Talk:Problem of induction

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
WikiProject Philosophy / Logic / Science (Rated B-class, High-importance)
WikiProject iconThis article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.
B-Class article B  This article has been rated as B-Class on the project's quality scale.
 High  This article has been rated as High-importance on the project's importance scale.
Additional information:
Taskforce icon
Taskforce icon
Philosophy of science

Old Stuff[edit]

This statement seems out of left field. I find it kinda crazy and even offensive to respectable scientists and maybe even philosophers.:

"The problem calls into question all empirical claims made in everyday life or through the scientific method."
It most certainly does NOT apply to modern science. In fact, the modern scientific method only uses induction purely to reinforce and balance the resulting outcome. I think it could be debated that the scientific method as it's used today does not include inductive reasoning at all and in fact exists partly to prevent it from influencing the results (see falsifiability and other comments below). And what the heck are "Empirical claims made in everyday life?" Not scientific, I'm sure. This sentence sounds like "Scientific Method Denial" if such a thing exists. I'm posting this in the discussion page instead of taking a hatchet to the text because I'm just a humble research scientist and I don't "have a background in philosophy" and I'm still new at this. If I've miss something big here, lemme know. Otherwise, I'm going to axe this whole statement.Swiftek (talk) 09:26, 23 December 2008 (UTC)

This sort of nonsense is not helpful in this article:

"Induction regarding the laws of nature is justified in practice by the fact that we would cease to exist if they change significantly. In addition, to a great extent they are based on a few symmetries, each of which can be broken only once."

If you don't have a background in philosophy, particularly epistemology or the philosophy of science, please do not waste other wikipedians time by posting sophmoric crap like the material above in a technical article like this one. It is hard enough for a well-versed philosopher to write a good article on this topic. B 02:37, 22 Oct 2003 (UTC)

Do we need this page? I suggest it be re-directed to inductive reasoning. It adds no content that is not better explained in the longer article. The stuff on Nelson Goodman is useless until someone writes an article on him worth linking to. Banno 08:35, 24 Oct 2003 (UTC)

Banno, there is much more to be written on this article as well as on the related inductive reasoning article. The article on inductive reasoning should briefly refer to the problem of induction, but the problem of induction should not be confused with inductive reasoning itself. Both terms, "problem of induction" and "inductive reasoning", are also fixed phrases for their distinct issues, and folks who are looking for info on one would be surprised to find it tucked in under the heading of another and have to wade thru the article to get info on the subject matter they are looking for. We don't merge articles on wikipedia just because they are stubs... —B 13:56, Oct 24, 2003 (UTC)

Thanks, B. I see your point. But you will have to help me here. What content will be included in this article that would not be appropriate in the other? A quick look will show that the inductive reasoning article is, as it should be, a discussion of the problem of induction. In what way do you see the problem of induction as being a "distinct issue" apart from the justification of inductive reasoning?Banno 19:11, 24 Oct 2003 (UTC)

Hey, Banno. Inductive reasoning isn't a discusion of the problem of induction. Otherwise it would need to be retitled from "inductive reasoning" to the "problem of inductive reasoning". It is or should be an article on: what inductive reasoning is (or as some call it, "inductive logic"). Along with its encyclopediac definition, it would include examples of it (written in formal logic, not just plain english); how it is or isn't used in science or philosophy; who recognized it; how it differs from deductive logic and whatever else I cant think of at the moment. It should make a brief reference to the justification of inductive reasoning with a link to the article that discusses the "problem of [justifying] induct[ive reasoning]" usually referred to as the problem of induction. —B 20:10, Oct 24, 2003 (UTC)

I still can't see a clear difference; Unless there is a loud protest, I'll move the stuff from inductive reasoning to here in a few days. Banno 10:36, 7 Dec 2003 (UTC)

I'm sorry if you can't distinguish Inductive reasoning and the problem of induction: one obviously is an article on what induction is and the other is an article on the philosophical problem of induction. Don't merge them or I will revert. What is inane, however, is your recent creation of the hypothetico-deductive method article as if that material is supposed to differ somehow from what should be in the article on deductive reasoning. What you need to do is move the material from the hypothetico-deductive method with a redirect and merge it into the article on deductive reasoning. B 16:59, Dec 7, 2003 (UTC)

All of what you describe would be equally at home in problem of induction. But I have no intention of getting into an rv. war with someone who thinks hypothetico-deductive method is the same as deductive reasoning. Thanks for demonstrating such an open and cooperative attitude.Banno 19:58, 7 Dec 2003 (UTC)

I erred regarding my comment on hypothetico-deductive method. It does deserve its own article separate from deduction. My apologies. B 05:33, Dec 8, 2003 (UTC)

No problem. Thanks. Banno 10:43, 8 Dec 2003 (UTC)

Look at me change my mind and compromise some more: go ahead and merge problem of induction into induction if you please. I think it is possible that the material under the problem of induction may eventually become too large and unwieldy in the induction article and will need to be spun off into an article of its own again. However, after some more thought and given the practices on other wikipedia articles, I no longer object at this point. B 21:51, Dec 8, 2003 (UTC)

Note that I have moved Inductive reasoning to Induction where it should be. B 21:51, Dec 8, 2003 (UTC)

I think the rock-toe example recently added (by BoNoMoJo I believe) should be deleted. It really adds nothing and just clutters the definition. If the example is worth including, it should be placed after the definition. Fairandbalanced 00:15, 6 Dec 2003 (UTC)

Pay attention Fairandbalanced or figure out how to use wikipedia better...then you don't have to speculate who made the changes. Ww made the changes, not me. B 03:56, Dec 7, 2003 (UTC)

The material on falsificationism is not particularly relevant here, namely:

Sir Karl Popper bypassed the 'problem' by noting that science actually does not rely on induction, but developed the notion of falsification as a way around the problem of induction, actually testing possible hypotheseses by experiment. Popper replaced induction with deduction, making modus tollens the centrepiece of his theory. On this account, when assessing a theory one should pay greater heed to data which is in disagreement with the theory than to data which is in agreement with it. Popper went further and stated that an hypothesis which does not allow of such experimental text is outside the bounds of science. This was his doctrine of falsificationism.

Popper's work on falsificationism was not directed at the problem of induction; falsificationism was more of response to the logical positivists' verificationism or confirmationism. B 02:12, Dec 8, 2003 (UTC)

See my comments in talk:falsifiability on this issue. Popper clearly intended his theory to be a solution to the problem of induction, and says so. Nevertheless, I will re-work the paragraph. Banno 09:07, 8 Dec 2003 (UTC)

Can anyone adjust the Problem of Induction Page? I accidently lost a line at the bottom of the summary while attempting to edit. Any help?


Karl Popper did in fact claim to have resolved the problem of induction through his deductive approach to science, but I think that as the paragraph appears in the article at the current moment, it is biased toward proponents of Popper's insistence on his having done away with induction. The debate as it actually stands is not so definitively in favor of Popper. Many of his critics have pointed out that induction is implicit in his method of deduction as the falsification of a theory is itself a scientific claim, and as such, for a falsification to be so incontrovertibly accepted as Popper believed it should, it would have to rely on induction since induction would necessarily be the manner of logical inference used to demonstrate the universality of a theory about another theory having been falsified. Batman Jr. 03:52, 10 October 2005 (UTC)

I need some help here. Has Salmon's criticism of Popper been addressed? I need more info so I can make up my mind as to where my own world view lies. If someone has any comments that go beyond something fitting to this article, contact me directly at EimacDude_at_aol_dot_com

ThVa 11:26, 18 Dec 2007 (UTC)


I'm thinking David Stove should be mentioned here, because he marshals arguments against Hume, Popper, and Goodman, all of whom are mentioned in this article. I wish I were able to present his views myself, but his technical writing is beyond me. Two complete topical works of his are available online: [Popper and After: Four Modern Irrationalists], and [Probability and Hume's Inductive Scepticism].

I think that this should be included in the main article as a critique of Popper. Wesley Salmon argues this point very well. The problem with Hempel is that he agrees that falsification says nothing about what is true, just what is not. Corroboration is not confirmation. But what grounds do we have then to trust a corroborated theory over a none corroborated theory? If one uses a corroborated theory to act on he/she is still guilty of induction. Reesebw (talk) 05:27, 19 November 2007 (UTC)

Bayesian inference[edit]

The following submission was recently placed by ananymous IP user at the head end of page, and I have moved it into normal positioning on the page...Kenosis 03:02, 23 April 2006 (UTC)

Hi all, where's Bayesian inference? It was my (limited) understanding that many philosophers appeal to Bayes to explain why they hold belief that the sun will rise tomorrow. No matter what the initial a priori probability is that the sun will rise, the a posteriori probability eventually converges to 1 after many many dawns. Bayes is referenced and discussed in inductive reasoning. Is there an expert that can help, or tell me that I'm all wet? Thanks.-- 02:25, 23 April 2006 (UTC)
Good point. Shall we copy some of the content from the Sunrise Problem to here? --winterstein (talk) 14:29, 7 April 2011 (UTC)

Inductive Reasoning v Problem of Induction[edit]

From the discussion above, and from the reverts that have been occurring, I think we need to be clear on the distinction between Induction and "the problem of induction". So: the "problem" is determining whether or not inductive reasoning can be logically justified.

A good introduction can be found here[1].

If you think this is inaccurate Nox (bot?), please use the discussion page before editing so boldly.

--Gdickeson 14:52, 24 October 2006 (UTC)

Removed original research (Kevin Kirchman notable?)[edit]

I removed some material posted by User:Kalexander which seems to be based on his own original research (see the link that had been inserted at the end of the removed section). From what I can tell, this doesn't seem to be an established approach to the problem of induction. flowersofnight (talk) 15:36, 26 March 2007 (UTC)

It has been re-insertered with a link to "Kevin Kirchman", who is not particularly notable. Not in the company of Popper and Goodman, anyway.1Z 15:09, 29 March 2007 (UTC)

Time will tell. 1Z 11:55, 22 September 2012 (UTC)

It doesn't even appear to deal with the problem of induction at all (as stated by Hume, et al. -- viz., whether inductive inference is a doxastically and propositionally justifiable form of discursion); it rather seems to address, very basically, the possibility of induction and the mechanism by which the mind makes inductive inferences. I'm not aware of any philosophers doubting the possibility or logistics of induction (Hume said on the contrary that he is certain we do make inductive inferences). So I don't see how this section is relevant to the article at all, notability notwithstanding. » MonkeeSage « 17:47, 28 April 2007 (UTC)
No one "notable" among the notable may doubt the existence of inductive process. But the justification of a concept doxastically and propositionally (and now, presumably, notably) was not Hume's issue. His issue was simply how can we justify an idea rationally from its formation as a generalization. All the new terminology tacked on to his original inquiry does not necessarily belong, nor are the newer views a reasonable standard from which to evaluate discussions of his original problem. 1Z 12:14, 22 September 2012 (UTC)
It seems to be int he Randian tradition , and Randians do tend to assume that you can solve problems by giving an account of psychological mechanisms. 1Z 21:20, 28 April 2007 (UTC)
This is an argument method to categorize one persons new idea as another's, in order to discredit the new idea. As the comment below shows, this attempt is unfair and not reasonable.

1Z 12:18, 22 September 2012 (UTC)

Hmmm, I'm not sure about I read Rand, her Objectivism is a form of Realism, which bases justification (at least propositional justification) on reasons, not causes. For example, we may be able to fully describe the psychology, process and context of belief that hens lay eggs because they are possessed by evil spirits, and this can perhaps supply doxastic/personal justification for the belief, but I don't think Randians would argue that it can supply propositional justification for the content of the belief. And as I read Hume and Russell on the problem of induction, that is the crux of the matter: whether our personal beliefs about induction can be propositionally justified -- whether our beliefs can be objectively proven to match the way things really are. So even if we can prove the possibility of induction and describe its logistics, or even provide doxastic justification, this doesn't do anything to solve the main problem of induction as described by Hume and Russell. » MonkeeSage « 10:02, 30 April 2007 (UTC)
So, is it the case that, on the basis of notability guidelines and standards of relevance, this section should go? » MonkeeSage « 04:26, 4 May 2007 (UTC)

Cut material[edit]

Kevin Kirchman[edit]

To induce facts from the past is part of what we mean when we talk about "reason" (we also are refering to deduction, a distinct mental process). It's meaningless to discuss whether we should "reasonably" trust induction: induction is part of what reason is all about.

The Problem of Induction is fundamentally about 'ideas', and whether or not they are rational. Aristotle established the concept of inductive reasoning, which is really a misnomer, and is one cause for the misunderstanding of the nature of inductive processes.

Concepts are formed by particular mental methods of behaviour. Concept formation is the basic process of forming all ideas, or identifying symbolic representations that have universal applicability.

The discovery of concepts that have universal applicability is not, therefore, a rational process per se. Validating that the concepts are universals, however, is rational, as deduction from concepts is used in the process of scientific validation. One can assert a universal (an inductive concept) by simply asserting a broad spatial or temporal scope of a simple descriptive concept, such as 'this dog has four legs'. By modifying the statement, it is possible to create an inductive concept, which may or may not be valid universally.

If we say 'all dogs have four legs', we have asserted an inductive concept. It remains to be seen [vague] whether this concept is valid or not--whether any particular referents of the concept contradict the assertion, for instance, a dog born with three legs. When Karl Popper discussed falsification of theory, he was referring to the identification of evidence which contradicted inductive abstractions.

Returning to the Problem of Induction, asking whether or not it is rational to assert inductive concepts is really too broad a question. The real issue is can we identify some concepts which have been asserted that do have universal validity. If we can, then we should ask more specifically is there a class of concepts which can have universal validity, and what is the nature of that class of concepts.[1]

Aristotle established the concept of inductive reasoning, which is really a misnomer

Because? You previously said induction was part of reason.

Induction is _generally_ considered as part of reasoning behaviour, largely because of Aristotle's confusion. 1Z 13:00, 22 September 2012 (UTC)
The Problem of Induction is fundamentally about 'ideas', and whether or not they are rational.

You previously said reasoning was a process.

No, I said deduction was a process. 1Z 13:00, 22 September 2012 (UTC)
Concept formation is the basic process of forming all ideas, or identifying symbolic representations that have universal applicability.

Why universal? Why not just more general than particular?

Because as human beings we have sought knowledge, which is universal concepts. And your comment presumes the lack of this explanation to be a failing in the rest of the discussion. It wasn't a mind dump. 1Z 13:00, 22 September 2012 (UTC)
The discovery of concepts that have universal applicability is not, therefore, a rational process per se.

You previously said induction was part of "reason".

No, I said Aristotle confused the issue by including induction as reasoning. The philosophic community, of supposed notable persons, still considers that induction is reasoning. For Aristotle, induction and deduction were reasoning.
But induction is a distinct mental process from deduction, therefore it is not intelligent to call it inductive reasoning, when a deductive syllogism is a mental behaviour, while inductive concept formation is a distinct mental behaviour.

My point is that Hume, using Aristotle as a starting point under the presumption that deduction and induction were types of reasoning, attempted to justify inductive concept formation from a deductive standpoint.

His argument, as Bertrand Russel puts it, "Just because the sun rises today, how can we say it will rise tomorrow?"
Well, from the Kirchman perspective (obviously presently failing the epistemological standard of notability), we can assert the inductive concept "the sun always rises" (limited in its temporal scope intelligently given our current knowledge of the Sun's lifespan), validating it by methods of science. Then we can use this concept in a chain of reasoning:
If the sun always rises (with temporal scope limitations).
Tomorrow is a new day.
=> Therefore the sun will rise (with temporal scope limitations).
Because the philosophical 'alchemists' do not want to acknowledge my historically distinct epistemological theory, which includes new theories of validation, induction, deduction, ethics and concepts, that was itself validated in use with commercial applications by many of Global 500 companies, the epistemological standard of "notability" is questionable, if those making the "note" have biases against the advance of human understanding. Mendel was not notable, nor were many other innovators in the history of science.1Z 13:20, 22 September 2012 (UTC)
When Karl Popper discussed falsification of theory, he was referring to the identification of evidence which contradicted inductive abstractions.

In a context where there is a differece between propositions and concepts.

If we say 'all dogs have four legs', we have asserted an inductive concept.

Inductive proposition.

No. Inductive concept, as redefined by my theoretical model. Propositions are only symbolic representations of concepts. And a concept does not have to be subjectively "believed" to be a concept. It can be held mentally without commitment. 1Z 13:24, 22 September 2012 (UTC)
Returning to the Problem of Induction, asking whether or not it is rational to assert inductive concepts is really too broad a question. The real issue is can we identify some concepts which have been asserted that do have universal validity.

That's easy We just have to examine the entire universe...

Not true. Do you know how else we might test the validity of a concept of knowledge? 1Z 13:31, 22 September 2012 (UTC)
If we can, then we should ask more specifically is there a class of concepts which can have universal validity, and what is the nature of that class of concepts.

Ask? Do you have the answer or not? 1Z 22:13, 19 June 2007 (UTC)

Of course. Why else would I ask the question. But then, if I am not noteworthy, then how could my knowledge be accepted by those whose standard of knowledge is that which is approved by some group of others, who may indeed be threatened by a chemistry that challenges their alchemy.1Z 13:31, 22 September 2012 (UTC)

Statements of the problem[edit]

Francis Bacon, Isaac Newton, and numerous others up until at least the late 19th century have considered inductive reasoning the basis of scientific method—indeed inductive reasoning is used today, though in a more balanced interaction with deductive reasoning and abductive reasoning.

Of course inductive reasoning is still used today. Even if this gets phrased better, it is unsourced and would belong in inductive reasoning, not here. –Pomte 12:44, 27 December 2007 (UTC)



Seems very complex- a triffle clearer please? Larklight (talk) 21:47, 13 February 2008 (UTC)

Added Ancient Origins section[edit]

I added the section on Sextus and Weintraub. ImperfectlyInformed (talk) 07:34, 19 April 2008 (UTC)

different from/different than[edit]

'Different than' is Standard in English. Admittedly, maybe it's not quite as accepted among grammarians as 'different from' -- however, it sounds better. ImperfectlyInformed | {talk - contribs} 17:15, 6 May 2008 (UTC)

That link observes, "Different than has been much criticized by commentators" and concludes, "best advice for Formal and Oratorical levels: stick with different from." "Different than" is rarely used in writing. The List of English words with disputed usage says "different from" is undisputed while "different than" is disputed. Why switch from an undisputed usage to a disputed one? More to the point, "different to" 'sounds better' to some of us -- that doesn't seem like a good basis for deciding. ThisIsMyWikipediaName (talk) 18:17, 6 May 2008 (UTC)

Mathematical induction section[edit]

The mathematical induction segment is simply incorrect, and doesn't have anything to do with scientific induction. Mathematical induction is a theorem which holds over natural numbers, and is equivalent to the fact that natural numbers are well ordered (every nonempty subset of natural numbers has a least member) This is a deductive procedure and has the flavor of induction, but it isn't induction.

