The Problem of Induction: A Student’s Wake-Up Call

Posted: January 15th, 2011 | Author: | Filed under: Finance/Economics, Philosophy | Tags: , , , , , | 11 Comments »
I’ve just finished another book on my summer reading list – Fooled By Randomness, by Nassim Nicholas Taleb. Like my post on Malcolm Gladwell’s Outliers, I’m not going to discuss the content of the book as a whole. Rather, I’m going to focus on a specific aspect of the text that struck me as significant and sparked my thought.Here, I wish to discuss the Problem of Induction. The problem of induction is nothing new – in fact, its origins date back to the 1st century BC. But Taleb provided an incredible argument on why we should pay attention to the problem of induction, and why it is relevant to our lives today. His argument led me to question why we are not made aware of this thinking in schools today, and wonder whether everything I have been taught could be incorrect.

Wikipedia states “The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge.” An example regularly given to describe the problem of induction is the belief that all swans were white, before the discovery of a black swan (this example is used both in Taleb’s text, and on the Wikipedia page). Through inductive reasoning, people used to believe that all swans were white. They had never seen a swan of a different color, and therefore our natural reasoning leads us to believe that “all swans are white” is a fact. But once Australia was discovered, people soon discovered black swans, leading their “facts” to be proven incorrect.

Just because we have not discovered something, or it has not occurred before, does not mean it does not exist or will not occur. It merely means that we have not yet proven our beliefs incorrect.

Taleb frequently cites the work of two philosophers who attempted to solve the problem of induction. David Hume, an 18th century philosopher and economist, and Karl Popper, a 20th century philosopher. They both disagreed with the scientific method because they believed it led people to false conclusions. They both believed that there are only two types of theory:

1.  Theories that are proven incorrect – falsified theories. (eg. a black swan is discovered, so the theory that all swans are white is falsified).

2. Theories that are exposed to be proven wrong. (eg. before the discovery of Australia, the theory that all swans are white was exposed to be proven wrong by the discovery of a swan of a different color).

This thinking goes against everything that I have learned in school. I am taught that through the scientific method (and inductive reasoning) we can acquire new knowledge. In addition, I am told that everything I learn is “fact”. Never am I told that a scientific theory is “exposed to be proven wrong”. It is always “this is fact”, “this is proven”, “don’t question it”. Why am I told this? Is our education system afraid to admit that what we know may not be “fact” after all? Is it thought that students cannot handle knowledge that is conjecture not yet proven?

Never once in school so far have I been told for one second that what I am learning may not be proven. I have never been made aware of the problem of induction, nor any thinking that strays away from the “this is fact” argument. By deciding to read Fooled By Randomness I’ve suddenly been awoken to a completely different way of thinking – and perhaps created a healthy skepticism for what I learn because of it.

I understand that for us to learn, we have to believe a certain amount of what we are told. But there is no reason for us not to be aware of the thinking around the problem of induction. I think that for our education system to work effectively, students need to be made aware of the different theories and ways of thinking. Education does not work in the “one size fits all” manner. Yet that “one size fits all” manner is taken and applied to the very fundamentals of education – namely, whether our knowledge really is fact.

I wish that I had been made aware of the problem of induction earlier. I think that by being told “this is fact” for everything I learn has created a false sense of security in my knowledge, and has wiped out any desire in me to discover new knowledge or prove “fact” wrong. The way of thinking that I have been taught likely goes with most people to their grave – they never question anything, and just blindly believe the “facts” that they are told.

And at the very least, if this thinking won’t be implemented into an education system, could the teachers reading this please make your students aware of the problem of induction? Take ten minutes in a class just to explain it to them, and let them discover more about it in their own time. I think it’s dangerous to continue with the “this is fact” way of teaching, unless students are aware of the problem of induction.

  • http://mmoorejones.com/2011/01/16/five-lessons-from-nassim-taleb/ Five Lessons From Nassim Taleb’s Fooled By Randomness –mmoorejones

    [...] Fooled By Randomness, Markets, Nassim Taleb, Trading | View Comments TweetI wrote earlier on the Problem of Induction, which I discovered by reading Nassim Taleb’s book Fooled By Randomness. While that was one of [...]

