everything, but this statement I like. The way I see it, induction is not problematic. Allowing for induction is simply saying that physical phenomena of the universe are interrelated. To deny induction is, to me, to deny the notion of phenomena altogether. The empiricist imagines it possible that tomorrow, fire would no longer require fuel, it could burn out of nothing. But by what criteria would you call a series of orange and white lights a “fire” and not 100 different unrelated flashes with mysterious unseen causes? Why when you see something fall to the ground do you not look up to see where it fell, because if it didn’t come from above, then how can you say it fell? Under this empiricist doubt of induction, it seems you have no reason to accept that there are objects or phenomena whatsoever. They have seized upon objects as if they could be understood without theory, purely by sensory perception, but it is arbitrary to restrain their skepticism with regard to objects, because objects are just figments of our imaginations, their extension being whatever portion of spacetime we have chosen to isolate in order to focus our attentions in some useful way.
Popper failed to solve the problem of induction: see my “A mug’s game? Solving the problem of induction with metaphysical presuppositions” (http://philpapers.org/rec/MAXAMG) and “(2005). Popper, Kuhn, Lakatos and Aim-Oriented Empiricism”. Philosophia 32 (1-4):181-239 (http://philpapers.org/rec/MAXPKL).
See also my “The Comprehensibility of the Universe” (OUP, 1998).
Best wishes,
Nick Maxwell
To see one black swan is to reject the hypothesis that ‘all swans are white’.
But from here, precisely, how does one go to accepting ‘[a particular number of] swans are white’.
Popper can only help eliminate false choices, but from within the uneliminated bundle, the problem of induction remains. And this uneliminated bundle of choices, can be quite large.