I didn't write that section, but it says that mathematical induction does not have the same issue that scientific induction does because it is based on deductive reasoning. So I'm not sure what your problem is. II | (t - c) 22:27, 22 November 2008 (UTC)

It's out of place, if mathematical induction is on here then why not epsilon-induction and transfinite induction too? My first impression was that someone was trying to equate the process to scientific reasoning, but even if that were not the case (as you pointed out) it's out of place on this article. —Preceding unsigned comment added by (talk) 06:13, 23 November 2008 (UTC)

I just checked some of the sources, and they even have mathematical induction on the stanford encyclopedia of philosophy. I think it's out of place, but if it's on the major sources then I guess it's okay, my initial thought was that it was just misleading to have something from the realm of mathematics on an article about induction (unless perhaps to speak of the status of axioms). —Preceding unsigned comment added by (talk) 06:20, 23 November 2008 (UTC)

I disagree that it's out of place to mention mathematical induction in an article on (the problem of) induction. Read Polya. Of course there is no "problem" of mathematical induction, but the thought processes are similar. (talk) 15:11, 6 December 2008 (UTC)

Mathematical induction is certainly based on statistical recurrence, just as scientific induction is, so there was no reason to remove that section.

"To over-simplify the issue, it could be said that mathematics replaces the question "Why should we use inductive arguments at all?" with "What conclusions do we reach if we allow certain kinds of inductive arguments?"
No inductive arguments are allowed; as said above, math induction is deductive. –Pomte 08:35, 14 December 2008 (UTC)


Does anyone remember Descartes making that argument somewhere in the meditations sometime after the cogito? I seem to remember him proving god's existence in order to justify the consistency of the world (thus we can rely on our empirical senses w/ god's existence validated). Asking this because maybe he should be included even if he didn't use the precise terminology? --Mr Bucket (talk) 07:56, 6 March 2009 (UTC)

Ordinary Language Solution[edit]

Why is there no reference to a Wittgensteinian-type solution to the problem? OLP solutions seem to be by far the superior ones in this case, and I think should be mentioned in the article. —Preceding unsigned comment added by (talk) 12:00, 14 September 2010 (UTC)

Relation to "Problem of evil"?[edit]

GuyHimGuy, you added a link to Problem of evil in the "See also" section, but I don't understand the connection to the induction problem. Maybe you could explain your reasons? Thanks in advance. - Jochen Burghardt (talk) 18:33, 3 March 2014 (UTC)

Thanks for addressing the matter Jochen Burghardt. Although the article isn't part of the religion portal, the ongoing Atheism-theism debate includes the problem of evil and the problem of induction as arguments for and against religion. I came across the Problem of Induction article while surfing the religion and atheism portals. The reason I surfed the portals was to find valid arguments for the debate. I just felt adding the internal link would make it less of a burden for the Wikireaders sharing the same interests as me. Although Probability theory and the Problem of evil both have nothing to do with the article, the problem of evil differs in that it would actually be useful for readers. I agree; many of the internal links in the "See Also" section should go. However, Apophasis and The Problem of Evil should be kept. They can actually be useful to some Wikipedians; no less so than the Law of large numbers, which was also kept. With a small degree of usefulness, the link is worthy of taking up some space. After all, WP is not paper so 22 extra bytes is no biggie. If the community doesn't mind would it be possible for the two internal links specified be re-added? Thanks. GuyHimGuy (talk) 02:01, 8 March 2014 (UTC)
Thank you for explaining. If you want to, add a link to this article (and the Problem of Evil page) to a page on the Atheism-theism debate. But this article has nothing to do with the problem of evil (or Apophasis, unless you care to explain), so a See Also link is not appropriate. In contrast, all of the current See also links (including Probability theory and Law of large numbers) are actually related to Induction. By your logic, every Wikipedia article would have hundreds of See also links, which would make it impossible for anyone to find the relevant ones. Please see the guideline at WP:SEEALSO. -hugeTim (talk) 02:13, 8 March 2014 (UTC)

Hi GuyHimGuy. I agree with Hugetim: in order to help Wikireaders who share your interest in atheism/theism to find arguments for that debate, a link from there to here (i.e. from some atheism/theism article to problem of induction) would be appropriate, not vice versa. I (still) can't imagine what readers interested in philosophical induction could benefit from being referred to the problem of evil, or to apophasis. - As a side remark: contrary to Hugetim, I think that the notion, although not the article, probability theory has a strong connection to induction; see e.g. the introduction of the publication [Rudolf Carnap (1947). "On the Application of Inductive Logic" (PDF). Philosophy and Phenomenological Research. 8: 133–148.] However, the wikipedia article is currently only about the "frequency concept of probability", while induction relates to the "logical concept of probability or degree of confirmation" (quotes from p.133). - Jochen Burghardt (talk) 11:26, 8 March 2014 (UTC)

Resolved. Thanks for the responses guys. I'll just leave the article as is for now. I now agree that the problem of evil has little to do with scientific philosophy. I guess readers can simply find this page the same why I did; a Google search concerning the reliability of science. GuyHimGuy (talk) 15:59, 8 March 2014 (UTC)

Induction Solves Demarcation Problem[edit]

Consider this example of the way induction must work in a particular science, specifically chemistry.

Mendeleev's periodic table was produced by noting the periodicity inherent in the physical and chemical properties of elements. For a long time, the table had weak acceptance, akin to the former pseudoscience of alchemy. Then along comes the particle physicists and Wolfgang Pauli's exclusion principle, which finally allowed a scientific explanation of both the electron configuration of atomic elements, and also the reason for the various groupings into periods, groups, etc.

This is already an example of how induction works in an actual science (where it had previously failed in alchemy). Isaac Newton himself was something of an alchemist. Where he succeeded brilliantly in physics, he failed miserably as a chemist.

The process of scientific iinduction continued with discovery of new chemical and later transuranium elements, always with the solid understanding of the periodic table serving as the foundation.

To throw induction completely out of the scientific method as Hume and Popper proposed is sheer folly. Moreover, a pseudoscience cannot possibly build on itself the way that science does. Induction applied to extending pseudoscience by even a tiny amount results in collapse of the premise(s) on which the pseudoscience is based. So, if Hume and Popper were so interested in the demarcation problem, why would they begin the process by throwing out the best working principle of the scientific method? It's bad enough that so much of science needs to rely on trial and error without throwing out all of the instrumentation that had previously been successful in revealing how the universe works. I suggest that we throw out the ideas of philosophers like Hume and Popper instead. Danshawen (talk) 23:54, 4 June 2014 (UTC)danshawen

Roy Bhaskar and Critical Realism[edit]

Y'all need to get Bhaskar and Critical Realism on this page!

Bhaskar says of Hume "[o]ne finds in the Treatise an eminently sensible realist methodology’, but that this description of scientific work is ‘in almost total dislocation from, and certainly lacking any foundation in, his radical epistemology’. (p. 41)

Bhaskar describes the scientific approach to establishing a law of nature:

In the process of the establishment of a law of nature three questions may be asked:

(i) is there an empirical regularity which constitutes a prima facie candidate for a law?

(ii) is there some reason, other than the regularity, why the predicates instantiated in the law-like statement should be conjoined?

(iii) is this reason located in the enduring powers of things and the transfactually active mechanisms of nature?

— Bhaskar p154

He then goes on to note that, "At the Humean level laws just are empirical regularities." (p. 155)

In comparison, science as practiced works on i, ii, and iii:

Most science proceeds by way of a two-tiered method designed to identify invariances in nature, normally under conditions which are experimentally produced and controlled, and to explain them by reference to enduring mechanisms. It is in the movement from the identification of an invariance to the mechanisms and structures that account for it that the logic of scientific discovery must be found.

— Bhaskar p159

In other words, Hume was just saying, you see a bunch of cases X and they have trait Y. Induction would say that the next case of X will also have trait Y, but this is illogical. You could see something else. But Bhaskar is saying that we know more about the world, on a number of different levels, and we're being more exacting about mechanisms.

Hume would say, Just because of all of your experience with ice cubes melting in the heat, you can't logically say that an ice cube in the sahara desert on a hot day will melt because, well, you know, maybe it won't! Nyah Nyah Nyah!

Bhaskar would say, well, we know rather a lot about ice cubes on hot days, not just from repeated experience (although that is pretty strong) but from our knowledge of different mechanisms. And so (to simplify, Bhaskar does tend to rather go on and on) the ice cube will melt -- or if it doesn't, there will be a good reason (it's in a freezer!).

All references are to Bhaskar, Roy. "A Realist Theory of Science." (2008).[1] Pigkeeper (talk) 22:54, 31 October 2015 (UTC)


  1. ^ Bhaskar, Roy. "A Realist Theory of Science." (2008).


Shouldn't he get a mention? Straw Cat (talk) 03:48, 13 November 2015 (UTC)

External links modified[edit]

Hello fellow Wikipedians,

I have just modified one external link on Problem of induction. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{sourcecheck}} (last update: 15 July 2018).

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 22:58, 6 December 2017 (UTC)

Induction & deduction[edit]

WP DEPENDS ON INDUCTION & DEDUCTION. THEIR MEANING SHOULD BE FIRM. This encyclopedia accepts the premise of enumerative induction that the more editors who agree on the content of an article, the more accurate and useful that content. Induction is practiced on every TALK page. Editors generalize from a few observations, and deduce concrete conclusions from their generalizations.

WP contains 4 repetitive and fragmentary articles on induction: Inductive reasoning, The problem of induction; New riddle of induction, Inductivism. I would like to rectify this chaotic situation by rewriting and merging these 4 articles, retaining only the reasoning title. I ask you—a participant in relevant TALK pages—to judge my rewrite/merge project: SHOULD I PROCEED? Below is the current proposed outline:

Definitions. Induction generalizes conceptually; deduction concludes empirically.

David Hume, philosopher condemner.

Pierre Duhem, physicist user.

John Dewey, philosopher explainer.

Bertrand Russell, philosopher condemner.

Karl Popper, philosopher condemner.

Steven Sloman, psychologist explainer.

Lyle E. Bourne, Jr., psychologist user.

Daniel Kahneman, psychologist user.

Richard H. Thaler economist user.

Please respond at Talk:Inductive reasoning. TBR-qed (talk) 15:58, 5 January 2020 (UTC)

Limited description of Popper's position on induction[edit]

This excerpt does not present all aspects of Popper's position on induction:

According to Popper, the problem of induction as usually conceived is asking the wrong question: it is asking how to justify theories given they cannot be justified by induction. Popper argued that justification is not needed at all, and seeking justification "begs for an authoritarian answer". Instead, Popper said, what should be done is to look to find and correct errors.

It does not incorporate Popper's organic view of science. To appreciate the importance of this organic view of science, another question must be considered, which is also a wrong question in Popper's view: how do we explain the inductive success of science, if induction is not valid logically? Popper argued that we do not have to explain this, because it's not happening that way. It's not only that justification is not needed, because this is compatible with the belief that there is an inductive process in science to be justified or not. Popper says that there is actually no inductive process in science, which is a much stronger statement. If there is no inductive process at all, of the Hume's kind or of any other kind, how can we explain that we have laws to put to the test? This is where Popper's organic view of science is important. A key point here is that an organic process does not have to be inductive at all, it does not even have to be a mental process. Yet such organic process is responsible for how amoebas evolved, etc. For Popper, scientific conjectures are the result of an organic process. Does it follow laws? Of course it does, but trying to understand this is beyond the scope of epistemology in Popper's view. It involves too many irrational aspects of the mind, etc. Therefore, one cannot even argue about the role of observations in that process and an induction process assumes that we start from observations. A very strong argument proposed by Popper against the idea that we start from observations is that observations are theory-ladenned and therefore there is no such a thing as an observation without first a theory. Dominic Mayers (talk) 17:29, 23 April 2020 (UTC)

Related bias in the article[edit]

In my view, the entire article is biased and makes Wikipedia affirms that there is an inductive process in science and in common reasoning. This bias shows up right at the start in the following excerpt (though it attributes it to Broad, putting this view at the start is a bias) :

The problem calls into question all empirical claims made in everyday life or through the scientific method, and, for that reason, the philosopher C. D. Broad said that "induction is the glory of science and the scandal of philosophy."

It also shows up in the picture of the raising sun and its caption (in this case, it is not attributed):

Usually inferred from repeated observations: "The sun always rises in the east."

I suspect that it shows up at other places in the article.

Usually corroborated by repeated observations: "The sun always rises in the east."
Usually not corroborated by repeated observations: "When someone dies, it's never me."

Dominic Mayers (talk) 18:04, 23 April 2020 (UTC)

@Dominic Mayers: You could just go ahead and delete the sentence with the C. D. Broad quotation. Anyone who objects can raise their objections here. According to wikiquote:C. D. Broad, the quotation is a paraphrase anyway.
As for the picture caption that you mentioned, I could be wrong but both picture captions in the article strike me as a little tongue-in-cheek. I don't think you're supposed to draw any conclusions from the rising sun picture caption by itself; you're first supposed to read the caption of the rising sun picture, and then read the caption of the funeral picture, and then realize what the problem is with the reasoning in the first caption. It's illustrating the problem of induction through a visual joke. Biogeographist (talk) 19:07, 23 April 2020 (UTC)
We don't want to take joke too seriously. So, I can only answer by, in my opinion, an even funnier joke (see pictures on the left). Dominic Mayers (talk) 20:27, 23 April 2020 (UTC)
I approve! Biogeographist (talk) 23:46, 23 April 2020 (UTC)
I address this issue in my suggested revision. See below.TBR-qed (talk) 21:03, 8 May 2020 (UTC)

Is this article obsolete?[edit]

In the near future, I intend to revise the article Problem of induction. I am motivated by the 2005 article with that name by Sloman and Lagnado in the Cambridge Handbook of Thinking and Reasoning, edited by Holyoak and Morrison. That article, it seems to me, makes this article obsolete in 3 ways. It eliminates detailed history of induction, easily available in descriptions of philosophical schools. It distinguishes kinds of inductive methodologies that are rarely noted. And it provides examples of current work on the topic, which is not elsewhere available. I ask editors interested in this topic to read Sloman and Lagnado and respond on this talk page whether they share my judgment of obsolescence or not.TBR-qed (talk) 15:02, 3 May 2020 (UTC)

This proposed revision may be related to what TBR-qed proposed at Talk:Inductive reasoning § WP DEPENDS ON INDUCTION & DEDUCTION. THEIR MEANING SHOULD BE FIRM. Editors should read that discussion, where there was some opposition to TBR-qed's ideas.
Regarding the article by Sloman and Lagnado, note that the authors are psychologists, and most of their chapter is focused "exclusively on the psychology of categorical induction" (p. 101) as part of a "descriptive account of inductive reasoning" (p. 99) as opposed to the "justificatory" concerns of many philosophers (p. 96). It seems to me at first glance that some material from Sloman and Lagnado's chapter would be appropriate both in Problem of induction and in Inductive reasoning, but to limit the scope of this article to the scope of Sloman and Lagnado's article would likely be controversial since the "justificatory" concerns that Sloman and Lagnado consider less interesting or even obsolete were nevertheless important to many philosophers' understanding of the problem of induction. That's my first impression. Biogeographist (talk) 00:52, 4 May 2020 (UTC)
I have just discovered your extended discussion, which I shall carefully study. Below is my response to your earlier comments. Thank you both for your acute observations. S&L are indeed psychologists who focus on the “psychology of categorical induction.” But their first 2 sentences—framing of the problem with Hume and the “fact” of sunrise— connects them directly to the WP article example of sunrise & its broader concern for justification. That is why I suggest relating 4 more scholars to S&L’s sample to show how modern scholars superficially adopt Goodman’s formalized knowledge while ignoring philosophical concerns—with negative results. I add Duhem & Dewey to show long-standing rejection of enumerative induction. I add Popper (who accepted the validity of sunrise) to support Hume & to critique S&L “induction as scientific methodology,” that conflates method of Duhem & Dewey with modern social science methods, including economist Thaler. I would leave [Inductive reasoning] & [Inductivism] unchanged to report more traditional treatments of induction. I have posted 2 sections of my draft revision in my sandbox, which I hope you can access and tell me your thoughts.TBR-qed (talk) 21:26, 8 May 2020 (UTC)

