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The riddle of induction

from Lars Syll

Recall [Russell’s famous] turkey problem. You look at the past and derive some rule about the future. Well, the problems in projecting from the past can be even worse than what we have already learned, because the same past data can confirm a theory and also its exact opposite …

For the technical version of this idea, consider a series of dots on a page representing a number through time … Let’s say your high school teacher asks you to extend the series of dots. With a linear model, that is, using a ruler, you can run only a single straight line from the past to the future. The linear model is unique. There is one and only one straight line that can project a series of points …

grueThis is what philosopher Nelson Goodman called the riddle of induction: we project a straight line only because we have a linear model in our head — the fact that a number has risen for 1 000 days straight should make you more confident that it will rise in the future. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1 001 …

The severity of Goodman’s riddle of induction is as follows: if there is no longer even a single unique way to ‘generalize’ from what you see, to make an inference about the unknown, then how should you operate? The answer, clearly, will be that you should employ ‘common sense’.

Nassim Taleb

And economists standardly — and without even the slightest justification — assume linearity in their models …

  1. Macrocompassion
    October 9, 2014 at 5:52 pm

    Thanks for pointing this out. Econometrics is based on the same assumption and for that reason it is unreliable and should be avoided when trying to make forecasts.

  2. October 9, 2014 at 7:35 pm

    Let us note in passing that a market economy endowed with positive and negative feedbacks is almost surely nonlinear.

  3. Steve
    October 9, 2014 at 8:17 pm

    There is a third possibility of course. And that is that there is a linear factor in effect that economists simply haven’t recognized yet due to either not looking for it at all or rejecting it because some aspect of current orthodoxy (falsely) says it is not relevant. For instance, rejecting the subset of double entry bookkeeping called cost accounting as merely a static look at the economy….when by its description alone it is actually both a statistical and dynamic look at the effects of the rules and conventions of the costing/pricing system of all commerce….and hence a moment to moment unchanging and elemental look at the deepest and most significant economic factor and reality in the entirety of commerce itself, namely cost.

  4. davetaylor1
    October 10, 2014 at 10:16 am

    The ‘common sense’ response to this is of course that the economy is not a series of points on a page. It is more like innumerable ships and boats sailing the oceans to whatever destination their owners or agents chose, using PID navigational methods with the positive and negative feedbacks of C-R D to avoid obstacles yet maintain their course. Straight line courses are likely to be assumed by ignorant cost-cutters wanting maximum speed or efficiency rather than safe and reliable journeys, with outcomes like the Titanic disaster. The intended destinations are only likely to be achieved (despite error-correcting negative feedbacks) so long as owners’ agents in the stock markets, looking out for the most profitable destinations, don’t keep moving the trade route refuelling stations and changing the courses faster than the navigators can correct and complete them.

  5. Dave Raithel
    October 10, 2014 at 12:28 pm

    Ikea does not sell boxes of Grue, only of Bleen. This stuff is killing me. My common sense tells me that I should assume things continue as I’ve seen unless I have reasons contrary. Call it the weakest version of the principle of inertia. Encumber that with fancy measures and I guess we get to some notion ergodicity – from what I can grasp of that muddle. And I know the author’s target is ideology masquerading as science. But to suppose the next point on the serious is someplace oddly displaced from the rest, with no reason, is, well, unreasonable. It has nothing to do with a linear model bounding my imagination. I can imagine the next dot anywhere. The question is, given what I’ve seen, what reason have I to think the next one is differently placed?

    • Dave Raithel
      October 10, 2014 at 12:30 pm

      I mis-typed “series”. Seriously. Sorry.

    • merijnknibbe
      October 10, 2014 at 5:07 pm

      Dave,

      a few years ago you had lost your job. What happened afterwards? I’m interested!

  6. October 10, 2014 at 6:24 pm

    Riddle solved: RWER- Bloggers ahead of the crowd
    Comment on Nassim Taleb’s ‘The riddle of induction’

    For economics, the perennial induction-deduction riddle has been explained and solved by J. S. Mill. And, as it happens, the outcome of the struggle between upwarders and downwarders has been told on the RWER-Blog a few days ago. See https://rwer.wordpress.com/2014/10/03/study-the-shocks/#comment-81229.

    Resume: common sense is not of much help.