  • Gareth

    I like your comment about the education system presenting everything as ‘fact’. We all instinctively know this to be false yet become quite apathetic to challenging such a system.
    I recently posed the question to some academics “isn’t it reasonable that all those people who got their Doctorates based on studying Pluto as a Planet, should give back their Doctorates as they were all wrong”. Needless to say those who have gained a reputation based on the acquisition of (dubious) knowledge, were not keen on ceding the point.

  • J C W Cox

    An excellent point that I think illustrates a previously undiscovered passion for philosophy. I came across this blog whilst doing research for an undergraduate philosophy and politics module at Exeter University, england. The module is entitled “knowledge and history: theories of scientific change”. Whilst full of rather dense material, the philosophy of science is completely saturated with interesting takes and attempts to solve the problem of induction.

    As for the “eye opening” effect of discovering said problem, I totally feel empathy with this reaction; I too have been involved in an education system that seemed to almost engulf students in a blind faith, something I certainly wouldn’t attribute to the main intention of scientific endeavour.

    If you want to go down an incredible philosophical road of discovery, basically lifting the veil on as much of what is held to be fact as possible, try researching evidence and argument styles; specifically fallacies. Whilst it goes more into the linguistics side of philosophy, when you examine any doctrine or document proclaiming a factual basis it develops a vision into the impurity of so many arguments.

    Enjoy, and consider doing a degree in philosophy, politics and economics.

  • http://jamesthornton.com James Thornton

    Spot on.

    For a while I have understood that people see the world in fundamentally different ways, but about two years ago I had an epiphany that really crystallized it for me. Now I see people existing in either one of two camps:

    1. Those who believe the world is the way they see it.
    2. Those who realize how limited their perspective is.

    Alan Kay has a developed a similar view (http://www.ted.com/talks/lang/eng/alan_kay_shares_a_powerful_idea_about_ideas.html ). He often quotes the Talmud saying, “We see things not as they are, but as we are.” And he often says, “We can’t learn to see until we admit we are blind”.

    When Jim Collins was doing his research for “How the Mighty Fall” (http://www.charlierose.com/view/interview/10565 ), he identified hubris as being the first stage of decline for great enterprises. This is the concept of “pride goes before the fall,” and I believe one of the reasons for this is because we stop asking questions and begin to “lean on our own understanding.”

    We become complacent with our picture of the world and continue on whatever trajectory we were on when we stopped recalibrating. Unless we were right from the start (which almost never happens in a dynamically changing world), we’ll veer farther off course.

    A better way to go is to constantly be asking questions and recalibrating your path based on what you learn — continually refining your perspective. When we are continually asking questions, we are continually adding to our perspective and not relying on what we think we know.

    This seems so simple, but admitting you don’t know everything and continually asking questions requires humility.

    When I had the epiphany two years ago, I wrote down a manifesto that embodies these ideas, and one of the central tenets is, “Your perspective guides your thoughts, your choices, your trajectory” (http://jamesthornton.com/manifesto ).

  • http://mmoorejones.com Michael Moore-Jones

    Brilliant stuff James – your manifesto is a fantastic read. And this comment in itself has a lot of valuable points! Thanks for taking the time to comment – really glad I’ve found your blog now.

  • http://twitter.com/bendingb Miss N

    This reminds me of the idea in philosophy where there’s no such thing as truth (http://atheism.about.com/od/philosophyepistemology/a/Skepticism.htm).

    I agree with you in terms of encouraging divergent thinking in our educational system but maybe the question is not so much on whether we should introduce this type of think but at what point is it best to introduce this?

    From my experience, elementary and high school years proclaimed facts as facts. However, when I reached college, I had the opposite experience. Most of my science and psychology courses actually did reiterate the transient nature of knowledge. In this regard then, the system does introduce the type of thinking you’re talking about but they just do it in later years (where, presumably, you have more skill to really criticize, judge and question the validity of facts).

    For example, every human brain is different. There are common structures but the location or size of one area may be larger in one person than another. Imagine, then, a kid learning biology. Will it help his learning process if you tell him immediately that what he’s about to learn is not exactly true? If I were that kid, I’d be overwhelmed. I not only have to juggle the complex idea of biology but I also have to judge whether or not I should accept this knowledge (at this early stage). Wouldn’t it be better if I deal with the latter (questioning the “facts”) when I have a better grasp (and have built a framework) of the subject?

    “The way of thinking that I have been taught likely goes with most people to their grave – they never question anything, and just blindly believe the “facts” that they are told.” What you said here is definitely problematic but only if schools never introduce the questioning of “facts” at some point in a person’s academic career. If it is eventually introduced though, do you not think that perhaps withholding (or limiting) this type of thinking is helpful in the early stages?