Discussion where one participant did not read the chapter
I share the same view as Biogeographist. I will add that the main assumption underlying the Sloman and Lagnado article or any part of this article that is controversial would have to be attributed to the authors: we cannot make Wikipedia states a controversial point of view as if it was a general consensus. The main assumption of this article is that there exists a psychological induction principle, which needs to be explained. This assumption is never put in question in the article. For Popper, this assumption is non sense.
Just sharing my personal understanding of Popper's argument. Human beings don't think with two categories of languages, one of them being specifically psychological. We have English, French, etc., but as far as reasoning is concerned these different languages are for the essential equivalent. There are, of course, some psychological, physiological, etc. processes behind the reasoning that is expressed in a language, but these are like different aspects of reasoning. Logic is just a formalization to explain our normal way of thinking. Of course, formally we can do whatever we want. We could have some inference rules that we qualify as "psychological" and others as (strictly) "logical", but all these rules have to interact, for example, the psychological rules might provide conjectures. All these rules together are just like a single logic with a psychological truth (with the obvious rule that logical truth implies psychological truth). All the well known arguments against induction would apply to that logic. Whether the truth is "psychological" or whatever makes no difference. It's just a new name for what we call truth. Here, let us recall that logic is a formalization for our normal way of thinking, that is, it always has been a model for our reasoning about real life. I share my understanding of the literature, because I am convinced that it's utopian to assume that editors can work together without a minimal shared understanding of the literature.
Dominic Mayers (talk) 17:08, 5 May 2020 (UTC)
Since the 19th century, what differentiated psychologists such as Sloman and Lagnado from philosophers is that the psychologists did empirical research (experimental, quasi-experimental, survey, etc.): they gave tasks to subjects (humans, or animals in the case of animal psychology) and recorded how the subjects performed the tasks. (By the way, the disciplinary separation of psychology and philosophy had an effect on how many philosophers conceived of philosophy, as Martin Kusch explored in his 1995 book Psychologism: A Case Study in the Sociology of Philosophical Knowledge. That is a very interesting history, somewhat tangential here, but it relates to what Dominic Mayers said above about the relation between "psychological" and "logical". Catarina Dutilh Novaes has written some interesting things about this, for example in her 2012 book Formal Languages in Logic: A Philosophical and Cognitive Analysis.) In the 1990s, some philosophers began doing empirical research too (experimental philosophy), but philosophers typically are not engaged in original empirical research (experimental, quasi-experimental, survey, etc.) with human (or non-human animal) subjects.
When Sloman and Lagnado focus their chapter on a "descriptive account of inductive reasoning", it means they are summarizing empirical studies that have given inductive reasoning tasks to subjects with the goal of trying to describe how people perform the tasks and what this tells us about their cognition during such tasks. But this "descriptive account of inductive reasoning" does not address many of the "justificatory" questions that have been posed (and answered) by philosophers about whether or to what degree or how inductive reasoning could lead to reliable knowledge. Biogeographist (talk) 18:38, 5 May 2020 (UTC)
Actually, it's not entirely true that philosophers typically are not engaged in original empirical research. Most philosophers of science, certainly Feyerabend, Kuhn, Lakatos, and Popper have considered history as if it provided some kind of empirical basis. It is at a different scale and perhaps the laboratory scale is more scientific than the history scale, but the study of the growth of knowledge through history share some fundamental issues with the study of learning in a laboratory. In particular, the issue whether we use induction or not is similar in both cases. Lakatos hoped to find some form of inductivism where a measure of validity based on observed corroborations and falsifications would be correlated with verisimilitude, more than a measure based on falsifications alone can be. Why? Because he wanted to explain the growth of scientific knowledge, which falsifications alone cannot explain. Again, induction was the natural explanation. The same story repeats itself again and again. I will have to read the research in laboratory, but I would be surprised if it is fundamentally different.
Dominic Mayers (talk) 20:34, 5 May 2020 (UTC)
Well, when researchers are asking subjects to do inductive reasoning tasks, it's different from behavior "in the wild" where people are not artificially constrained by the researchers' instructions! And the spatio-temporal scale of the world "in the wild" is vastly different. So it's very different indeed.
Each time I used the term "empirical research" above, I qualified it with a parenthetical set to indicate that I meant a subset of empirical research, not historical or case study research. That may not have been clear because the "etc." that I used made the set indefinite. The subset of empirical research to which I was referring did not really characterize philosophy before the 1990s, and is still rare in philosophy as far as I have seen. I remember reading an article by philosophers of science, writing in the 1980s, who complained about the lack of empirical research in their discipline: Laudan, Larry; Donovan, Arthur; Laudan, Rachel; Barker, Peter; Brown, Harold; Leplin, Jarrett; Thagard, Paul; Wykstra, Steve (November 1986). "Scientific change: philosophical models and historical research". Synthese. 69 (2): 141–223. doi:10.1007/BF00413981. JSTOR 20116337. Nothing resembling the standards of testing that these very authors insist upon within science has ever been met by any of their theories about science. Those of us who claim some modest expertise in the logic of empirical inference have been notably indifferent about subjecting our own theories to empirical scrutiny, even though our own philosophies of science suggest that without such scrutiny we might well be building castles in air.CS1 maint: ref=harv (link) Biogeographist (talk) 21:01, 5 May 2020 (UTC)
I understood what you meant. I still maintain that the fundamental issue of induction is similar in both cases, because it is very basic and universal. I might add that there are some aspects in the large scale of the history of science that is lost in the laboratory scale, but this is another story. Dominic Mayers (talk) 21:20, 5 May 2020 (UTC)
Just to be clear, what do you mean by "the fundamental issue of induction"? Biogeographist (talk) 21:24, 5 May 2020 (UTC)
The same fundamental issue that existed between Lakatos and Popper. Zahar described it in these terms:

Thus Popper and Lakatos differ only over the levels at which they locate non-rationality in science: Lakatos at the level of an inductive principle which justifies technology, and Popper at the lower-level of technology itself.

In my words, Popper explained progress in science as the result of a connection with nature (at the level of the technology) whereas Lakatos adopted an irrational induction principle, which Popper considered as non sense. I disagree with Zahar that a connection with nature is irrational. On the contrary, it's the most natural thing possible, because obviously the laws of nature created human rationality and the thesis that at some point in evolution human rationality got severed is not so natural. When did it get severed? When life was created? When some part of the brain was created? When? What is most natural is that it never get severed, but only human rationality became more and more elaborated and thus appeared more and more independent, but there is no reason why it should be severed. Note that Zahar makes a mistake in analyzing Popper's position. He assumes that nature is like a provider of random numbers (the mutations) and this is why, he says, that it does not work, but obviously that is an incorrect model.
You might not see the link with laboratory experiments. The link is that once we see that in science the most natural explanation is not induction, then it starts to be weird to consider that we use induction in smaller tasks. My guess is that there is no induction in the laboratory experiments and, most likely, the process can be explained using a simple probabilistic approach, which is consistent with logic. They must simply confuse ordinary statistical inference with induction.
Dominic Mayers (talk) 00:07, 6 May 2020 (UTC)
As I see it, the issue in your first paragraph is unrelated to the scope of Sloman and Lagnado's chapter, which is focused on how people deal with categorical induction problems that have been given to them by psychologists, and what the psychological research says about how people tend to think about such problems when psychologists pose those problems. The authors don't claim that induction is the engine of scientific progress. Despite the grand philosophical background in the first few pages of their chapter and the references to philosophy of science, the scope of the psychological research that they review is quite modest.
Sloman and Lagnado claim at one point that induction is "one of the main activities of science" (while also citing "opposing views"): "According to one common view of science (Carnap, 1966; Hempel, 1965; Nagel, 1961; for opposing views, see Hacking, 1983; Popper, 1963), scientists spend much of their time trying to induce general laws about categories from particular examples" (p. 107). But this claim is not central or necessary. And since the psychological research that Sloman and Lagnado review shows "the apparent plurality of procedures and mechanisms that people use to make inductions", it seems to me this implies that what is called induction in philosophy of science is also a "plurality of procedures and mechanisms" (p. 111). They say: "We believe that the bag of tricks describes most completely how people go about making inductive leaps" (p. 112). If we were to make an analogy to philosophy of science, that sounds like Feyerabend, not like inductivism as traditionally understood! That didn't occur to me when I wrote my first comment above. Still, I think the scope of Sloman and Lagnado's article is narrower than what the scope of this article should be, even with my Feyerabendian analogy added. Biogeographist (talk) 01:47, 6 May 2020 (UTC)
I am not sure that I understand what you wrote, but if the chapter "The problem of induction" final goal is not about induction as in the problem of induction (in science), but only about a related concept, then it does not seem a good source for this article and it does not have a good title. Dominic Mayers (talk) 02:13, 6 May 2020 (UTC)
Sloman and Lagnado begin the article with a summary of Hume on the problem of induction, but as I said in my first comment above, the rest of the article is "descriptive" and not directly related to the "justificatory" concerns that many philosophers understood as the "problem of induction", so the title does seem to be like a bait-and-switch, and this Wikipedia article would be the same if it were modeled on Sloman and Lagnado's article. Controversial indeed. Biogeographist (talk) 10:15, 6 May 2020 (UTC)
I realize that I had not understood your first comment. I assumed that the chapter was a form of support for inductivism. I am guilty of not having read carefully the part after the switch. Dominic Mayers (talk) 15:14, 6 May 2020 (UTC)
I think there is a conflation in the literature of (description of) learning with (description of) induction, the latter being very difficult to distinguish from the former. I schematize the situation as follows. Let H be the current knowledge, O be the observation. H + O might allow an ordinary statistical inference of C. That's not induction. It is only induction when C cannot be logically and statistically justified by H + O. The problem is that it's very difficult to determine H. What is the original "knowledge" of a rat in a laboratory experiment? So, it's hard to describe an induction process and, most likely, there is no induction. In the history of science, we naively assume that it's different. We assume that before the discovery of Einstein's theory of general relativity H did not contain it at all. So, naively, we assume that there is an induction process when we move from H + O to C, where C includes Einstein's theory. Popper's answer is that, as in the case of a laboratory experiment, it's hard to define the initial H in the history of science, because we must include natural processes. Ultimately, H is all the "knowledge" in nature. So, Popper says, induction is a myth. Dominic Mayers (talk) 16:27, 6 May 2020 (UTC)
As I see it, Sloman and Lagnado's chapter does not make the assumption (call it the "inductivist assumption") that all learning is induction. (Not that you implied that it did.) Any psychologist today knows about many kinds of reasoning and learning. The statement that it's a myth that all learning is induction is irrelevant to people who have never assumed that all learning is induction! Perhaps Sloman and Lagnado did their bait-and-switch with the problem of induction because they don't subscribe to the assumptions that led to the problem of induction in the first place. (Something like this seems to be implied when they bid adieu to Hume on their second page: "we might accept that no reflective reasoning can justify our inductive inferences, but this does not entail that reflective reasoning cannot be the actual cause of some of our inferences.") For them categorical induction is just a kind of task that some psychologists have given to their subjects (and not a kind of task that could be given to rats, since it requires language) with the purpose of trying to explain their subjects' performance in those tasks. Biogeographist (talk) 19:04, 6 May 2020 (UTC)
Perhaps some other kind of induction task could be given to rats, but not the tasks described in Sloman and Lagnado's chapter! Biogeographist (talk) 19:07, 6 May 2020 (UTC)
The myth is not all learning is induction. The myth is that some learning can be inductive. One might define "induction" as learning that cannot be explained deductively, but this is the wrong definition and is another way to conflate induction with deductive learning but where the original knowledge is unknown. The correct definition of induction is a learning process that is explained with inference rules that are not deductive, which we would call inductive rules. The distinction is important, because the most natural thesis is that any occurrence of induction in valid learning is a myth and the only reason why we cannot explain a process deductively is simply that we don't know the original knowledge. I was not specifically concerned with the experiments described in Sloman and Lagnado's chapter. I was concerned with a conflation of these two concepts in general, in a context where we discuss induction. Only an absence of a distinction between these two forms of learning would be already problematic. There would be no problem if the distinction between these two forms of learning and the fact that one of them is a myth was folk's knowledge, but obviously it is not. Note that, if we only speak of learning and don't mention induction, I have nothing to say. My concern is bound to the standard use of induction to refer to non deductive inference rules. (Personally, I always felt that learning is a process that brings out knowledge that somehow I already have within and it's the common experience.)
In general, I believe the confusion is related to the idea that the laboratory experiments are necessarily fundamentally different from the situation in the history of science. There are certainly differences, but this is another story. As far as inductionism is concerned, the situation is very similar in both cases. It's naive to think that a scientific discovery is not influenced by what occurred in the many million years of evolution before the discovery. It's almost impossible to define the original knowledge H, say before the discovery of Einstein's theory. This is the same problem as we have when we try to determine the original knowledge of a rat in a laboratory experiment. Dominic Mayers (talk)
A couple of thoughts: (1) Learning requires memory, so any time we talk about learning we're talking about something more than inference; we're talking about a complex material system. So even just to say some learning is inferential or can be explained by inference alone, even deduction, would be incorrect. "All learning is induction" is just a special case of the incorrect claim that "all learning is inference". (2) You said that any occurence of induction in valid learning is a myth, but validity implies deduction, so by definition "valid learning" would exclude induction! And as noted in point 1, learning is more than inference, so we shouldn't speak of "valid learning", but instead "valid inference" in a learning process. In the real world, people make invalid inferences, sometimes as part of their learning. This is partly (though not only) why people behave irrationally. Biogeographist (talk) 21:11, 6 May 2020 (UTC)
Regarding point (2), you can take out the "valid" before learning and move it after as in "learning valid knowledge". We meet the issue of what is valid knowledge, what is truth, etc., but this has been taken care by the study of logics. Yes, induction can be used and it's called a fallacy in logic. What is a myth is an inductive learning, i.e. the use of a rule that is not deductive and that would not be a fallacy. In the years 1930, logic was not as advanced as today. Nowadays, we have studied so many different kind of logics and the goal was exactly to model ways to get valid knowledge in mathematics and in science. None of them are inductive. (Perhaps still today some propose inductive logics, but it's the same old story: the belief that different kind of logics are valid outside science). Inductive learning is a myth. Popper has proposed a valid replacement that makes so much sense. I don't see why there is even a need to even discuss this.
I agree with point (1), but it was implicit in what I wrote. Obviously, besides deduction and in fact perhaps even more important than deduction, we need the process that brings out from the hidden H a formal conjecture that can be used deductively. Yes, thinking more about it, fallacies might be involved in this process. Why not, it's a complex process that is mixed with many things. The key point is that this process cannot be modeled as purely inductive and there is a need to assume a resource H that is unknown. The fact that you say that fallacies might be involved is consistent with Popper's view that it can hardly be made rigorous. We could guess a model, but a model where H is unknown will be difficult to test, even to conceive.
Dominic Mayers (talk) 21:30, 6 May 2020 (UTC)
I would just point out again that of course ways to get valid knowledge don't include induction, because by definition validity excludes induction! But psychologists such as Sloman and Lagnado have still investigated induction, not because they are trying to show that induction is valid, and not because they are trying to justify induction, but because they want to explain what people are doing when psychologists give them induction tasks. I keep coming back to that chapter because the question that started this section is about the implications of that chapter for this Wikipedia article. If further discussion would help answer that question, then we should continue; if not, we should stop. Biogeographist (talk) 22:09, 6 May 2020 (UTC)
If the chapter is not about gaining valid knowledge, then it does not fit in this article. Otherwise, there is an implicit assumption in the chapter (at the least in the way that you describe it) that people use induction as a part of gaining valid knowledge. Yes, I agreed that induction might be involved in some hidden process, but I don't see how we can possibly detect it, not to mention how to study it. That's why, if they say that they describe the learning process, fine, if they say that they describe an induction process, I will have to read the details, but I am pretty sure there must be a very strong assumption, perhaps simply the direct assumption that it is induction. If really, they have strong arguments (without too strong assumptions) that there is a use for induction in gaining valid knowledge, it is certainly related to this article. Dominic Mayers (talk) 22:20, 6 May 2020 (UTC)

Using the chapter (subsection added for easy editing)[edit]

After having read the chapter and related sources, I agree with Biogeographist that the distinction between "descriptive account of inductive reasoning" and the "justificatory concerns of many philosophers" is important. My understanding, and perhaps also the understanding of Biogeographist, is that, if this distinction is understood and taken into account in the way the chapter of Sloman and Lagnado is used, this chapter, especially the part after the history, can be used as a main source for the article as suggested by TBR-qed. Yes, in this perspective, the current article is obsolete, because it is too much about history.

But, if we don't see this basic distinction, the content of this chapter (and perhaps of many other sources that adopt the same descriptive approach) can become the source of a false controversy. Clearly, when Popper wrote that induction is a myth, he did not mean to say that the processes studied by Sloman and Lagnado are a myth. He only meant that, though these processes can be described as inductive rules, which relate premises to conclusion, what truly is going on is different and involves other "knowledge" perhaps not yet formalized.

We can schematize the situation as follows. Let B denotes the non formalized knowledge, P denotes the premises and C the conclusion. Because, B is in the background, what is observed is that P is used to infer C. So, we say that we have observed the inductive rule P |= C, but what truly happened is B Λ P |= C. This is an important distinction, because the inductive rules P |= C are well known in logic to be fallacies, but the hidden processes B Λ P |= C are most likely not fallacies.

It's very obvious that the chapter of Sloman and Lagnado refers to the way people normally think using their background knowledge. There is an implicit assumption that there is some uniformity among people in the way they think, i.e, some uniformity in this background knowledge. This is not at all opposed to Popper's view. On the contrary, it is a support for Popper's view. I agree with Biogeographist that we need to make a link with the philosophical perspective and that some other sources will be needed to make the link. However, I might be wrong, but I feel that not much needs to be added to the chapter to accomplish that.

There is a terminological issue here, because we refer to these processes as "inductive reasoning" and yet there is, hopefully, no claim that they are inductive fallacies. This can be taken care easily by making a little bit clearer that "inductive reasoning" refers to the description of observed processes, not to rules to rationally justify these processes. Dominic Mayers (talk) 16:58, 7 May 2020 (UTC)

I have just discovered your lengthened comments, which I will carefully study. Below is my response to the earlier comments:

Thank you for your acute observations. S&L are indeed psychologists who focus on the “psychology of categorical induction.” But their first 2 sentences—framing of the problem with Hume and the “fact” of sunrise— connects them directly to the WP article example of sunrise & its broader concern for justification. That is why I suggest relating 4 more scholars to S&L’s sample to show how modern scholars superficially adopt Goodman’s formalized knowledge while ignoring philosophical concerns—with negative results. I add Duhem & Dewey to show long-standing rejection of enumerative induction. I add Popper (who accepted the validity of sunrise) to support Hume & to critique S&L “induction as scientific methodology,” that conflates method of Duhem & Dewey with modern social science methods, including economist Thaler. I would leave [Inductive reasoning] & [Inductivism] unchanged to report more traditional treatments of induction.

The lead could be simplified[edit]

I propose to replace

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense,[1] highlighting the apparent lack of justification for: ...


The problem of induction is the philosophical question how to rationally justify inductive reasoning processes, which are observed, such as: ...

I would also propose to remove the following sentence:

The problem calls into question all empirical claims made in everyday life or through the scientific method, and, for that reason, the philosopher C. D. Broad said that "induction is the glory of science and the scandal of philosophy."

This sentence presents a false controversy. It does it, because it conflates two different things: the requirement for a rational justification of observed processes and these processes per se. The correct sentence (not that I propose that we use it) would be:

Induction processes are seen in everyday life and through the scientific method and, for that reason, C. D. Broad famously said that induction is the glory of science, but, if that is the case, Popper who found the way to rationally explain these processes must be the glorious hero of the philosophy of science.

— Dominic Mayers, This talk page

Dominic Mayers (talk) 16:12, 7 May 2020 (UTC)


  1. ^ Vickers, John, "Can induction be justified?", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.)

The new section on David Harriman's book[edit]

First of all, it's clear that the content is not verified. It's a favorable evaluation of the book and an interpretation of its scope made in the voice of Wikipedia, which breaks WP:NPV. Even if it was sourced in and attributed to some secondary source, a review of a book, even a brief one, is not in the scope of the current article.

That does not mean the content of the book is not acceptable in Wikipedia. I don't want to enter into the question whether the content is acceptable, because this would require a search for secondary sources that verify the same content (in respect of WP:NOR) and I am not going to do that now. However, I could not stop myself from looking at the main thesis of the book, which has 30 citations in Google scholar and thus is a good candidate. The book starts by doing a good job at describing the distinction between deduction and observed induction in science. It brings out a key point: deduction requires that there has been some previous induction, which, of course, is well known and understood. The main thesis of the book starts with this excerpt:

The problem is to identify the method of induction, not to seek its “justification.” One cannot ask for a justification of induction, any more than for a justification of deduction. Inducing and deducing are man’s means of justifying anything. Their validity as cognitive processes, therefore, is an unchallengeable given. Aristotle did not ask: Is deduction legitimate? but rather: How should it be performed so as to reach valid conclusions? Similarly, our question regarding induction is not: Is it legitimate? but rather: Given the validity of induction, how should one perform it so as to reach a knowledge of facts?

— Harriman, David, The Logical Leap (p. 8). Penguin Publishing Group. Kindle Edition.