    Egmont Kakarot-Handtke

  7. October 11, 2014 at 11:55 am

    Common sense is worse than misleading
    Additional comment on Nassim Taleb’s ‘The riddle of induction’

    “… it is precisely the task of science to supersede crude common-sense notions by critical analysis, and further that it is the unsatisfactory state of the foundations beneath the common-sense surface which is the most serious and crippling deficiency of contemporary economic science, …” (Hutchison, 1960, p. 18)

    “The truth is, that common-sense, or thought as it first emerges above the level of the narrowly practical, is deeply imbued with that bad logical quality to which the epithet metaphysical is commonly applied; and nothing can clear it up but a severe course of logic.” (Peirce, 1992, p. 113)

    More about the relationship between common sense and nonsense on the web page
    http://www.axec.org/#!formalization-w/cl4s.

    Egmont Kakarot-Handtke

    References
    Hutchison, T.W. (1960). The Significance and Basic Postulates of Economic Theory.
    New York, NY: Kelley.

    Peirce, C. S. (1992). The Fixation of Belief. In N. Houser, and C. Kloesel (Eds.),
    The Essential Peirce. Selected Philosophical Writings., volume 1, pages 109–123.
    Bloomington, IN: Indiana University Press.

    • robert r locke
      October 11, 2014 at 4:13 pm

      Wilbur Steger wrote in 1979, after 15 years of urban planning that there had been a ‘virtual avalanche of urban/regional models about new planning, program analysis, budgeting and other ‘futuristic’ models about making policy-related decision-making using urban/regional models,’ but he noted how unsuccessful these OR techniques had been. “When reviewing this era it is difficult not to wonder at the relative unsophistication of the assessment techniques, which proved not to be very useful and often caused more damage than good in dozens of over literal applications.” In 1977 Frederichs and Kuebler wrote about the reliability of German econometrics model building. “Neither the econometric, nor the naïve prognosis nor the judgmental forecasts could satisfactorily predict future economic development.” Why not common sense then?

      “Assessment of Fifteen Years of Urban Modeling,” OMEGA, 716, 1979, 545-51

      “Die Leistungfaehigkeit oekonometrischer Prognose-Systems,” Operations Research Verfahrens, 26, 1977, 814-26.

  8. Steve
    October 11, 2014 at 4:08 pm

    Agnosticism is the true open minded stance, not atheism. I am a rigorous agnostic. Hence I am able to see the cognitive/conceptual alignment of the traditionally religious concept of grace and the powerful and the economically necessary policy effects of monetary grace the free gift…without grasping at dogmas/foolishly rejecting the policy/experiential Wisdom of same.

    As for empiricism and observation which are the basic mental activities of science, I could not agree more that economics suffers from a lack of these. In fact the soft/social sciences are not alone in ad hoc re-affirmation of current dogmas as opposed to actual looking and comparing; the hard sciences are actually plagued by this as well.

    Reality is more inclusive than science or religion. The world is actually awash in orthodoxies of both science and religion. Let us look, actually look. Let us “break up our intellectual fallow ground” and embrace the wider, deeper truth.

  9. Rhonda Kovac
    October 11, 2014 at 4:29 pm

    Induction is something that we do when we don’t know what to do. We attempt to ‘induce’ the occurrence of an event when we don’t and/or can’t know exactly what will make that event happen. The defining parameters of an inductive situation typically are arrived at via specifying two things that we know–the present situation and the outcome about which we are concerned. However, what has driven us to induction in the first place is what we DON’T know, and that may include processes that reach farther out than those implied by the initial specification.

    Thus when economists attempt to project the price of housing based on the behavior history of the housing market as embodied in its conventional metrics, they can easily be–as they have repeatedly been–blind-sided by the eruption of a bubble, the totality of whose processes are NOT accommodated by those metrics.

    Induction, therefore, in order to be dependable, must account for ALL possible factors/forces/causes/etc. that participate in producing the outcome at issue, not merely those that appear intuitively at first sight to be involved. (This reflects Popper’s falsifiability assertion, that the correctness of a theory is not established by what positively supports it but rather when it has survived all attacks to prove it false.)

    To speak in general of the reliability of induction, or to attempt to develop broad rules of thumb for drawing inductive conclusions–such as for ‘linear’ vs. ‘non-linear’ kinds of situations–is pointless. Reliability depends on what particular items are present on the comprehensive list of possible determining factors involved in the particular situation and for the particular outcome under consideration.