  • http://mmoorejones.com Michael Moore-Jones

    Hey, really interesting points!

    I completely agree that different people need to be told different things – some people may really need to be told that nothing is proven, but others shouldn’t be told that in order to not become confused. I think there is a huge contrast between these two groups though, and perhaps that’s the difference between advanced students in the early stages and students who are yet to mature.

    But also, that’s possibly the difference between different education systems? Last year I did New Zealand’s national education system, NCEA, and it is very much “remember this “fact” then regurgitate it in the exam”. This year I’m doing IB, and we actually take a Theory of Knowledge class on understanding these different ways of thinking.

    In response to your last point, I think withholding this type of thinking could be helpful to SOME people. To others, not knowing it could merely frustrate them and make them hate academia. I suppose all we can do is develop the different education systems separately, to suit different students.

    Thanks heaps for sharing your thoughts!

  • http://twitter.com/bendingb Miss N

    That’s very true. If you ask the good teachers, they’ll tell you that it’s not an either/or solution (memorization VS critical thinking). The good ones approach each individual differently – probing those advanced students to think further and dialing down a bit for the beginning student. There’s a place for both, for sure, it’s just trying to find a balance that could cater to different students. I don’t know about developing separate systems, I think that’s the problem sometimes, institutions chose one method and go solely with that instead of offering choices.

    Knowing how we know what we know is a fascinating topic. If you ever get the chance, check out the philosophy of mind (functionalism, dualism, idealism, etc.), those thinkers touch upon some of the problems of knowledge too.

  • http://jamesthornton.com James Thornton

    I don’t think this is an argument against absolute truth, but rather it is saying that that our understanding of truth, at any given time, is not absolute.

    Truth is absolute, but our perspective — our framework for how we understand and process the world — is relative to our understanding of what we have perceived.

    Holding steadfast to and making long-term choices based on your present-level of understanding results in path dependence (http://www.nytimes.com/2011/03/29/opinion/29brooks.html).

    The way to prevent path-dependence is to work toward continually developing your level of understanding while continually recalibrating your path based on your new insights.

  • http://twitter.com/michaelbirks Michael Birks

    Your point here is well taken, and one that I didn’t get to until somewhat later than you’ve found it. However, I’m not sure I would support the idea that the induction problem be taught as part of the regular curriculum.

    The biggest issue that I have with the idea is that handled badly, it would put an enormous strain on already stretched teaching resources. Imagine every bored smart-alec taking the opportunity to challenge what’s being taught, or the need, having presented one thing as a theory, to present balanced teaching on ‘alternate’ theories.

    Also, I’m not sure how much the secondary school curriculum would be improved by throwing the uncertainty out there for the sake of it. I can’t speak to senior secondary social sciences, but the baseline inorganic chemistry, and Newtonian physics taught at that level are so well established that saying ‘this is only a theory’ before handing out what is effectively a test in properly setting up the apparatus is almost meaningless.

    Lastly, I’m not sure that all students are equally able to appreciate or maturely handle being taught things that are not ‘the truth’. Or their parents, for that matter. Sure, for the kids who pick up Taleb, or @JamesGleick’s biography of Feynman on their own, no problem. For others, as @twitter-280796041:disqus suggested, you’re going to overwhelm or confuse them.

  • Pohutukawa63

    You ask an excellent question – you could ask a slightly wider one: Why aren’t thinking skills taught more widely?
    I had a similar response to your feelings about induction, when I learnt about structural analysis.I think subjects such as gender studies are one of the few places at University in New Zealand where it is taught.  For example, there would be no feminist movement, or social welfare systems worldwide, without structural analysis. It has has had a profound affect on the world’s political systems – but it is not taught at school, and only very rarely in OECD countries, at University.
    I have read all the posts, and there are some very good points made. However there is ons socio-economic factor that is not mentioned that could go a long way to answering your question. Before industrialisation education and learning happened in a very different way. Schools developed alongside industrialisation, partly or wholly to provide trained and useful participants in industry.
    Today, there is still this tension in education – is education a  means to achieve a job, or does it have it’s own inherent value?
    Do we teach people how to question, or do we train people who will work quietly and not ask the hard questions?
    Perhaps that’s why structural analysis is not taught – because it is a structure that helps us ask the hard questions.