This is not the problem of induction that most people try to address. Harriman argues that people try to address the wrong question, but his argument can be criticized. It is based on a similarity between deduction and induction: they are both a way to do inference. He says "One cannot ask for a justification of induction, any more than for a justification of deduction." But induction and deduction are more different than they are alike, so one cannot conclude that we can proceed with induction as we do with deduction. An important distinction is that induction is ampliative, i.e., it generates information that is not implied in the premises. So, as Carl Sagan said, "extraordinary claims require extraordinary evidence" and thus induction requires extraordinary evidence. The most important distinction, though, is that deduction has almost never been put in question, whereas induction has always been put in question. So, the natural question is given that we accept deduction as a valid mean of inference, because it is very ordinary, how can we justify induction, which appears extraordinary.

In contradistinction, the book denies from the start any form of justification for induction. I have not read the book, but it's possible that it provides a valuable description of recent induction processes in science and try to extract from this an observed scientific methodology. If it is that, it can hardly claim any novelty. It is exactly what Lakatos argued that should be done. Yes, Lakatos rejected, as did Popper, inductivism but only as a rational justification, not as an observed phenomena that follows rules. Only a small glance at Lakatos work shows that he wanted to find the inductive rules that are followed in the history science. He was explicit about that in his book "The methodology of scientific research programmes" (pp. 162-165). Most of this book concerns the history of science and the observation of these inductive phenomena. The only difference is that Harriman denies any chance of justification, whereas Lakatos did not. Popper, we can say, also denied a rational justification for these observed rules, that is, he never tried to turn them into rules that can justify steps of inference or to find such rules that would justify them.

In this manner, Popper might seem close to Harriman, but there is a big difference. Popper did not deny a rational explanation for these observed induction processes and, in fact, he offered a very natural explanation. Zahar presents this as the fundamental difference between Popper and Lakatos. This rational explanation makes a big difference, because otherwise one is tempted to interpret these observed rules as if they were some kind of ampliative rules of valid reasoning, which we should follow. Why not? If they are observed and they are successful, why not use them as rules of inference? Popper's explanation explicitly rejects this interpretation. Popper offered methodological rules, which were prescriptive, but they were not inductive. By the way, Lakatos proposed descriptive inductive rules, but these rules were either deprived of any form of inductivity or rewritten so that they could not be prescriptive before they found their way in his proposed methodology. Here is an excerpt that illustrates the first case (emphasis mine) :

Musgrave in a letter containing some major constructive criticisms of an earlier draft, in which he demanded that I specify, for instance, at what point dogmatic adherence to a programme ought to be explained 'externally' rather than 'internally'. Let me try to explain why such objections are beside the point. One may rationally stick to a degenerating programme until it is overtaken by a rival and even after. What one must not do is to deny its poor public record. Both Feyerabend and Kuhn conflate methodological appraisal of a programme with firm heuristic advice about what to do. It is perfectly rational to play a risky game: what is irrational is to deceive oneself about the risk.

— Lakatos, The Methodology of Scientific Research Programmes: Volume 1. p. 117

Here is an excerpt that illustrates the second case:

"It is very difficult to decide, especially since one must not demand progress at each single step, when a research programme has degenerated hopelessly or when one of two rival programmes has achieved a decisive advantage over the other. In this methodology, as in Duhem's conventionalism, there can be no instant − let alone mechanical − rationality. Neither the logician's proof of inconsistency nor the experimental scientist's verdict of anomaly can defeat a research programme in one blow. One can be 'wise' only after the event."

— Lakatos, The Methodology of Scientific Research Programmes: Volume 1. p. 113

So, at the end, Popper's and Lakatos' methodology were both non inductive and consistent one with the other.

Dominic Mayers (talk) 18:32, 8 May 2020 (UTC)

Implicit assumption that no background knowledge is involved[edit]

The following sentence suggests that no background knowledge is involved in observed induction processes:

In inductive reasoning, one makes a series of observations and infers a new claim based on them.

Some thinking is needed to find a better way to describe the problem, but the description must clearly distinguish between a rule to describe observed processes, which usually involve some hidden background knowledge, and an ampliative rule to infer new knowledge. By definition, the ampliative rule does not use any background knowledge that, if made explicit, would allow to deductively infer the "new knowledge".

Dominic Mayers (talk) 20:37, 8 May 2020 (UTC)

I think my proposed revision addresses this issue. Please see below.TBR-qed (talk) 20:57, 8 May 2020 (UTC)

Plan suggested by TBR-qed[edit]

These are explanations of TBR-qed for his plan:

S&L are indeed psychologists who focus on the “psychology of categorical induction.” But their first 2 sentences—framing of the problem with Hume and the “fact” of sunrise— connects them directly to the WP article example of sunrise & its broader concern for justification. That is why I suggest relating 4 more scholars to S&L’s sample to show how modern scholars superficially adopt Goodman’s formalized knowledge while ignoring philosophical concerns—with negative results. I add Duhem & Dewey to show long-standing rejection of enumerative induction. I add Popper (who accepted the validity of sunrise) to support Hume & to critique S&L “induction as scientific methodology,” that conflates method of Duhem & Dewey with modern social science methods, including economist Thaler. I would leave [Inductive reasoning] & [Inductivism] unchanged to report more traditional treatments of induction.

I have no opinion, because I don't have yet a clear understanding of the plan. So, I will only mention points that come to my mind.

Regarding S&L are indeed psychologists who focus on the “psychology of categorical induction” I am guessing that the key word here is "psychology", because I don't see what would be an example of a "non categorical induction", except the cases where we have difficulty to make the induction because we are uncertain about the category. Therefore, in a way, it's always categorical. Collections in which the similar elements are distinguished by space-time coordinates are special kind of categories, but I don't see that the arguments to reject induction are specific to this kind of categories.

Regarding But their first 2 sentences—framing of the problem with Hume and the “fact” of sunrise— connects them directly to the WP article example of sunrise & its broader concern for justification I should point out that the example of sunrise in the article is biased. There is an implicit assumption that there is an observed induction and, moreover, that this observed induction is explained by the use of an ampliative rule, which thus need justification. As editors, we do not have to start the article by making a big assumption with no basis. No matter what the sources say, our terminology and our way to organize the article is our choice as editors. A source makes this assumption or it does not make it and it must be used accordingly in our article. But, I don't think that you had that aspect in mind when you wrote that sentence. Your point, I believe, is that you agree that we should have a link with the philosophical concern for justification.

Regarding That is why I suggest relating 4 more scholars to S&L’s sample to show how modern scholars superficially adopt Goodman’s formalized knowledge while ignoring philosophical concerns—with negative results I did not know much about Goodman, but I just read [2] and I found it very interesting theoretically, but also a very good example of a source that makes the big assumption that induction exists as a set of ampliative inference rules, not only as observed processes. So, he goes into a very interesting (but useless) argument how these inference rules can be "justified", just as we "justify" deductive rules. But, there is no evidence at all that ampliative inference rules are used. We only have evidence that inductive processes occur, which is completely different. These observed inductive processes do not need to be justified, as many pointed out. They only need to be explained and the simplest explanation is the use of an hidden background knowledge together with normal non ampliative rules.

Regarding I add Duhem & Dewey to show long-standing rejection of enumerative induction this seems to suggest that only this particular form of ampliative inductive reasoning is ruled out. That is a big claim. Of course, (observed) inductive reasoning does not need justification, because it is observed. However, I would say that any form of ampliative rule is ruled out and I would be very surprised that no argument was provided in the literature to reject the extraordinary claim that an ampliative rule, i.e., a fallacy, can be useful.

Regarding I add Popper (who accepted the validity of sunrise) to support Hume & to critique S&L “induction as scientific methodology,” that conflates method of Duhem & Dewey with modern social science methods, including economist Thaler I think the main contribution of Popper on the problem of induction is his very natural proposal that the use of ampliative rules is a myth and that the observed inductive processes are more naturally explained by an evolutionary process that created the required hidden background knowledge. He used a different terminology. What I call "ampliative rules" here, Popper called it "induction" and, what I call "observed induction processes" here, Popper called it "growth of knowledge".

Regarding I would leave [Inductive reasoning] & [Inductivism] unchanged to report more traditional treatments of induction, yes let us focus on this article.

Dominic Mayers (talk) 01:52, 9 May 2020 (UTC)

I hope you will be able to access my sandbox which outlines my plan. Your first paragraph above comes close to my main concern: uncertainty about the category. I find endless disagreement about operations called inductive and about their consequences. Your next paragraph says the sunrise example is biased, which is precisely why I discuss its widespread use as demonstrating the inseparability of description and justification. I think I agree with your point about editor choice, but do not understand "an ampliative rule, which thus need justification." Does your next paragraph saying "induction exists as a set of ampliative inference rules" identify operations, or conclusions of operations, or explanation of operations? TBR-qed (talk) 14:53, 9 May 2020 (UTC)

Subsection response to sandbox for easier editing[edit]

Please relate your answers to Popper's practice and to my section on sunrise. Thanks.TBR-qed (talk) 14:53, 9 May 2020 (UTC)

After having read your sandbox and considered your questions here, I think my paragraphs could have been clearer, but the main issue is with the terminology. We must first clarify the terminology before I can discuss Popper's practice, the section on sunrise and answer your questions about my paragraphs.
There is an important difference between the concept of an observed process in which some conclusion is drawn given some premises and the concept of rules of inference that can be used to explain this process. I could replace "explain this process" with "justify this process", which is what we say when inference rules explain a process, but I prefer the term "explain" because it brings out the notion that these processes are like other natural processes that need to be explained.
extra explanation
Consider the following incorrect argument from the observed q="here is a white swan" to the universal p'="all swans are white". Seeing this argument, one might conclude that the fallacy ∃x α(x) ⊧ ∀x α(x) was used (I made up that fallacy, but it more or less corresponds to what is some times called Hasty_generalization). However, the person who draw the incorrect conclusion p' might say, no I used the rule p → q, q ⊧ p, which is the fallacy affirming the consequent. Indeed, if we take p= p'∧q, then we have p → q. So, from the observed q, using the fallacy, we can infer p and then logically infer p' (because p= p'∧q). The details are not important, we could have many other examples, to illustrate that there is an important difference between an observed process in which some conclusion was drawn given some premises and the actual rules of inference that were used. We cannot know what were the rules, unless the person writes in the margin the rules that were used. Even this can be misleading, as illustrated by Newton's famous claim that he used inductive inference rules to infer his theory from observations alone, which we know cannot work. (On purpose, I have not respected the terminology used by Newton, because there would be a cyclic issue if I tried to explain a terminology by using a different and non consistent terminology.)
There are two distinct concepts: the processes that need to be explained and the rules that can explain them. A confusion between these two concepts might arise from the use of the expression rules of induction by S&L in sentences such as:

... normative rules of inductive inference that are generally accepted in the scientific community. One such rule is that properties that do not vary much across category instances are more projectible across the whole category than properties that vary more.

These are rules to classify observed processes, not to explain them. They are not basic inference rules similar to the deductive rules of inference. They exist at a completely different level.
extra explanation
These rules have not much to do with the deductive or inductive explanatory rules that could explain them, just as we have illustrated before. The explanatory inference rules are hidden and they cannot be justified by these observed rules, because there are a lot of things behind these observed rules, a lot of background knowledge, etc. To put it in another way, the inductive method of reasoning considered in S&L are emerging methods. They emerge from a background knowledge, which includes some fundamental empirical or perhaps metaphysical laws that are assumed. They are not basic inference rules similar to the deductive rules of inference. They exist at a completely different level. Some of these rules could be theorem based on some properties assigned to the categories, but that would be almost the same thing: we would need laws to verify that these properties hold.
I did not prove my previous claim and I cannot formally rule out the possibility that inductive rules might constitute a different logic for truth in science, but if it was the case it would be a very very important new branch of logic. In any case, S&L cannot prove that they have such a logic and it is a big assumption. The terminology should make clear from the start that there is another option, which do not require a new logic. In this other option, the so called inductive rules in S&L are not (explanatory) inference rules, but just rules used to classify observed processes. This other option uses only the standard, deductive, inference rules together with the assumption of a complex background knowledge provided by the evolutionary process. Because this other option does not require a new logic, it is in my view much easier to believe.
extra explanation
The point here is that, if someone has discovered a new inference rule that is ampliative, that is a big big deal. Let's keep in mind that we are talking about the "truth" of scientific laws, after corroborations. If we have a new logic with ampliative rules for this kind of truth, it is a big big deal. So big that it should totally change the face of logic. In fact, historically, logic has always been the logic of the practical truth used in science. Mathematics itself is only a tool for science. So it should lead to a new branch of mathematics based on this new logic of science. So, I am sorry, but S&L have not proposed that. I am aware that Goodman proposed a very interesting way to "justify" such a new logic using a notion of equilibrium, but this does not mean that we have found this new logic and, even if we have found such a new logic, it does not mean that it is the one used in science. Again, it would be a very big deal. In any case, our article cannot be written under this assumption. So, it should be only an option and the terminology should make it clear, from the start, that there is another option.
Given that the explanatory rules are abstract, not observed and not uniquely determined, should we ignore them as possible explanation for what is observed? Of course not. We have the same problem with the question what law is used when an apple falls from the branch of an apple tree to the ground. We cannot say that it is Newton's law, because one could rightfully reply that it could also be Einstein's law. Nevertheless, we do not abandon the question what law explains an observed phenomena. In the same way, inference rules are like laws that can explain observed reasoning processes. So, in our terminology, it is important to distinguish between observed inductive reasoning and (explanatory) inductive rules. Otherwise, the problem of induction cannot even be formulated correctly.
In contradistinction, if we use the correct terminology, then the problem can be formulated in one short sentence. The problem is how to explain observed inductive processes without using (explanatory) inductive rules or else how to justify these (explanatory) inductive rules. It can even be shorter : how to rationally explain the observed inductive processes. This is because justifying the (explanatory) inductive rules simply means arguing that they can be rationally used to explain the observed reasoning processes. Here, we see a closely related terminological distinction that is also important: explaining observed reasoning processes and justifying hidden inference rules are two different things, simply because hidden inference rules and observed reasoning processes are different things.
Here is the first paragraph in your sanbox:

The problem of induction is the philosophical question of whether knowledge humans gain by inductive reasoning can be as warranted as knowledge they gain by deductive reasoning—the alternative method of human reasoning.[1] How can one infer that observing a unique sample of an object or event is evidence of an unobservable universal kind or class of object or event?

I don't see in this paragraph where (ampliative) inductive rules enter into play. I don't see the two options: justifying these inductive rules or explaining the observed inductive processes without using these inductive rules. My personal opinion is that Popper is right that the first option is pointless, because there is a much simpler explanation that do not require the inductive rules. In any case, the problem of induction is certainly not how to do the first option only.
extra explanation
I am guessing that the paradigm in your first paragraph is simply that we can ignore or at the least not refer to inference rules as a way to explain observed reasoning processes. The suggested paradigm is that we have different kind of observed processes that we classify in terms of rules, the inductive ones and the deductive ones, but these rules are only ways to classify processes, not some kind of hidden laws to explain them. The question then becomes how the (descriptive) inductive rules can be as warranted as the (descriptive) deductive rules. This is confusing. It hides the possibility that the inductive rules (as description of observed processes) can be explained without using inductive inference rules (as laws used to explain observed processes). A better paradigm is that we simply want to explain what is observed using rules of inference and we accept that these rules interact and must be considered as one set of rules. It is fine to consider the option of adding inductive rules to this set, but it must be only one option. Another option is that we don't need to do that, because there is another way to explain what is observed.

I am not attach to any particular terminology as long as we use a terminology that does not conflate different concepts and that we use it consistently from the start. Dominic Mayers (talk) 17:57, 9 May 2020 (UTC)

I think we are now down to cases. I don't understand "(ampliative) inductive rules." I think it involves your effort to distinguish between explaining processes and explaining rules, which are both distinct from observing processes. But I think the inductive method means the following: 1)WE have a conjectural proposition--the sun [object assumed known in unspecified conditions] rises. 2)We ask whether observation [test statement] is true or false. Will it rise again [a conjectural universal predicate]? 3) Popper claimed we can't answer TRUE, but may be able to answer FALSE if it does not rise. 4)Absence of failure to rise temporarily confirms both conjectures as best tested theories.Objective Knowledge:10,20,26.
If determining what predicate is to be observed be excluded from inductive method, then Popper's purely logical conclusion follows. Duhem & Dewey show the error of this method, and sunrise instantiates it. My sandbox tries to set this scene. Do I fail, or am I mistaken?TBR-qed (talk) 13:39, 10 May 2020 (UTC)

Subsection perspectives on the problem of induction for easier editing[edit]

It seems that my attempt to explain my understanding of the perspective of Popper and many other philosophers on the problem of induction failed. You seem to say, I paraphrase, "I don't understand because here is my perspective and I cannot see how your perspective match with my perspective." It is surprising that you don't see a match, because you seem to attribute your perspective to Popper (Objective Knowledge:10,20,26). So, instead of trying again to explain "(ampliative) inductive rules", etc., I will try to discuss your understanding of Popper, your understanding of the inductive method and above all your understanding of the problem of induction. For a start, can you give one or more excerpts from Objective knowledge that correspond to the inductive method that you attribute to Popper, because I don't see where Popper has described the inductive method as you suggest that he did. If it is not from Popper (and the reference Objective Knowledge 10, 10, 26 was a mistake), please provide the correct reference and some excerpts, so that I can be certain about your sources. Dominic Mayers (talk) 19:21, 10 May 2020 (UTC)