  10. October 11, 2014 at 10:12 pm

    Why J. S. Mill had no friendly word for the bigots and votaries of common sense
    One more comment on Nassim Taleb’s ‘The riddle of induction’

    When the discussion is about induction/deduction then the appeal to common sense is utterly misleading.

    To be quite clear: nobody denies that common sense is good for getting out of the bed, crossing the street, and for a lot of other practical purposes. However, the task is to keep it out of science. Why? Because common sense is so convincing.

    There is no need to go back a few hundred years. If, in a discussion, participant A says that it is nonsense and a conspiracy of these arrogant scientist to claim that the earth moves with a tremendous speed, because he and nobody else in this room feels the slightest movement, then he has a good chance to get the assent of roughly 80 percent of an average audience (cf. Mirowski, 1995, p. 104). Participant B who tries to explain the optical illusion with the theory of relative motion has a hard stand.

    It is a curious fact that science is necessarily counter-intuitive.

    “… that the new physics of the seventeenth century, which replaced the older concepts of motion, rest, and change, involved a radical reorientation of the view of the cosmos and the possibilities of an infinite void space, thus yielding an almost entirely new philosophy of nature and a wholly different physics that contradicted ordinary intuition and common sense.” (Cohen, 1977, p. 318-319)

    The problem with economics is that is has a strong and proud tradition of common sense.

    “… [Adam Smith] disliked whatever went beyond plain common sense. He never moved above the heads of even the dullest readers. He led them on gently, encouraging them by trivialities and homely observations, making them feel comfortable all along.” (Schumpeter, 1994, p. 185)

    This tradition has a stronghold in Cambridge.

    “In the early thirties he [Keynes] confessed to Roy Harrod that he was “returning to an age-long tradition of common sense”.” (Coates, 2007, p. 11)

    And this explains why Keynesianism is not a science until this day (2011). Again and again it turns out that common sense is a millstone around the neck of economics. This was already clear to Mill (!) and this is why he had no friendly word for it (2006, pp. 783, 790).

    As Einstein famously put it: “common sense is the collection of prejudices acquired by age eighteen.”

    Egmont Kakarot-Handtke

    References
    Coates, J. (2007). The Claims of Common Sense. Moore, Wittgenstein, Keynes and the Social Sciences. Cambridge, New York, NY, etc.: Cambridge University Press.

    Cohen, I. B. (1977). History and the Philosopher of Science. In F. Suppe (Ed.), The Structure of Scientific Theories, pages 308–349. Urbana, IL, Chicago, IL: University of Illinois Press.

    Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–15. URL http://ssrn.com/abstract=1966438.

    Mill, J. S. (2006). A System of Logic Ratiocinative and Inductive. Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation, volume 8 of Collected Works of John Stuart Mill. Indianapolis, IN: Liberty Fund.

    Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.

    Schumpeter, J. A. (1994). History of Economic Analysis. New York, NY: Oxford University Press.

  11. October 11, 2014 at 11:10 pm

    On COMMON SENSE: ‘common’ meaning crude? ‘common’ meaning belonging to everyone? ‘sense’ meaning residing in the senses? ‘sense’ meaning making sense? And somewhat finally, whose common sense?

    There are a large number of reasoning methods, roughly divisible into DEDUCTION and INDUCTION. All are based on premises, at least one of which must be indemonstrable, ie accepted as true without itself being deductively provable. Certainty is therefore beyond human power. We should refine our tools and use them carefully and wisely for the sake of answering questions, explaining situations and solving problems that are USEFUL for our selves and other beings.

    The assumptions of orthodox economics are not only demonstrably untrue, but they have led to catastrophic theoretical and practical consequences.

    We should stop all this academic philosophic nonsense just for the sake of throwing up dust to fiddle around in it, unless it has the real use of refining of our tools for USE. J. S. Mill was a practical human. Goodman I’m not at all so sure about.