Let me explain how I got from Popper’s Objective Knowledge to my second sentence. OK starts with Hume’s and the common sense definition of method of induction: “reasoning from [repeated] instances of which we have experience to other instances [conclusions] of which we have no experience.”(4). Popper renames Hume’s experienced instances “test statements” and his potential instances “explanatory universal theories.”(7)
S&L open their article defining the method as reasoning from “observed fact” to unobserved “conclusion.”(95) They then define a “rule of induction by enumeration” as “a universal hypothesis H being confirmed by positive instances E”(97) and the “propensity to group kindred entities and [to] project [Goodman’s name for potential universal theories] them into the future.(99) S&L eventually name the method “categorical induction,” defined as “how people generate degrees of confidence that a predicate [Goodman’s name for any conjectured test statement] applies to a stated category …”(111)
I find all these names identifying a single method: induction means counting empirical instances to confirm theoretical categories. Hume and Popper explicitly and legitimately condemn this method, which condemnation defines the logical problem—the assumption/belief that certain test statements are true, a conclusion NOT justified by repeated test statements as evidence.(7) Induction is not able to justify what it does.
Returning to Popper, he uses sunrise 4 times in OK as an example of the method and the problem. (Hume and S&L use same example). p.3 commonsense definition of method “repeated observations made in the past: we believe that the sun will rise tomorrow because …” This usage does not affirm Popper’s endorsement, but the fourth usage does, as example of psychological problem. p.26 assurance of truth of “best-tested theories, such as that the sun rises every day.” Sunrise has never been falsified. His second usage p.10 is explicitly falsified by universal theory/conjecture including time and location predicates. His third usage p.20 finds sunrise theory “preferred” because supported by background knowledge (71; Goodman called background “entrenchment by projectability” S&L p. 97). Here Popper endorses the very theory he rejects. How is it possible that knowledge of earth’s rotation does’t falsify all examples? Comments?TBR-qed (talk) 20:16, 11 May 2020 (UTC)
Two questions. First, in the sentence Here Popper endorses the very theory he rejects could you be more explicit about the theory that he endorses in p.20, but elsewhere rejects. It seems that this theory should be implicit in his third usage p.20, but I would like that you spell out explicitly what is this (general) theory that you think Popper inconsistently endorses in p 20. Second, in the sentence How is it possible that knowledge of earth’s rotation does[n]’t falsify all examples?, you speak of "examples", but examples of what? It's not only that I don't know the examples that you refer to. I also don't know what is exemplified. Dominic Mayers (talk) 01:01, 12 May 2020 (UTC)
p20. He finds "Sun rises [for earth-bound observer] in Rome every 24 hours," supported by Newton & 24 hour rotation. The experience is constant despite its false meaning. This statement differs from p10, which he interprets to mean 24 hours for every earth-bound observer in any location, an experience falsified at poles, ergo rejected. P10 logically false, p20 logically true. P3 theory is "sun will rise tomorrow because of" inductive observation interpreted as causation. P26 theory that sun rises every day" is "best tested" and must be pragmatically accepted, even though it cannot be eternally true. It is contradictory to accept a conjectural principle of transference p6 but to argue that the pragmatic problem of induction is independent of the logical problem BOTH EXEMPLIFIED BY A COMMON PATTERN OF BEHAVIOR--ENUMERATED SUNRISES. Imputing incompatible meanings to a common pattern of behavior is arbitrary metaphysics.TBR-qed (talk) 21:27, 12 May 2020 (UTC)
We have to put these four usages in their context. What he wrote in p.20 is not about induction. An argument that Popper uses in p.10 against inductivism can be turned against him in p. 20, that is, Newton + 24 hour rotation does not formally imply that the sun will rise every day, because it can explode, etc., but this would not affect much his main point in p. 20, which, anyway, is not about induction.
Similarly, p.10 is not about a method of induction proposed by Popper, but about a criticism of the method proposed by "inductivists": he basically says that even the standard examples of laws supposedly obtained by this so called method are not true universal laws. Inductivists might say that they did not claim that the method leads directly to universal laws, but only that the method exists and is used to obtain some laws. Popper discusses that also. In any case, p.10 is not at all about a method of induction proposed by Popper.
Similarly, in p.26, Popper only says that the "feeling of assurance" that inductivists claim comes from repetition is actually better explained in a different manner, more related to our pragmatic nature. He does not say it in Objective Knowledge, but elsewhere he says that it is the expression in our psychology of the natural mechanism of evolution. Popper had an organic view of science. He cites our assurance that the sun will rise every day in that context. He says that it is not the outcome of induction.
Let me add an important point in regard to p.26. One might think that the claim that no induction is used is equivalent to the claim that our experiences have no impact on our beliefs, but that would be a mistake. There are many ways other than induction through which experiences can affect our beliefs in some laws. One of them, but not the only one, is simply that our experiences can eliminate alternative theories such as the sun rises only twice a week. This is perhaps the point that interests us the most in our consideration of S&L, because it says that we must not conclude that a correlation between observations of premises and a resulting belief in a conclusion (that cannot be logically deduced from the premises) is necessarily the result of induction. This might be shocking for some people who see such a correlation as the very definition of induction, but this is only a problem of terminology. In the terminology where an inductive rule is analogous to a deductive rule in logic, we have to make sure that we can eliminate confounding factors such as some extra hidden knowledge, a correlation only is not sufficient.
Similarly, in p. 3, Popper clearly describes the standard method of induction without endorsing that it exists and is used. The whole thing is perfectly consistent. Dominic Mayers (talk) 01:32, 13 May 2020 (UTC)
I appreciate your questions, but can't accept these answers. Every reference to sunrise is an example of approval or rejection of an inductive theory of the cause of such motion. I can't follow you any farther into Popper's metaphysical third world. But I trust I have demonstrated that I am familiar with his work, and that discussing such a concrete example can promote useful discussion of that work and insight into the problem of induction by future encyclopedia readers.TBR-qed (talk) 19:40, 13 May 2020 (UTC)
My purpose was only to help you understand the literature, because a minimal understanding of the literature is necessary to edit this article. Of course, I do not want to patronize you. I sincerely thought you wanted my help. Dominic Mayers (talk) 20:30, 13 May 2020 (UTC)


I feel bad a bit, because we have cluttered this talk page with a long discussion that apparently was pointless. I hope that others such as Biogeographist have not been moved away by this. For what it's worth, I retract any support that I had in favor of TBR-qed plan, because I suspect that it is based on an incorrect interpretation of texts, which are taken out of context. However, my opinion about the value of S&L did not change. Dominic Mayers (talk) 20:30, 13 May 2020 (UTC)

No problem. In fact, I had stopped watching the page, so I didn't notice the discussion. I just looked at TBR-qed/sandbox, and I find it to be just as idiosyncratic as the suggestion to rewrite this article based on Sloman and Lagnado. In addition, TBR-qed/sandbox smells strongly of original research to me. What do you think of the article on the problem of induction at the Stanford Encyclopedia of Philosophy? I skimmed through it, and I think it would be a better model of what Wikipedia's article should be aiming for, although its style is not Wikipedia's style; the Wikipedia Manual of Style recommends against addressing the reader as much as SEP's article, which uses the word "we" 140 times. Biogeographist (talk) 22:31, 13 May 2020 (UTC)
I certainly enjoyed reading Henderson's article on the problem of Induction. He misinterprets Popper, but this is because most people don't realize that Popper was very close to Kant as far as a priori are concerned, especially in the years 1989 to 1994, the last years of his life. Of course, unlike Kant, he never accepted that individuals had a priori valid knowledge, but he replaced that by an apriori at the level the evolutionary process in nature. So the apriori of Kant was replaced by the acknowledgment that if the laws of nature were not supporting progress in science, then scientific knowledge would not grow. One might argue that this a priori was still a conjecture for Popper. Sure, but this conjecture plays the same role with respect to the problem of induction as Kant's a priori: if the problem of induction exists, for Poppper, the conjecture must be true, because, for Popper, if the conjecture was not true, there would be no growth of knowledge to explain and thus no problem of induction. Henderson should have classified Popper's solution in section 3.1 "Synthetic a priori", not in section 6 "Living with Inductive Skepticism".
In accepting this a priori, Popper was not so different than many other great scientists who are or have been (if they passed away) in bewildering admiration in front of the fact that the laws of nature are such that we can learn, we can be there and admire and understand the universe, more and more. The difference is that he also used that fact as a solution to the problem of induction. His argument, which is made clear in "All life if problem solving" and "The myth of the framework", is simply that whatever was there to support evolution before the rational aspect of the mind existed is still there and there is no reason why this evolutionary process should now require induction, a process at the level of the human mind. He starts by considering the "knowledge" in a dog and he goes back to unicellular life. At every level, he says, there are problems to solve and the evolutionary aspect of nature guesses solutions in a successful manner, with the need of trials and errors, but he sees no induction at all. This quality of the laws of nature is a big a priori. The fact that it is a big apriori, which we simply have to posit if science is to have any hope to succeed, is clearly mentioned by Popper in Objective Knowledge.[A] Not only Henderson incorrectly classify Popper's solution, it also so obviously misses an important aspect of the solution. So much that it would be inadequate to give too much weight to his critic of Popper's solution.
But that's OK, the remainder of the article is very enlightening. His analysis of Hume's argument is very precise. He brings out the premises and the conclusions and consider how we can evade the argument by rejecting the premises. It's excellent. I am not opposed to this approach.
I would also keep the part on Pyrrhonism and Indian philosophy that we currently have in the article, even though the article confuses these rejections of induction with a discussion on the problem of induction. The problem of induction only arises when we also ask the question how knowledge grows, i.e., how induction as growth of knowledge can be explained. What is written about Pyrrhonism and Indian philosophy does not ask this question. It only rejects induction as a formal method of inference. Again, the confusion lies on the fact that we do not distinguish between induction as growth of knowledge and induction as a method of inference. These are completely different things. This confusion does not exist in Henderson's article for the simple reason that induction only refers to growth of knowledge and instead of using the term induction to refer to rules of inference, he speaks of arguments "having an empirical premise", which are the other arguments besides the arguments "deductively valid with a priori premises". The key point is because we assume a priori premises (such as Popper's assumption about the role of the evolutionary aspect of nature), we don't need induction ... oups, may be I should have written "we don't need arguments having an empirical premise".
Dominic Mayers (talk) 05:00, 14 May 2020 (UTC)


  1. ^ Popper 1972, p. 23 : "There are many worlds, possible and actual worlds, in which a search for knowledge and for regularities would fail. And even in the world as we actually know it from the sciences, the occurrence of conditions under which life, and a search for knowledge, could arise—and succeed—seems to be almost infinitely improbable. Moreover, it seems that if ever such conditions should appear, they would be bound to disappear again, after a time which, cosmologically speaking, is very short."

Avoiding making implicit assumptions.[edit]

I just want to summarize what are my concerns. The article should not in the voice of Wikipedia implicitly conflate two notions of induction:

  • any move from observations to a conclusion, in which the conclusion cannot be deductively obtained from the observations and
  • the use of inductive inference rules to execute such a move.

I think the first notion is the standard concept of induction in philosophy or may be it depends of the author. For example, I think Goodman refers to rules of inferences when he explains how induction can be justified. The same terminology "induction" for totally different concepts might create some confusion. In addition, the article must distinguish between

  • a process of induction with a clear causal relation from observations to a belief in a conclusion and
  • a presumed process of induction where this causal relation is not so obvious.

For example, Popper argues that the causal relation between observations of sunrises and the belief in the law "the sun rises every day" is nonexistent. I am only saying that the article should not have Wikipedia implicitly adopt one of these two views, when there is no consensus about it in the literature.

However, I must say that most of the article is fine with regard to these concerns. There are the images on the left side, which incorrectly assume an inference from observations of sunrises to the corresponding law. There might be nothing else. I would have to read it again.

Dominic Mayers (talk) 21:57, 13 May 2020 (UTC)

Is this article obsolete? (continued)[edit]

I’m glad Biogeo has returned to the discussion, so now I can ask both of you a question that has dogged me since beginning to edit WP. Please humor me, in the interest of improving the encyclopedia. As Biogeo gently put it, I have been judged “idiosyncratic” from the first, engaging in original research, and violating NPV. I reject these charges for the following reasons.

My first post revised the existing article on Instrumentalism. Its flaw was to ignore John Dewey who, for decades, was the philosopher spokesman for that “school.” Excluding Dewey completely violated NPV.

My revision described Dewey and Popper as representative supporter and critic of the school, followed by numerous social science examples of current debate on their positions. Critics reverted my post, arguing that I should just have added a reference to Dewey to the existing conventional article.

I found that impossible, because Dewey had “reconstructed” the debate. This required me to reframe the topic neutrally to include both positions. I find that same imperative in Problem of induction. I am not being original or violating NPV to try to define both the activity and the problem of induction in precise terms applicable to objective discussion of all positions taken. My sandbox draft is the current result.

I hope you will not dismiss my effort for being idiosyncratic. I hope you will critique my effort if it fails to achieve my purpose within WP parameters. That should be possible without entering into philosophical minutia, if I demonstrate familiarity with the representative positions. I think you might even enjoy seeing Popper confronted by a worthy adversary.TBR-qed (talk) 20:25, 14 May 2020 (UTC)

The reason why I don't reply is that I don't know what to do when an issue is not about the article or about (our understanding of) a source or an eventual source for the article. Dominic Mayers (talk) 16:43, 15 May 2020 (UTC)

@TBR-qed: I can appreciate that you don't like my judgment of your draft as idiosyncratic, but after looking at it again that's still my verdict.

Above, your response described (if I understand you correctly) an analogous "reconstruction" and "reframing" that you attempted in another article. I agree that you have done some reconstructing and reframing of the problem of induction in your draft, but it seems narrowly done, which is what I mean by idiosyncratic. If you were aiming in your draft for a more comprehensive and neutral perspective, as you claim above, and not merely a change of perspective to your own point of view, then you haven't yet succeeded. Your draft reads like your own original argument, and not a very clear one.

The following quotation is an example of a more comprehensive and neutral perspective, from the lead to the article on the problem of induction at the Stanford Encyclopedia of Philosophy: "A number of philosophers have attempted solutions to the problem, but a significant number have embraced his conclusion that it is insoluble. There is also a wide spectrum of opinion on the significance of the problem. Some have argued that Hume's argument does not establish any far-reaching skeptical conclusion, either because it was never intended to, or because the argument is in some way misformulated. Yet many have regarded it as one of the most profound philosophical challenges imaginable..."

That your draft is original research is clear enough from the lack of citations, although one could also point to other indicators of original research. To be clear, no original research means: don't make claims or arguments that are not attributable to a reliable source, and don't use statements from a source to reach a conclusion that is not in the source. You cite Sloman and Lagnado's article, of course, but I don't think Sloman and Lagnado's article is a good basis for radically reconstructing this article, as explained above. Sloman and Lagnado could be used for some details, but despite its title it is not appropriate as a model for massively reconstructing this article. When you look up Sloman and Lagnado in Google Scholar and look at the list of publications that cite it, you see that almost none of them are about the problem of induction! Scholars who have found Sloman and Lagnado's article useful enough to cite are not generally writing about the problem of induction. There is an interesting exception: Jackson, Alexander (June 2019). "How to solve Hume's problem of induction". Episteme. 16 (2): 157–174. doi:10.1017/epi.2017.32.CS1 maint: ref=harv (link) Jackson's citation of Sloman and Lagnado's article is a good example of the minor role Sloman and Lagnado would have in a philosophical discussion of the problem of induction, although Jackson's article is not a good model for reconstructing this article either, since Jackson was making an original argument and was not attempting to follow Wikipedia's WP:NOR and WP:NPOV policies.

Perhaps a better strategy for adding the information that you want to add to this article would be: Find a highly cited source that contains the arguments that you think are important and unrepresented in the article, and then accurately describe that source in a new subsection in Problem of induction § Notable interpretations. Or two subsections, if there are different arguments in two different sources. Biogeographist (talk) 21:03, 15 May 2020 (UTC)

Thanks. Let me digest your remarks.TBR-qed (talk) 14:25, 16 May 2020 (UTC)
I sincerely thank Dominic Mayers & Biogeographist for answering my question about the obsolescence of the existing problem of induction article. Everything you wrote revealed some element of that problem.
DM (23 April) found the entire article biased because it assumes that this reasoning method starts with observation: an empirical claim. This claim ignores Popper’s thesis that reasoning starts with a theoretical conjecture about an observed-&-known phenomenon. The bias is revealed by the author’s treating repeatedly observed sunrise as an effect of unobserved solar motion, and by the Broad quote: "induction is the glory of science and the scandal of philosophy.” Popper replaced enumerative induction with falsification, making sunrises & Broad irrelevant.
I find the existing article unbiased but incomplete. It does not do justice to Popper, but correctly reflects the traditional interpretation that induction is illogical but sometimes successful in identifying natural kinds of phenomena—such as sunrises. I intend to restore the Broad quote, retain the sunrise photo, and expand coverage of Popper, Duhem, & Dewey.
Biog (15 May) makes 3 points. 1) Possible bias in existing article and my idiosyncratic definition of induction might be “merely a change of perspective to your own point of view.” 2) My draft “is original research … clear enough from the lack of citations,…”. 3) “Sloman and Lagnado's article is [not] a good basis for radically reconstructing this article.”
All fair and constructive observations. 1) is an example of the problem of induction: establishing that a single sample is, in fact, representative of a natural kind. My unfamiliar definition might be a unique idiosyncratic conjecture or a genuine continuing factor. Only subsequent observation will establish whether it fits each of the 8 scholars on whom I report. 2) Lede doesn’t need sources. It sets the stage for well-documented content to follow. 3) I find S&L discussion of kinds of induction extremely useful, but I use only 4 of their scholars as samples. I hope to have my revision ready for further critique by September.TBR-qed (talk) 14:08, 20 May 2020 (UTC)
Are you suggesting that any work to improve the article, perhaps reorganize it, should wait until after you have your revision ready for further critique by September? In addition, you stopped any effort to have a minimal required shared understanding when you wrote I can't follow you any farther into Popper's metaphysical third world. That's not the way it works in Wikipedia. There is no way editors can work together on an article without sharing a minimal understanding of the literature.
By the way, I did not even mention "third world" once in all my comments here. In fact, I never been much interested about what Popper wrote on this subject. I recently read about it because other editors mentioned it and what I found was not much. It is just the standard separation that many philosophers do. In Popper's view, the first world is the real world. From this first world emerges the world of mental activities, the second world. From this second world, emerges the objective knowledge that can be written in books, etc., the third world. It's not a big deal and it's not even necessary to use this terminology, because most of the times Popper does not use it. Instead, he refers to divisions as seen by other philosophers. For example, Hume made a distinction between the rational and the psychological in human thinking, which more or less corresponds to the distinction between the second and third worlds, but Popper uses Hume's terminology when he discusses Hume.
Any way, I think it was very unfair from you to say that you cannot discuss further with me, because [you] can't follow [me] any farther into Popper's metaphysical third world and then add that your revision [will be] ready for further critique by September.
Dominic Mayers (talk) 15:44, 20 May 2020 (UTC)
@TBR-qed: A technical detail. You said: Lede doesn't need sources. More precisely, statements in the lead don't need sources when they summarize content that appears later in the article with citations, but the lead often includes other statements that are not repeated again in the article: these statements would need sources. Biogeographist (talk) 22:07, 20 May 2020 (UTC)
Biogeographist, I do not understand. Do you mean that you encourage TBR-qed to work on his own on this article for three to four months, without any attempt from him to get a consensus on his ideas, because this is how I interpret his plan?
I am even more concerned when I see that the little he wrote above is full of misinterpretations. He wrote DM found the entire article biased because it assumes that this reasoning method starts with observation: an empirical claim. This claim ignores Popper’s thesis that reasoning starts with a theoretical conjecture about an observed-&-known phenomenon. I did not mention this. What I mentioned on April 23rd is that the article misses a key ingredient in Popper's solution, namely, his view that the problems in explaining the growth of scientific knowledge are part of the problems in the theory of evolution in general. I also mentioned a bias in the article, but finally, after looking at it, it turned out to be only Broad quote and the captions for the pictures, two points that TBR-qed disagree with, which is fine. But he also does not intend to discuss these points or any other aspects of his understanding further. This, on the other hand, is problematic.
My main concern was at a different level and I think that, if we could clarify this main concern, the other points will be easier to address. As we see clearly in the Henderson's article on the problem of induction that Biographist suggested, there is a fundamental distinction between (reasoning) arguments and the inductive processes that we try to justify using these arguments. One needs to understand this distinction to see that Sloman and Lagnado only study the inductive processes themselves and thus ignore the philosophical problem how to justify them using reasoning arguments, a point that was made by Biographist from the start.
This is related to a very important problem of terminology. Nowadays, as can also be seen in Henderson's article, we refer to these reasoning arguments as inductive and deductive. There is no confusion in Henderson's article. Nevertheless, this terminology issue can create a big confusion, because now we have very similar terminology for two different concepts: reasoning arguments and inductive processes. To make things worst, Sloman and Lagnado classify the inductive processes using rules, which they call induction rules, which make them look like rules of argumentation. I would not be surprised that there is an implicit claim in Sloman and Lagnado that there is no fundamental distinction between these rules, which only classify the observed induction processes, and the inductive rules of argumentation, also called inference rules. I see a very very big problem in this implicit claim, because these observed processes can not be under question, because they are observed, and we cannot also complains about a classification of these processes. In contradistinction, the inductive rules of inference are certainly under question and, in fact, it is nowadays widely accepted that they don't really exist.
I suspect that TBR-qed also rejects this fundamental distinction, but I am now asking TBR-qed about that. TBR-qed, when you wrote I don't understand "(ampliative) inductive rules." I think it involves your effort to distinguish between explaining processes and explaining rules, which are both distinct from observing processes, were you implicitly rejecting that there is a fundamental distinction between the so called "Induction Rules" in Sloman and Lagnado and what Hume calls arguments? This is very important, because this is definitively part of a minimal understanding that editors (except those that only look at grammar and things like that) must share before they can work on this article.
Dominic Mayers (talk) 01:11, 21 May 2020 (UTC)
@Dominic Mayers: Sorry for the terseness of my previous reply; no, I was not endorsing TBR-qed's plan. But if he wants to come back and present his revision after three months, he is free to do that, and we are free to reject it if we find good reason to do so (and if we are still around). In the meantime, editing of this article will continue as usual just like the rest of Wikipedia, of course.
You mentioned evolution a number of times in the preceding discussion and it occurred to me to mention that the general term for the study of the relation of knowledge and biological evolution is evolutionary epistemology, a term coined by Donald T. Campbell and then adopted by Popper and many other thinkers. Biogeographist (talk) 04:01, 21 May 2020 (UTC)

Yes, regarding TBR-qed's plan, I expected that you would say that he is free to do that. I do not disagree at all. In fact, I also had the same thought. However, I feel that I have to offer an alternative approach, which is to try to achieve a consensus on some minimal shared understanding.

Regarding evolutionary epistemology, Popper had this concept even before LSD was published. Here is a quote from Popper of a text originally written around 1952. This quote refers to LSD which was being translated at the time.

Sometimes I have also described it as the degree to which the theory in question ‘has been able to prove its fitness to survive by standing up to tests’. But as the context of such passages shows, I meant by this no more than a report about the past fitness of the theory to survive severe tests: like Darwin, I did not assume that something (whether an animal or a theory) that has shown its fitness to survive tests by surviving them has shown its fitness to survive all, or most, or any, future tests.

— Popper, Karl, Realism and the Aim of Science (p. 64).

But of course, the notion might have existed way before Popper. That's not important. What is important is who has seen the significance of this connection and used it. Popper understood that it was a fundamental ingredient in the solution to the problem of induction.

Dominic Mayers (talk) 10:40, 21 May 2020 (UTC)

Sure, there's no doubt that Popper was the major inspiration for Campbell's coining of the term evolutionary epistemology. I wouldn't know whether Popper was the first to connect Darwin and the problem of induction. I just searched on Google Scholar for Darwin + "problem of induction" before 1952, and discovered some fascinating stuff. I had heard of F. C. S. Schiller before, but I had never paid attention to his work. Consider this passage from his 1912 book Formal Logic, a Scientific and Social Problem (page 242, boldface added):

If in order to know anything we must first know that our principles are eternal a priori truths, and our facts absolute and immutable, it is painfully clear that knowledge is impossible, because we have not even now such facts and principles. But then we do not need them. All the equipment that we need to start upon the discovery of truth is a willingness to experiment and a willingness to learn. Granting these (and they are by no means common qualities), our experience will supply us with abundance of material. Indeed the chief difficulty will be to select the best and most workable from among the multitudinous suggestions and analogies with which the world bombards an actively inquiring mind. Fortunately there is abundant time for such selection. It has been going on for ages, and even the lowest organisms are to some extent selective in their reactions to stimulation. The selectiveness of man is enormous and all-pervading, and he is also conscious of it. Is it a wonder, then, that the results of this whole history should have crystallized into 'axioms' which now seem self-evident, and into 'facts' which now seem solid? Yet the logical value of the products which our ordinary thinking now takes for granted is not original but acquired. Nor are they, even now, immutable, or worthy of superstitious reverence; but they are secured against frivolous attacks.

Of course, merely to say "fortunately there is abundant time for such selection; it has been going on for ages" is not a fully developed evolutionary epistemology, but it seems clear enough that Schiller was thinking of evolution, given his abundant references to Darwin in this book—there is a section titled "Darwin v. formal logic"! And a section titled "The problem of induction". The basic ingredients are there, which is impressive for 1912. I searched for Schiller + "evolutionary epistemology" and noticed that Campbell mentioned Schiller in a paper published in 1989, "Fragments of the fragile history of psychological epistemology and theory of science" (page 28): "Finally, such thinkers as Dewey, Schiller, and Rignano have seemed to think that logical principles have some sort of psychological justification or else foundations in some kind of natural history."
The search for Darwin + "problem of induction" before 1952 also returned: Ritchie, A. D. (July 1926). "Induction and probability". Mind. 35 (139): 301–318. JSTOR 2249587.CS1 maint: ref=harv (link) This article does not propose anything like an evolutionary epistemology (it just happens to mention Darwin) but the similarity to Popper in some other aspects is striking. In fact, looking at the list of publications that have cited Ritchie's paper (not many), one sees that Lakatos cited Ritchie and even combined Ritchie's paper and Popper's LSD into one term: "the Ritchie-Popper argument"! Very interesting—I did not know this. Biogeographist (talk) 14:13, 21 May 2020 (UTC)
TBR-qed, just letting you know that none of what follows make sense if one does not accept the fundamental distinction between (reasoning) arguments and observed scientific knowledge (i.e. the existence of universal laws in science, in particular, the fact that we can learn new laws). The philosophical problem of induction cannot be formulated without accepting this distinction. The problem is how arguments + observations can be used to obtain the laws, the current laws or new laws. A key point is that the arguments must be universal formal rules that stand alone such as A ⇒ B, A ⊧ B, not categories of observed processes, in which there can be some hidden informal knowledge. The universality of the arguments is fundamental.
Biogeographist, your comments are interesting ! But, of course, you cannot expect a book written in 1912 to get even close to Popper's view. I quickly went over the chapters, reading only some excerpts, and I think the most relevant is the section "Concessions to Psychologic" at page 392. It's the traditional "solution". People are forced to admit that there is no formal inductive argument, because they see that it cannot be valid, but then, because they assume that knowledge grows from observations within human reason, they conclude it must be in the "psychologic".
The mistake, if we accept Popper, is to assume that our connection with nature is only through observations that can be translated in observation statements. Popper's view is that the conjectures themselves must be "explained" as the result of evolution. So, in the same way as, obviously, the laws of nature created large molecules without the help of any human reason, then created life without the help of human reason, the same laws of nature have created in some form in our brain the ability to make useful conjectures. This is NOT psychological, not entirely anyway, because it happened in parts even before our psychology existed. If we had to formalize the process, unless we personify nature, that would not be the description of some reasoning process. Such formal process would somehow have to consider that the knowledge existed before it becomes human knowledge. For Popper, this is a tautology: no formal machine can know what is not known.
My way to explain this is simply that the problem of induction is an artificial problem that arises when we separate the universe in two parts: the part that tries to know and the part that contains what must be known. Given this artificial separation, we ask the question how the laws of nature in one part can discover the laws of nature in the other part using only a formal process (a formal and limited view of itself) and observations of what is going on in the other part? The answer that Hume and others correctly obtain is that the laws of nature cannot do that and we have the problem of induction. Popper's view, the way I see it, is that this separation is artificial, because the conjectures also, not only the observations, arise from natural processes. That is amazingly simple and natural. It does not break any special thesis. It certainly does not break the Church–Turing thesis, unless we consider that Nature itself (not working in two parts, where one part is restricted to be a known formal process and the other part is considered unkwown) breaks this thesis. It is only common sense. It's very similar to Kant's solution and Popper acknowledged that. The difference is that Popper says that at any given time the conjectures formulated in human brains are only guesses. They are apriori, but not valid apriori. The valid apriori of Kant are replaced by the unknown (but by definition correct) laws of nature that, luckily, allows us to make useful conjectures. Popper believes in Darwin theory and therefore said that trying to explain how it happened is difficult because it happened as a result of many accidents.
Dominic Mayers (talk) 15:54, 21 May 2020 (UTC)
Right, Schiller was writing in an era when "computers" were people. Popper in 1952 was writing in the same milieu that gave birth to artificial intelligence and later to generalized cognitive science. Still, it's interesting that in a chapter on the problem of induction Schiller clearly refers to an evolutionary epistemological process, even if he is not clearly generalizing it from individual organisms to nature in general, much less connecting it to computation. Biogeographist (talk) 17:01, 21 May 2020 (UTC)
That's it. Popper would agree. He benefited a lot from Godel's and Tarski's results in logic and foundations of computer science. Of course logic existed before. In particular, Hume considered two kind of arguments: “demonstrative” and “probable”. But the formalization of logic with a clear notion of semantic based on separate formal interpretations must have been very helpful for Popper. Perhaps even more important was the discovery of general relativity, which was just beginning in 1912. Schiller could not benefit from the fundamental philosophical consequences of this. Dominic Mayers (talk) 17:43, 21 May 2020 (UTC)

The recent big edit of TBR-qed[edit]

I am not sure this big edit is an improvement. The problem of induction is one of the most challenging, if not the most challenging, subject in the philosophy of science and I think, we need the contribution of other editors here. It's going to be a challenge, if we want to make major modifications to this article. I intend to revert the last edits of TBR-qed. Dominic Mayers (talk) 15:26, 15 November 2020 (UTC)

Mcc1789 (talk) on 18:12, 15 November 2020 (UTC) wrote It seems fine.
I am glad to have this opinion, but still think that a more substantial discussion is needed. Dominic Mayers (talk) 18:20, 15 November 2020 (UTC)
@Dominic Mayers II: Please revert the edits by TBR-qed. If you don't revert, I will. The edits by TBR-qed suffer from the same issues that we discussed above regarding the draft at User:TBR-qed/sandbox, etc. For example, it over-relies on Sloman & Lagnado. The first paragraph is insufficiently clear for Wikipedia. Other parts of the lead section are unencyclopedic in tone. Dominic noted other problems below. I appreciate TBR-qed's enthusiasm for this topic, but what TBR-qed is trying to do in these edits may be better suited to an original journal article, not to Wikipedia. I suggest further discussion here with TBR-qed about what he is trying to do, if he wishes. Biogeographist (talk) 19:18, 15 November 2020 (UTC)
Yes, I am looking forward toward useful discussions with TBR-qed. I don't feel his points are wrong and disconnected from the literature, not at all, but they need to be attributed and balanced with other POV. Dominic Mayers (talk) 19:48, 15 November 2020 (UTC)
And yes, in view of the controversial nature of the subject, these points might be too recent and better suited in an original journal article. Yet, I think some balance is needed. Editors should work together to include as much recent and established knowledge as possible, but in respect of WP:RSUW. Dominic Mayers (talk) 20:09, 15 November 2020 (UTC)

What method of reasoning?[edit]

The first sentence in the lead is

The problem of induction is that this method of human reasoning, unlike its mate deduction, mysteriously and paradoxically creates illusions of knowledge of universal patterns out of fragments of experience.

It assumes from the start that there is an actual method of reasoning called induction and do not attribute this view to any philosopher. It is as if the encyclopedia states this as a fact. All recent edits of TBR-qed are based on this bias toward one point of view. Given that this is at the center of most debates on induction, this is not acceptable in Wikipedia. Dominic Mayers (talk) 18:59, 15 November 2020 (UTC)

Yes, I mostly agree. I'm not totally sold on the current wording but it's significantly better than the previous one. GliderMaven (talk) 22:00, 15 November 2020 (UTC)
Given that we have Inductive reasoning it would not appear to require further sourcing. What concerns me about the sentence is 'mysteriously and paradoxically creates illusions of knowledge" which seems to me to be editorializing.Teishin (talk) 18:11, 16 November 2020 (UTC)
You are right. The issue is not that the method of inductive reasoning is not defined and attributed to an author. The issue is the indirect assertion that it is actually used in practice and "mysteriously and paradoxically creates ...". The current version is more neutral, more adequate for a lead. Though, I am also not totally sold on the current wording either. Dominic Mayers (talk) 20:26, 16 November 2020 (UTC)

Reconsidering progressively the article[edit]

The revert of TBR-qed major edits should not be interpreted to mean that the article cannot be improved, of course. In my view, the article mostly contain excellent well sourced content. Something bothers me a little though. It seems to fail to distinguish between different descriptions of induction, which may or may not be equivalent and thus should not be considered a priori as one and the same concept of induction in Wikipedia. The challenge here is that not only different descriptions of induction seems to exist in the literature, but also different ways to distinguish between different descriptions seem to exist. It becomes easily a mess if one wants to consider all of this. On the bright side, I believe there is a classical notion of induction and it is not the notion of induction in Sloman & Lagnado, for example. I am not sure how we should manage this situation.

However, at the least, we should make sure that the article does not mess up different notions as if they were the same. I believe the article suffers from this kind of problems at few occasions. My main criteria is that the traditional notion of induction, even the probabilistic version, has clearly been rejected in philosophy, starting from ancient Greek and Indian philosophy and more recently with Hume. There has been many attempts to find a valid classical notion of induction, but no success. My favorite example is the entire work of Lakatos. He criticized Popper because he did not propose an inductive process and took for himself the task of finding inductive rules, but at the end he only obtained descriptive rules. He could not find rules that could be used by scientists and he acknowledged that. He argued that it was good enough, but many others philosophers noticed that it was not the original goal. For example, Feyerabend wrote in "Against Method" that Lakatos' methodology of scientific research programmes is epistemological anarchism in disguise and Musgrave made a similar comment. Anyway, if the article speaks of induction as inference rules that are used in practice and differ from deduction by the fact that they are uncertain or probabilistic, then a big red signal should be raised, because most likely if we look carefully at the source, we will see that it's not the classical notion of induction. Dominic Mayers (talk) 03:23, 16 November 2020 (UTC)

Rebutting my reverters[edit]

Dom’s and Bio’s reasons for reverting me are so flimsy that I cannot take them seriously.

Dom starts by asserting—without authoritative support—that the problem of induction is so large in the philosophy of science, that a single editor or a pair of psychologists can’t revise it. There must be a multitude of editors who presumably will agree on what the problem is. This is precisely why the existing article is obsolete. It is futile to keep repeating old inconclusive arguments

He goes on to deny the problem exists, asserting that my post is biased because I assume “that there is an actual method of reasoning called induction …” Ignoring centuries of philosophical debate, and the 9 scholars I discuss in the body of my post (which he has not seen), he seems to endorse Popper’s denial that inductive reasoning exists in the formal logical sense of deductive rules. I do NOT assume the existence of that which I analyze under the label of “problem of induction” Having judged the problem and the method to be illusions, he denies I have a right to examine ancient and modern debates about it. He is the biased one.

He condemns my reliance on two psychologists whose recent publication studies philosophers AND psychologists who practice and debate what they call induction.

Bio condemns my effort to reframe traditional debates in the terms currently employed by practitioners, labeling my definitions “unencyclopedic in tone.”

I will not permit these two to forbid my use of the lede to introduce the vocabulary currently used by practitioners of induction, nor to dictate which professional publications may be permitted to argue the illusions and facts of that kind of rationality.

I am going to restore and complete my revision, bringing the problem of induction into the 21st century. This not an uncyclopedic or biased enterprise.TBR-qed (talk) 13:41, 16 November 2020 (UTC)

A 15k+ character revision of an article is almost certain to be contentious. In the case where such large revisions are needed, they should be done piecemeal, over an extended period of time.Teishin (talk) 14:39, 16 November 2020 (UTC)
@Teishin: your point is important. @TBR-qed: you should consider it. You should also apply a similar principle when you write points that expect an answer. Take into account that each single point that you make that expects an answer, even if the point is short, can require a long answer. Please focus on one point that you want to be answered, so that we can actually have a discussion. I am waiting. Dominic Mayers (talk) 16:26, 16 November 2020 (UTC)
I too agree with Teishin's comment. See also WP:Consensus. If TBR-qed does not want to do the recommended small, gradual edits, then an alternative is to do a more large-scale revision in User:TBR-qed/sandbox and ask for a review by other editors. Then other editors could comment on what, if any, of the sandbox draft would be acceptable for merging into the article. Given our objections to what has already been reverted, it's unlikely that the other editors here would accept a whole replacement of this article by one written entirely by TBR-qed.
Above, in May, I said: What do you think of the article on the problem of induction at the Stanford Encyclopedia of Philosophy? I skimmed through it, and I think it would be a better model of what Wikipedia's article should be aiming for, although its style is not Wikipedia's style. I would like to hear TBR-qed's opinion of the SEP article (setting aside its interpretation of Popper, to which Dominic objected), and an explanation of how and why TBR-qed's approach would be different from the SEP article's general approach. Biogeographist (talk) 23:31, 16 November 2020 (UTC)
Just to quickly say, regarding Popper, that it's not my personal view versus SEP. The SEP article presents Salmon's view on how Popper cannot answer the strong interpretation of the Duhem-Quine thesis (see Lakatos, The methodology of scientific research programmes). It says nothing about Popper's evolutionary epistemology and how it relates to this thesis. Not so surprisingly, because many editors contributed to it, the current article does a better job on this respect, though I think it can still be improved. Dominic Mayers (talk) 23:53, 16 November 2020 (UTC)
I didn't mean that it was Dominic's personal view, but he happened to be the one who voiced that view here. Interestingly, an earlier version of the SEP article (Fall 2011) mentions evolutionary epistemology briefly, and in fact the last section of the article is devoted to it. But that section disappeared in the subsequent version (Winter 2012), and then several more substantial changes were made to the article and eventually a new author wrote the current version. Biogeographist (talk) 02:36, 17 November 2020 (UTC)
I also would like to hear TBR-qed's opinion on the SEP article. I feel that it will help us to understand what he is trying to do. Dominic Mayers (talk) 15:50, 17 November 2020 (UTC)

Thanks for correcting my ignorance.[edit]

Your replies have finally penetrated my ignorance of how I can use a sandbox to present a proposal rather than making a drastic revision. I shall do that. I shall review and comment on the SEP article. But first, let me make 2 assertions to show where I am coming from--which is doubtless as controversial as my content:

An encyclopedia is a living tool, not a crypt or mausoleum. Would it not be more useful to users of Wikipedia to learn how Daniel Kahneman’s Thinking Fast and Slow perpetuates the problem of induction than to learn what Sextus Empiricus wrote about it?TBR-qed (talk) 17:31, 17 November 2020 (UTC)

Wikipedia serves a wide variety of users who have a wide variety of information needs. Our concern as editors is not so much about whether X is more useful than Y, but whether X is useful enough to include. Teishin (talk) 18:17, 17 November 2020 (UTC)
Teishin's point is essential. I would actually be interested in reading about how Daniel Kahneman's Thinking Fast and Slow perpetuates the problem of induction. But keep in mind that such an account would need to be based on at least one secondary source to be included in Wikipedia. We can't make original arguments about primary sources (WP:NOR), so if you're making original arguments about Kahneman and the other authors that you listed above at § Induction & deduction, Wikipedia is not the place to do it. WP:PSTS says: "Secondary or tertiary sources are needed to establish the topic's notability and to avoid novel interpretations of primary sources. All analyses and interpretive or synthetic claims about primary sources must be referenced to a secondary or tertiary source, and must not be an original analysis of the primary-source material by Wikipedia editors." Biogeographist (talk) 18:39, 17 November 2020 (UTC)

Your points are well taken. I am making progress on my sandbox proposal which you can judge. I report my reaction to the SEP article.