  12. davetaylor1
    October 11, 2014 at 11:21 pm

    Egmont, since you haven’t refer to my common sense distinction between a graph and what it is supposed to be a graph of, I don’t suppose you saw the point of my analogy, which was also an example of the use of an analogy to get one thinking structurally at a more relevant and functionally different level of reality. I think Dave Raithel’s version of common sense is nearer the mark than a quotation from Peirce taken out of Humean context. I’d be interested to know how Peirce defined metaphysics, and whether his own metaphysical axioms started from observable chaos or how energy could be transformed into localised and persistent particles, i.e. things which, as Dave says, one should assume will continue unless one has reasons to the contrary. Curiously, the great technological breakthrough here this week, demonstrating what scientists didn’t actually didn’t know was possible, concerns the reversal of the spin of the superconducting current in an electron so it can be used as a bit of data. http://engineering.ucsb.edu/news/88/.

    Rhonda, your concept of induction sounds to me like what most people would recognise as deduction applied to appearances rather than knowledge of energetic causal relations: “methods that predict or infer, in Hume’s words, that ‘instances of which we have had no experience resemble those of which we have had experience’ “. http://plato.stanford.edu/search/searcher.py?query=induction . That actually works for mathematical induction, where what is true for an arbitrary integer value of a variable is also true for the next. What Hume (and after him Popper) were attacking was Aristotle’s usage, almost as a synonym for intuitive classification. That was not how Francis Bacon, the founder of modern science, redefined the word. His method (perhaps first used by his doctor, Harvey, who worked out the circulation of the blood) was “to take things to bits to see how they worked”. He used the word for the slow laborious process of coming to an understanding of that in terms of the observed interactions of the bits, i.e. at a lower level rather than in finer detail. Hume, let me insist, was not a scientist but a sophistical atheist on the make, denying Aristotle’s First Cause and Christian purpose in life to clear the way for his slave-age prescription of a democracy in which an elite defines morality and determines policy. Unfortunately, money speaks louder than understanding.

  13. October 12, 2014 at 12:31 pm

    Why Feynman, too, had no friendly word for commonsensers and why this is not philosophic nonsense but decisive for science in general and economics in particular:

    Youtube 1:14 min: https://www.youtube.com/watch?v=iMDTcMD6pOw.

  14. davetaylor1
    October 12, 2014 at 1:03 pm

    PS. Having slept on the above, perhaps the difference between Bacon and Aristotle was an emphasis on the need for intuition to be mature, appropriately informed and physically experimental rather than childish Humean imagination. One wonders how long the youthful Newton, escaping the Black Death in the dark skies of the countryside admiring God’s creation of the starry skies, had been thinking about gravity before his ‘gestalt’ experience. But as Chesterton put it, “a man is not really convinced of a philosophic theory when he finds that something proves it. He is only really convinced when he finds that everything proves it”. Newton did not write his Principia until twenty years later, by when he had reduced mountains of geometrical observations into the Cartesian algebraic form which (until Einstein’s work on energy) DID appear to work on every THING..

  15. davetaylor1
    October 12, 2014 at 7:26 pm

    Thank you, Steve. The only point I would make is that if you want to get anything done you have to choose between the options, and not many people take the trouble to make an informed choice. I could say a lot about mine but G K Chesterton tells it more amusingly in “Orthodoxy”.

    In response to Egmont’s link following up Peirce on metaphysics, I’ll go along with this:

    “A formal approach gives the opportunity to make assumptions explicit and to prove results which may previously have been perceived intuitively, or even to deduce conclusions from self-evident truths. These results can then be communicated unambiguously, because they are obtained within a system of agreed rules. There can only be disagreement about the assumptions or the chosen method itself.” (Chick, 1998, p. 1867).

    Actually, the disagreement seems to be about both. That there is no God, that affirmation of Christ’s resurrection is false, and [therefore] Christ’s teachings are insignificant, are all assumptions. Having long worked in the field studying both human and artificial logical hardware, the logic is the hardware and not the formal representation of its, while the data-processing hardware circuits required for input, output, data indexing (i.e. language), picture processing and error correction are quite different. As to the disagreements being significant, here’s GKC’s Christian “Orthodoxy” on the Economic version:

    “All sane men can see that sanity is some kind of equilibrium: that one may be mad and eat too much, or mad and eat too little. Some moderns have indeed appeared with vague versions of progress and evolution which seeks to destroy the μέσον or balance of Aristotle. They seem to suggest that we are meant to starve progressively, or to go on eating larger and larger breakfasts every morning for ever. … these people have not upset any [mental] balance but their own. But granted that we have all to try and keep a balance, the real interest comes in with the question of how that balance can be kept.”