RANSON ON SEP “The Problem of Induction.” First published Wed Mar 21, 2018 by Leah Henderson

Henderson’s discussion of Baysian probability (section 3.2.2) accurately states the problem of induction: “We want to infer not what the sample will be like, with a known hypothesis, rather we want to infer a hypothesis about the general situation or population, based on the observation of a limited sample.” I find this completely compatible with my opening statement: “The problem of induction is that this method of human reasoning, unlike its mate deduction, mysteriously and paradoxically creates illusions of knowledge of universal patterns [hypotheses] out of fragments of experience [limited but representative sample].”

Unfortunately, her opening paragraph does not state the problem. Instead it gives an example of the method of enumerative induction as the prototype of inductive inference. She follows with a common sense inference “from the observed to the unobserved, or to general laws… as ‘inductive inferences,’” further enforcing the belief that induction means counting observed samples as evidence of unobserved kinds, denying that other methods can legitimately be called inductive. This denial ignores the existence of a well-established scientific alternative—a terrible oversight which Sloman and Lagnado and I correct.

I present Duhem and Dewey as practitioners of scientific induction, which neither Henderson nor S&L do. The closest she comes is to identify Reichenbach’s “pragmatic vindication” of induction. Why not Dewey’s? To exclude Dewey’s Logic: the Theory of Inquiry is rank bias.

Henderson does not name Hume’s method enumerative induction. She attaches names recognizable only by philosophers to empirical-evidence-joined-to-conceptual-generalizations. “For convenience, we will refer to this claim of similarity or resemblance between observed and unobserved regularities as the ‘Uniformity Principle (UP)’. Sometimes it is also called the ‘Resemblance Principle’, or the ‘Principle of Uniformity of Nature’. S&L use the name common among psychologists: “similarity-based induction.” Both accept without debate that observable similarity is an empirical universal attribute of every sample of inductive inference.

Henderson and S&L accept without question Goodman’s premise that the attribute green is attached to emeralds by enumeration, and might change at any time. All ignore its scientific definition which cannot change metaphysically. None of its attributes is observable. All are predictable once kind is defined scientifically. “Emeralds are formed when chromium, vanadium, and iron are present in the mineral beryl. The varying presence of these three elements gives emerald its range of color.” Seeing Green: All About Emeralds - GIA › seeing-green

Henderson’s “meta-induction (section 7.3) seems to encompass S&L’s “categorical induction,” but she is unaware of the psychologists’ idea, much less its similarity to the philosopher’s idea.

My conclusion is that Henderson’s piece does more to conceal the nature of the problem of induction than to clarify and resolve it. — Preceding unsigned comment added by TBR-qed (talkcontribs) 18:32, 19 November 2020 (UTC)

TBR-qed: Thanks for your commentary on the SEP article. A quick response to one point you made: You said, comparing Reichenbach and Dewey: To exclude Dewey's Logic: the Theory of Inquiry is rank bias. I'm not sure exactly what you mean by "rank bias", so I may just be restating your point, but I think Henderson's inclusion of Reichenbach and not Dewey reflects the fact that Reichenbach's book has been much more commonly discussed in scholarly accounts of the problem of induction than Dewey's book has been. This can be seen quickly, for example, on Google Scholar by searching for "problem of induction" in publications that cite Reichenbach's and Dewey's books; Reichenbach comes out far ahead of Dewey. Nevertheless, I will be interested to see what you say about Dewey and which secondary sources about him and the problem of induction you are summarizing. Biogeographist (talk) 19:43, 19 November 2020 (UTC)

Proposed revision in User:TBR-qed/sandbox[edit]

@TBR-qed: I just looked at this latest revision of your proposed changes to Problem of induction. I understand that it may not be finished yet, but overall there is a major problem with your method: You are just commenting on primary sources. This is the same method that you used to rewrite two previous articles, Instrumental and value rationality and Instrumental and value-rational action, and your rewritten versions of those articles have been appropriately tagged by Omnipaedista with the {{Essay-like}} cleanup tag. Your method is not an appropriate method for Wikipedia, as it produces an original argumentative essay that violates the WP:NOR policy. If you want to produce content that is appropriate for inclusion in this article, you will need to adopt a different method: Instead of commenting on quotations from primary sources, find secondary sources about how those primary sources relate to the problem of induction, and then summarize the secondary sources. One can cite primary sources, but the content should be based mostly on secondary sources and should not make original arguments. This has already been explained above, and has probably been explained to you on other talk pages as well. Thanks, Biogeographist (talk) 15:02, 21 November 2020 (UTC)

I second what Biogeographist said. TBR-qed's method of writing articles is unacceptable for Wikipedia. --Omnipaedista (talk) 15:34, 21 November 2020 (UTC)
These comments finally make me recognise how you distinguish an essay from an encyclopedia article, and I grant some of my earlier posts violated this position. I think the present proposal is minimally guilty of the charge, and I ask you to suspend judgment until you see the final product. Over 1/2 is directly reporting on Sloman and Lagnado.TBR-qed (talk) 15:43, 21 November 2020 (UTC)
Just to say that the very structures of both the present article and the proposed revision are somewhat inappropriate. This type of structure might be problematic even if secondary sources have been used. Wikipedia articles about major concepts in analytic philosophy are rarely mere anthologies of summaries of philosophical works. Wikipedians tend to avoid this style of essay-like article structure. Philosophy articles tend to be organized around major themes, not organized around a collection of opinions of famous commentators/philosophers (see SEP's take on the problem of induction or the Wikipedia article about the new riddle of induction). --Omnipaedista (talk) 19:01, 21 November 2020 (UTC)
@Omnipaedista: One of my previous responses above, commenting on an earlier draft in User:TBR-qed/sandbox, was similar to your most recent comment, and I too pointed to the SEP article. A problem with your comparison to Goodman's new riddle of induction is that the problem of induction is much older, and so an adequate treatment of the subject has to cover more historical material than the article on Goodman's new riddle does; this fact can be seen even in the SEP article. And if you look at the history of the SEP article (some previous versions are mentioned above), it has gone through radical changes over the years, and has had very different approaches to presenting the topic. There are so many different views that it is a challenging subject to summarize, and I don't think one can entirely avoid organizing the subject by different views to some extent, as even the SEP article does in its second half; as the current SEP article says: "A number of philosophers have attempted solutions to the problem, but a significant number have embraced [Hume's] conclusion that it is insoluble. There is also a wide spectrum of opinion on the significance of the problem. ... In this article, we will first examine Hume’s own argument, provide a reconstruction of it, and then survey different responses to the problem which it poses." Having said all that, you are right that Problem of induction § Formulation of the problem is very underdeveloped. To complicate things even further, TBR-qed's approach is largely outside the area of what you called analytic philosophy. TBR-qed relies especially on a chapter by Sloman & Lagnado in The Cambridge Handbook of Thinking and Reasoning that presents psychological research and happens to be titled "The problem of induction" but has little relation to how the problem of induction is treated in analytic philosophy, and as I said above, I have found no evidence that Sloman & Lagnado deserve the prominence in this article that TBR-qed wants to give them. Biogeographist (talk) 19:52, 21 November 2020 (UTC)

Some issues that jump out to me are editorializing in the lede "mysteriously and paradoxically creates illusions of knowledge" and it barely says anything about the early history of the problem of induction. For those interested in ancient philosophy (which, it is important to note, is not dead philosophy. There are modern Stoics, Epicureans, and Pyrrhonists, for example) it is an important subject. Teishin (talk) 22:11, 21 November 2020 (UTC)

I disagree with your judgment that WP should do more than recognise ancient philosophy. The ancients are easily accessible; modern practices with ancient roots are not--a lack suited for WP to fill.TBR-qed (talk) 17:20, 22 November 2020 (UTC)

reforming writing style[edit]

I am trying to relate secondary sources to primary sources to be more encyclopaedic. I hope you will help me correct my lapses rather than just counting them.TBR-qed (talk) 17:15, 22 November 2020 (UTC)

Proposed replacement submitted for review[edit]

I have submitted my sandbox proposal. I feel it demonstrates that the existing article is obsolete and that contaminated inductive reasoning exists at pandemic levels. Critique invited.TBR-qed (talk) 17:02, 5 December 2020 (UTC)

It seems fine to me, but my expertise in only in the ancient/early modern history part. It might be nice to add a mention of Taleb's work here, as I suspect if we don't someone else try to add it. Teishin (talk) 18:07, 5 December 2020 (UTC)
I have not read the draft yet and won't have time to read it today, but I would not be as quick as Teishin to declare that it "looks good". Note that it was submitted to AFC and was quickly declined with the explanation: "This submission reads more like an essay than an encyclopedia article." I would say that even TBR-qed's summary of it above is essay-like: "I feel it demonstrates that the existing article is obsolete and that contaminated inductive reasoning exists at pandemic levels." That description seems to indicate that TBR-qed is arguing for a thesis, which is not what Wikipedia articles do. I expect I will have more to say after I read the draft, although it has already been declined at AFC, which I already predicted above when I said that it's unlikely that the other editors here would accept a whole replacement of this article by one written entirely by TBR-qed. The better approach is to consider whether any parts of it are suitable for merging into the existing article. Biogeographist (talk) 23:09, 5 December 2020 (UTC)
I was unaware that it was submitted to Articles for Inclusion. Here it is there: . Such a submission seems to me to be inappropriate, as we already have such an article. It seems to me that the reviewer should have rejected it on that basis. While I agree that prior versions of the proposed article had many problems, and its author clearly started it based on opinion motivation, this latest version seems much improved. Further, it does not seem to me to be a "whole replacement" but it instead appears to incorporate large parts of the existing article. Teishin (talk) 23:50, 5 December 2020 (UTC)
I haven't read the draft yet, but I saw in its edit history that TBR-qed was the only contributor of content to the draft except for minor technical edits to inline citations, and there is no indication in the edit summaries that he copied material from any other Wikipedia article (indication of the source of within-wiki copied content in edit summaries is required per WP:COPYWITHIN), so it is reasonable to assume at this point in time that TBR-qed is the sole author of it, and a "whole replacement" it is. Biogeographist (talk) 01:25, 6 December 2020 (UTC)
Thank you for continuing to reason inductively with me about induction. If you answer the following question, I will understand how large our agreement might be. Do you agree that my coverage table columns 1&2 is empirical evidence that my classification of existing article as obsolete and biased is warranted, and column 3 is empirical evidence that classifying my proposal as biased and original research is not warranted?TBR-qed (talk) 17:22, 9 December 2020 (UTC)
I don't like the word "obsolete" here: The problem of induction may be obsolete, but we still have an article about it, and it is helpful to describe the history of the problem, even if some of the history is "obsolete". "Incomplete" seems to be a better word: I think we all agree that the article is incomplete. I only think your draft is biased if you are proposing it as a whole replacement of the current article. Biogeographist (talk) 20:18, 9 December 2020 (UTC)
I share this view, but maybe for different reasons. Many many people have written about the problem of induction with different perspectives, different terminologies, etc. often promoting their work as being very different. The article will become a mess if we start to cover every single new perspective on the basis of neutral point of view. Before neutral point of view there is WP:NOTEVERYTHING. What I agree with is that it can be useful to mention the notion of induction as seen in social science and artificial intelligence in the article. This recent view is simply a move ahead in modern research that ignores the problem (not making it obsolete at all) and
  • classify the different relationships between laws and observations, which relationships are recognized by Popper and others, or
  • consider non ampliative "inductive methods" to generates laws. For example, in inductive logic the problem of induction is not considered at all. Hume is not even cited. One sentence in this article clearly indicates to me that it's not ampliative, but is a set of results that can be proven deductively given hypotheses:

    The [criterion of adequacy] stated here may strike some readers as surprisingly strong. Given a specific logic of evidential support, how might it be shown to satisfy such a condition? Section 4 will show precisely how this condition is satisfied by the logic of evidential support articulated in Sections 1 through 3 of this article.

The challenge to include this kind of material in the article is that we cannot make a link with the problem of induction that is not made in the literature and we should not also accept a link that is made quickly by a researcher that is not an expert in philosophy of science, because it will not be pertinent. In particular, this article in inductive logic is not pertinent, because it makes no reference at all to the problem of induction. Moreover, if there is an article by some experts that makes the link with the problem of induction, it is not sufficient. There must be a few articles so that we can be convinced that it represents the view of at least a significant minority of experts. Dominic Mayers (talk) 21:40, 9 December 2020 (UTC)

coverage table[edit]

TBR-qed reports that the table below was not properly formatted and will be replaced.--Quisqualis (talk) 20:15, 12 December 2020 (UTC)

I mistakenly thought my coverage table was posted here. Here it is.TBR-qed (talk) 17:45, 9 December 2020 (UTC)

TABLE OF SCHOLARS IN 3 VERSIONS OF “Problem of induction.”

|- column 1 = EWP; column 2 = S&L; column 3 = SBox

Philosophers Hume Hume Hume
Popper Popper
Goodman Goodman Goodman
Pyrrhonists Logical empiric Pyrrhonists
Carvaka Hempel Carvaka
Quine Quine Dewey
Stove & Williams Miller & Lipton
Campbell & Costa Carnap
al-Ghazali & Ockham Hacking
Scotus Nagel
Salmon Kuhn
Hard scientists 0 0 Duhem
Social scientists 0 Rosch Rosch
Kahneman Kahneman
Gelman & Coley
Mandler & McDonough
Gopnik & Meltzoff
and more.

The introductory sentence in the lead[edit]

I consider the following sentence:

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense,[1] highlighting the apparent lack of justification for:

The problem I see with this sentence is that it refers to inductive reasoning which can refer to inductive justifications or to what is now seen as inductive methods in social science and in artificial intelligence or even simply to any relationship between a law and observations that corroborate it. These concepts are totally different and operate at completely different levels. The problem of induction is about missing justifications. For example, this is clearly explained in SEP. The first paragraph in SEP describes the well known relationship between laws and observations: if a kind of bread has nourished thus far, we are not surprised to see the (false) law that it will keep be nourishing. However, when it comes to the problem of induction, the expressions used in SEP are "on what grounds" and "arguments that do not serve". So, clearly, the problem is the missing justifications. Therefore, I suggest that we do not refer to the nowadays vague term "inductive reasoning" and focus on missing justifications. I propose

The problem of induction is the philosophical question of what are the justifications, if any, for any growth of knowledge understood in the classic philosophical sense that goes beyond a mere collection of observations[1], highlighting the apparent lack of justification in particular for:

Dominic Mayers (talk) 18:26, 9 December 2020 (UTC)

I understand your reason for not wanting to use the word "induction". But I would keep the link to Inductive reasoning in there. It could be helpful for people who end up at this page but don't already know what the word "induction" means in "problem of induction". One possible solution: You could link it like this: "mere collection of observations". Biogeographist (talk) 20:18, 9 December 2020 (UTC)
Looks great! I changed the proposal above accordingly. Dominic Mayers (talk) 20:21, 9 December 2020 (UTC)


  1. ^ a b Vickers, John, "Can induction be justified?", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.)

The sentences introducing the inductivist view and Popper's view[edit]

First, I consider the following sentence in the article:

The problem calls into question the traditional inductivist account of all empirical claims made in everyday life or through the scientific method, and, for that reason, C. D. Broad once said that "induction is the glory of science and the scandal of philosophy".

This sentence plays a useful purpose, because indeed there is notable belief, justified or not, that knowledge grows through some kind of reasoning, thus inductive reasoning, because deductive reasoning is not ampliative. The first problem is that I don't feel it's written in a neutral manner. It's not attributed in a clear way. It's not attributed to Broad (except the quote of course), because on the contrary Broad is presented as an innocent witness of the fact. It is not clearly attributed to the traditional inductivist view, because the term "account" again suggests that it is an observed fact. The second problem is that it refers to all empirical claims, but there is no problem with claims of simple observations. It's a nice sentence, but it needs some work. To address the first problem I suggest the following

The traditional inductivist view is that all empirical claims, either made in everyday life or through the scientific method, can be justified through some form of reasoning. The problem is that many philosophers tried to find such a justification but their proposals were not accepted by others. Identifying the inductivist view as the scientific view, C. D. Broad once said that "induction is the glory of science and the scandal of philosophy".

The middle sentence is not attributed, but that's ok, because it is well known. To address the second problem, "empirical claims" must be replaced by something else. I propose "claimed empirical laws". So, it becomes

The traditional inductivist view is that all claimed empirical laws, either in everyday life or through the scientific method, can be justified through some form of reasoning. The problem is that many philosophers tried to find such a justification but their proposals were not accepted by others. Identifying the inductivist view as the scientific view, C. D. Broad once said that "induction is the glory of science and the scandal of philosophy".

Second, let see how this fits with the next sentence

In contrast, Karl Popper's critical rationalism claimed that induction is never used in science and proposed instead that science is based on the procedure of conjecturing hypotheses, deductively calculating consequences, and then empirically attempting to falsify them.

It could be simply:

In contrast, Karl Popper's critical rationalism claimed that inductive justifications are never used in science and proposed instead that science is based on the procedure of conjecturing hypotheses, deductively calculating consequences, and then empirically attempting to falsify them.

I addressed a problem of terminology here by replacing "induction" with "inductive justifications". Of course, Popper never claimed that the inductive relationships usually seen between laws and observations do not exist. If asked why do you accept that the sun raises on the east every day, he would have replied that he sees it every day, just like anyone else. Note that this is no justification at all for the inference of the law. If one is asked how can you infer B from A and one replies because I have A, one has provided no justification at all for the inference. In other words, he believed in the value of corroborations, just like every one else. The only thing he rejected is the existence of a rational justification for the laws.

Dominic Mayers (talk) 17:25, 9 December 2020 (UTC)

This change looks good to me. Biogeographist (talk) 20:18, 9 December 2020 (UTC)

The historical considerations[edit]

I consider the sentence:

The most famous formulation of the problem was proposed by David Hume in the mid-18th century, although versions of the problem date back to the Pyrrhonist school of Hellenistic philosophy and the Cārvāka school of ancient Indian philosophy.

There might be an anachronism here when we refer to Indian philosophy and perhaps also the Hellenistic philosophy as presenting the problem of induction. No evidence is given that it was seen as a problem at the time. Especially in the case of the ancient Indian philosophy, it is very likely that they simply knew that inductive justifications were not valid and that is it, no problem. Unless sources are provided that show that these ancient philosophies supported the inductive view, at the least during a period of time, I propose that we simply mention that they rejected inductive justifications without suggesting that it was seen as a problem. This means that to our knowledge the most ancient formulation of the problem was given by Hume. This is, for example, the position taken in SEP. I suggest the following

The original source of what is known as the problem today was proposed by David Hume in the mid-18th century, although inductive justifications were already argued against by the Pyrrhonist school of Hellenistic philosophy and the Cārvāka school of ancient Indian philosophy in a way that shed light on the problem of induction.

Dominic Mayers (talk) 18:01, 9 December 2020 (UTC)

"Problem" appears here to have some slipperiness. The bulk of the surviving works of Sextus Empiricus are about flaws in the justifications for knowledge provided by the dogmatists. "Invalid" is a little slippery too. The Pyrrhonists were explicitly fine with using induction to infer that if there was smoke there was fire or that if there was a scar there had been a wound. Such things in Pyrrhonism are "commemorative signs" involving "evident" matters and are fine (albeit prone to occasional error) for dealing with practical matters. The problem the Pyrrhonists were pointing out that induction from the evident to the non-evident could not provide adequate justification for knowledge (e.g., lightning is a sign that Zeus is displeased). This was just one of many Pyrrhonist arguments regarding the lack of adequate justification for knowledge, e.g., regress and circularity, found in the Five Modes of Agrippa. The one major fragment we have from Pyrrho, about 500 years before Sextus, appears to be substantively about the problem of induction.
In addition, plenty of people were aware of the issues with induction before Hume. "Original source" seems to be an overstatement of the case. Consequently, the sentence proposed for replacement seems to be more accurate than the proposed replacement. Teishin (talk) 19:52, 9 December 2020 (UTC)
You might be right. I am just saying that until we have the sources to verify this view, we need to restrict the article to what is verifiable. Right now, what we have is SEP that says "The original source of what has become known as the “problem of induction” is in Book 1, part iii, section 6 of A Treatise of Human Nature by David Hume." Please help us by providing precise references with sections and even pages. Ideally, even point to key sentences. Also, ideally in recent sources. Dominic Mayers (talk) 20:29, 9 December 2020 (UTC)
"Verifiable" is sort of a matter of having a source, and of course there are sources for all sorts of things that cannot be verified.... I tend towards caution with such claims. Of course, Sextus did not put the problem in the same way Hume did, hence the slipperiness of "problem", but it seems difficult to exclude Sextus from having addressed the "problem of induction". I have tracked down a very fresh 2020 book that addressed the topic, Epistemology After Sextus Empiricus edited by Katja Maria Vogt, Justin Vlasits. Here's a bit from it:

I want to isolate and explore what is puzzling about induction. Only with a clear sense of the problem can we begin to understand what a satisfactory solution would be. The normal way into the puzzle is through Hume’s justly famous argument against induction. In section 2, I argue that, interesting as Hume’s argument is, it fails to isolate what is puzzling about induction and, in fact, crucially presupposes that induction is puzzling. In section 3, I analyze an argument in Sextus Empiricus against induction—as far as I know, the very first in the history of philosophy. This argument does, I claim, get at what is interesting and puzzling about induction. Sextus’ argument has received far less attention than Hume’s.

— Justin Vlasits, chap. 11: The First Riddle of Induction
Teishin (talk) 21:14, 9 December 2020 (UTC)
I read the chapter up to the passage and a few pages after. The chapter seems to agree with both the inductivist view and the arguments against it, not a comfortable position to hold, but that's not a relevant concern here. A relevant point is that it does not appear from Vlasits's citation of Sextus that the latter saw a problem with the lack of justification for induction. I see instead that Vlasits found that Sextus's argument against inductive justification sheds more light on the problem of induction than Hume's argument. So, it is Vlasits, not Sextus, that sees the problem of induction here. Sextus only provided a nice argument against inductive justification. In my understanding, it is very unlikely that these people saw a problem. They were not in a context for that. In any case, even if Sextus expressed a support for the inductivist view, which is a requirement to feel a problem, it would still remain that it is Hume's view that it is at the origin of the problem as we know it in the following sense that modern philosophers learned it from Hume and Hume did not learn it from Sextus. You know that it's not that important as far as conveying the key idea is concerned. My only concern here is that I do not want to support an anachronism by assuming that the inductivist view was sufficiently strong at the time to be at the basis of a problem of induction. Dominic Mayers (talk) 00:36, 10 December 2020 (UTC)
I modified the sentence in view of this discussion. Dominic Mayers (talk) 00:54, 10 December 2020 (UTC)
The modified sentence seems fine. (As to whether Hume learned it from Sextus, it's awfully fishy that Hume went to some effort to mischaracterize and dismiss Pyrrhonism and then in his own writings to largely re-invent Pyrrhonism.) Teishin (talk) 19:48, 10 December 2020 (UTC)

Correct or replace?[edit]

Continuing to try to correct present article is recognition that something must change. Can we agree on what needs change? Is anyone making classification errors? Dom seems to want to ignore the whole social science effort to deal with the "problem of induction." I find that rank philosophical bias in favour of traditional classifications. If many social scientists say they are dealing with the problem, how can WP editors judge them wrong?

Allow me to explain how I came to describe and judge the present article biased and obsolete.

I read S&L “Problem of induction” after reading WP “Problem of induction.” I quickly recognized the bias of the WP article because it ignored the range of information in S&L. I classified it as violating WP NPOV rule. This classification is at once a descriptive fact and a valuation. See columns 1&2 of coverage table.

I thought the bias could not be eliminated by adding S&L info to present article--WP standard operating procedure--because S&L content and definitions framed problem differently. I was delighted to learn that SANDBOX provided means for me to attempt revision. See column 3 of coverage table. Editors Dominic Meyers & Biogeographist, unaware of my evidence of bias, logically classified my sandbox revision as violating NPOV & NOR rules and reading like an essay—unencyclopedic. SK2242, equally unaware of the evidence in my table, accepts these classifications.

My proposed revision does not violate NPOV because it describes modern alternatives to present WP article. It partially corrects existing bias.

My proposed revision does not violate NOR because it reports existing scholarship in S&L. Reporting existing scholarship requires comparing modern classifications with traditional, regardless of whether or not it appears “encyclopedic.”TBR-qed (talk) 15:42, 10 December 2020 (UTC)

I believe that there is a good consensus on what is the subject "problem of induction". It is the same old problem of induction that was raised by Hume, the one that involves justifications for laws given observations, the kind of justifications that were considered in ancient India and ancient Greece. This subject is not obsolete at all. One rule in Wikipedia is that the subject of the article must be well defined so that we can evaluate accordingly the pertinence of information to include. If you do not accept the subject, because you think it is obsolete, then you are against the consensus. This being said, it does not mean that nothing should be said about how some recent views on induction is related to this subject. It will be very helpful that you accept the subject as it is and explain how the information that you want to include is pertinent given that subject. Note also that any controversial information to include would require more than a single source. You will have to convince us through a few sources in philosophy of science that this information reflects the opinion of at the least a minority of experts on the subject "the problem of induction" as defined here so that the link with this subject is pertinent. I am not writing this with the belief that you cannot succeed. I think that there might be something there that would improve the article, but we need the sources and of course, a specific information to include. One idea would be that you write one or two sentences that could be added to the lead as it is now to show the link with the subject as it is defined now. Dominic Mayers (talk) 16:42, 10 December 2020 (UTC)
TBR-qed described how he first read this article, then read Sloman & Lagnado, and then decided that information from Sloman & Lagnado needed to be in this article. His conclusion may be partially correct: it may be true that some of the information that he encountered in Sloman & Lagnado belongs in this article. But what is missing is larger contextualization of Sloman & Lagnado's chapter: Where does Sloman & Lagnado, and the information they present, fit in the larger body of knowledge that this article is supposed to summarize? As Dominic said, we need the sources. TBR-qed's arguments have been repetitive so far because he is just comparing three sources: the present article, Sloman & Lagnado, and his draft. There needs to be comparison among a larger body of secondary and tertiary sources, not just Sloman & Lagnado. Biogeographist (talk) 16:04, 11 December 2020 (UTC)

My personal view, in case it might help thinking about the article.[edit]

I know that no original research is allowed in the article, but sharing our understanding in the talk page can help the discussion. Besides, what I am going to say is not really original research in the following sense that many others have noticed the same thing. I see that before Popper, induction was strongly associated with justification, especially in the Vienna Circle. It was important at the time to separate science from non science and the hoped difference was that science is justified knowledge and that every thing else was not even meaningful. I think that after Popper it has becomes generally accepted that justified knowledge was the wrong objective, though there is still a remain of justificationism for knowledge that is uncertain. But, even among those that stopped to fight for justificationism in any of its forms, induction was not abandoned. This new trend is that induction does not have to be justified, because it is an observed fact. This is a complete shift in comparison with the pre-Popper notion of induction. This notion of induction is not at all opposed to Popper's philosophy. In fact, it perfectly goes along with it, because it starts with the premise that justification is not needed. They would even say that, for that reason, the problem of induction does not really exist, which is exactly Popper's point. I find it weird that those who support this notion of induction pooh-pooh Popper's philosophy. The explanation, I believe, is that the true meaning of justificationism is lost. In artificial intelligence, they create machines that can infer laws from observations. The principles used by these machines are considered as some kind of justifications for the laws and they are called inductive principles. Similar notions have spread in social science. However, these inductive principles are not universal. They have nothing to do with the kind of justifications that were hoped for in pre-Popper time. There was a very good reason for the pre-Popper time justificationism. It was puzzling in ancient Greece, for Hume and in Popper's time that no true justifications can be found and it is still puzzling today. It's not obsolete at all. Dominic Mayers (talk) 18:58, 10 December 2020 (UTC)

This is just a response to Dominic's personal view, not so relevant to the article: One reason why some people are not so impressed by Popper's account of "justificationism" may be because they are already epistemological fallibilists with no help from Popper. Epistemology cannot be simply divided into infallibilist/foundationalist "justificationism" before Popper and fallibilist/nonfoundationalist "non-justifications" after Popper. There was fallibilist epistemology before Popper (e.g., C. S. Peirce), and there has been non-Popperian fallibilist epistemology during and after Popper's career (e.g., Neurath's boat). One need not be a Popperian to appreciate the absence of absolute foundations of knowledge. Biogeographist (talk) 16:04, 11 December 2020 (UTC)
Part of the lack of agreement might be due to definitions. For me, fallibilism and anti-justificationism are different in at the least two ways. First anti-justificationism rejects even the justification of uncertain inference. So, in that sense, it is stronger. Second, anti-justificationism is by definition only concerned with (rational) justification at the level of objective knowledge and therefore does not concern itself with ways to gain knowledge that operate between subjective knowledge (expectation, predisposition, etc.) and objective knowledge. Popper's view is that non objective ways of gaining knowledge are fallible, involve chance, a lot of it, but they are nevertheless not a part of anti-justificationism. Anti-justificationism per se does not exclude the possibility of some infallible aspects in subjective ways to gain knowledge. So, in that other sense, it is weaker. I disagree that it's irrelevant to the article. It's not directly relevant, but it's indirectly relevant, because if we do not agree on this kind of notions in the talk page, then it is very difficult to understand each others when we discuss the article. Dominic Mayers (talk) 18:33, 11 December 2020 (UTC)
I think I understand what you're saying; I don't see any misunderstanding here on my part. You're basically summarizing Popper's philosophy. My point is that not all epistemology before Popper was "justificationism". This is not a refutation of anything you said, since you didn't explicitly claim that all epistemology before Popper was "justificationism". I am just pointing out something you omitted, since you only mentioned Popper and "pre-Popper-time justificationism". Biogeographist (talk) 19:03, 11 December 2020 (UTC)
Another way of phrasing my point: Someone who is not a justificationist has little use for anti-justificationism. Biogeographist (talk) 19:09, 11 December 2020 (UTC)
I suspect that this is the situation with many modern "inductivists". They are inductivists that are not justificationnists. They have little concern for this obsolete view, they would say. But, this is a big source of confusion, because in the problem of induction, as defined here, the inductivist view is a justificationist view. If it was not, then indeed, there is no problem of induction. I am sorry if I referred to Popper only, but Popper was not in the same context as Peirce. He came at a time where the justificationism view was at its extreme value. So, he directly addressed the issue. Peirce might have done better than Popper had he been in a similar context. Popper had a lot of appreciation for Peirce. Nowadays, (classical) justificationism is replaced with what I would call synthetic or non universal justificationism, the one that emerges in artificial intelligence in particular. There is no problem (of induction) with this kind of justificationism. I personnally see it as a natural continuation of the death of classical justificationism and as such it does not make the original problem obsolete. In particular, it does not remove, though it might contribute to hide, the puzzling aspect of a lack of classical justification. My point is that we need primary and secondary sources to include this kind of considerations in the article. Until we have secondary sources that make the connection with the original problem of induction, the article cannot cover that. Dominic Mayers (talk) 19:58, 11 December 2020 (UTC)
I agree with all that. Biogeographist (talk) 20:31, 11 December 2020 (UTC)

Draft:Problem of induction[edit]

Draft:Problem of induction is a proposed rewrite of Problem of induction. It was declined by User:Theroadislong for two reasons, both because it reads like an essay, and because it is a rewrite of an article, which is not how Articles for Creation works.

There has been extended discussion of the content of this article. Three years ago, this might have been a good case for formal mediation by a member of the Mediation Committee, or even longer ago for informal mediation by the Mediation Cabal. Two years ago, in a remarkably stupid action, the community disbanded the Mediation Committee. This content dispute is too large to be handled by the dispute resolution noticeboard. Without studying the details of the content dispute, it appears to me that a mediator is needed, and that the mediator should largely assist in the formulation of multiple Requests for Comments.

This draft was resubmitted, and I removed the resubmission tag while moving the commentary to the talk page. I restored the resubmission in order to decline it again with comments. I recommend a combination of mediation and Requests for Comments. Robert McClenon (talk) 00:59, 14 December 2020 (UTC)

Improving this article is going to be a long process which will require a lot of proposals by editors, each one for some step of progress, not to completely change the article. Unless we have proposals, I don't see what would be the specific issue that a rfc will be able to decide. What will be useful is more people with some expertise on the subject that want to put the time needed to make specific proposals or discuss proposals made by others. This cannot be a one shot process. There is a consensus that a coverage of the cognitive science + AI perspective should be added, but we need specific proposals that are based on a few secondary sources and a good will to discuss them with an open mind. The draft was declined formally, but the main issue is that it rejected totally the current view of the article as being obsolete. The draft might contain elements that are useful for the article, but TBR-qed should make a specific proposal for some step of progress without totally rejecting the article. I have not edited this article until recently and I think it was good even before my edits. I suspect that it reflects a lot of consensus to which I add my support and I believe that other participants here do the same. It does not mean that it cannot be improved, but throwing it away as being obsolete makes no sense. Dominic Mayers (talk) 01:54, 14 December 2020 (UTC)
Well, in a second thought, a rfc might be useful to get some general opinions or guidelines from the community. Dominic Mayers (talk) 03:33, 14 December 2020 (UTC)


The leading sentence is too complicated, and without reason, because the "knowledge understood in the classic philosophical sense" is the same thing as "justified knowledge". Therefore it does not need to mention both the justification and the "classic philosophical sense". My suggestion was "The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense...", but there are other possibilities, how to solve it. In any case, the current lead should be changed because it lacks the required conciseness.Ioannes Pragensis (talk) 07:31, 14 February 2021 (UTC)

For many readers "knowledge understood in the classic philosophical sense" does not mean much more than "knowledge in the usual sense". I don't think it conveys the idea that a justification (other than a self justification) is searched, thus is missing and that it might not even be possible. For other readers, if the notion of justification is seen in this expression, it is in the form of a belief that normal accepted knowledge in practice is justified knowledge. With such a belief, any description of a method that leads to that justified knowledge is the solution to the problem of induction, that is, the method is confused with the justification. Dominic Mayers (talk) 09:30, 14 February 2021 (UTC)

Rethinking the first sentence of the lead.[edit]

@Ioannes Pragensis, Biogeographist, and Teishin: what is your opinion on the following proposal, an attempt to make the first sentence in the lead simpler. The current sentence is:

The problem of induction is the philosophical question of what are the justifications, if any, for any growth of knowledge understood in the classic philosophical sense—knowledge that goes beyond a mere collection of observations[1]—highlighting the apparent lack of justification in particular for:

  1. Generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (e.g., the inference that "all swans we have seen are white, and, therefore, all swans are white", before the discovery of black swans) or
  2. Presupposing that a sequence of events in the future will occur as it always has in the past (e.g., that the laws of physics will hold as they have always been observed to hold). Hume called this the principle of uniformity of nature.[2]

I don't think it is so bad, but I propose to change it to

In philosophy, the problem of induction is the apparent or true absence of justifications for a growth of knowledge that goes beyond a mere collection of observations as understood in inductive reasoning,[1] in particular for:

  1. Generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (e.g., the inference that "all swans we have seen are white, and, therefore, all swans are white", before the discovery of black swans) or
  2. Presupposing that a sequence of events in the future will occur as it always has in the past (e.g., that the laws of physics will hold as they have always been observed to hold). Hume called this the principle of uniformity of nature.[2]

I removed the reference to "knowledge understood in the classic philosophical sense", which is linked to justified true belief, a concept that gained approval during the Enlightenment, "justified" standing in contrast to "revealed". The concept of justified true belief in relation with the Gettier problem, etc. is still discussed in epistemology in general, but not in the article. For our purpose, the concept of inductive reasoning does a better job in distinguishing revealed knowledge from scientific knowledge. So I replaced it with "as understood in inductive reasoning". To simplify further, I also used "apparent lack of justification" from the start instead of highlighting it later. Also, I made the sentence more neutral by adding that the lack of justifications might not be apparent only, but be actually a real absence of justifications.

Dominic Mayers (talk) 19:40, 17 February 2021 (UTC)


  1. ^ a b Vickers, John, "Can induction be justified?", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.)
  2. ^ a b Hume, David (January 2006). An Enquiry Concerning Human Understanding. Gutenberg Press.#9662: Most recently updated in 16 October 2007