    Chesterton’s answer to that was captured in his friend’s image of a spinning top.

    Egmont’s latest on Feynman puzzles me, for in his clip Feynman was defending common sense against convenient simplifications: the very things with which he made his name. “Each Feynman diagram could replace an effective lifetime of Schwingerian algebra”. (Gleick’s “Genius”, p.275). I have a lot of time for Feynman, who brought home to me the mathematical significance of symmetry, and I accept the fact that he’d chosen the atheist option. But here he’s on about what the world looks like, discounting what he cannot see and (given his atheistic major premise) is unable to infer. If one dwells on how flows, waves, turbulence and sprays form and deform, and how a whole flow may remain unseen in a closed 0 but empty from a 1, one can begin to imagine what Feynman could not.

  16. chdwr
    October 12, 2014 at 8:00 pm

    Both Science and Economics urgently need a paradigm change from Onlyness to Bothness (or more), a change from from fragmentation to integration and from a consideration of the mere conventional “wisdom” of profit to actual Wisdom…which, after all, is the integrative process itself.

  17. October 12, 2014 at 10:55 pm

    Answer to Nassim Taleb

    The riddle of induction has been solved argumentatively by J. S. Mill and practically by the history of economic thought. Inductivists and commonsensers have achieved not much, if anything, of scientific value. More proof is not needed.

    Egmont Kakarot-Handtke

  18. davetaylor1
    October 13, 2014 at 2:49 pm

    Egmont, I’m sorry if my not acceding to your viewpoint is frustrating you. I’ve come back because a couple of things you said earlier have stayed in my mind as worthy of discussion.

    “There is no need to go back a few hundred years.”

    I think there is, thinking in epidemiological terms. Atheistic capitalist irresponsibility has by now become endemic, so students not familiar with how different economic theory was pre-Reformation (and in other economics systems like the Buddhist and Muslim) are deprived of points of contrast for assessing whether their norms are healthy or, like sickle cell anaemia, compensating for disease. Given the latter, the source of the disease can be triangulated historically, back via Hume’s amoral theorising of democracy to the Settlement of Constitutional Monarchy funded by the Bank of England’s usurious reserve banking after William of Orange’s takeover of the British monarchy (funded by the citizen-guaranteed Bank of Amsterdam), back to Henry VIII (heavily disguised as Shakespeare’s Merchant of Venice) “selling off the family silver” and re-legalizing usury to pay off military debts incurred through matrimonial folly.

    “It is a curious fact that science is necessarily counter-intuitive”.

    A scientific view of intuition would have noticed the difference between naive intuition and intuition informed by science. Intuition doesn’t go away as a result of scientific findings and expertise, it just matures. I don’t see (old theory) the heavens revolving. I see movement, remember the imaginative experience of counter-factually feeling the train next to mine starting away, and understand the world (new theory) as turning slowly on its axis.

    Chdwr: “Both Science and Economics urgently need a paradigm change from Onlyness to Bothness (or more) …”?

    I agree, and as a communications engineer/scientist that’s what I’ve been offering these thirty years and more to scientists and economists who seem unable to imagine what it means. The ancient common-sense paradigm was a grocer seeking an equilibrium between goods and weights on either side a pair of scales. Hume came along and claimed you cannot see that, only what you (as the grocer – pun on “grosser”) see, including perhaps “doctored” weights of which he knows a customer will see only the appearance.

    Imagine instead an electric circuit, in which the components are connected to each other (i.e. “integrated” into a system) by wires or equivalent communication channels. The wires are not to be overlooked or treated as just “fragments” like any other, for they inter-relate the other components to determine the order in which events happen (and hence circuit function). I’m saying that, in science, the order of reductive, inductive and deductive thinking and experimental evaluation matters, and likewise the ordering of events in economics. That has evolved from provision for biological maturation and reproduction (fathers and mothers feeding children and old folks using leisure to improve the process) to a monetised semi-automatic control system (Smith’s “invisible hand”), which insofar as it is used only to control itself, i.e. the efficient creation of money, will succeed only in doing so. (We are seeing it reducing economics to chrematistics and bifurcating humanity into the monetarily obese and the biologically starving). In systems engineering terms, we need to invert the interpretation of money value from positive to negative (i.e. from representing wealth to representing what money is created as, debt). Its destabilizing positive feedbacks will then become negative and insofar as they are needed will have to be applied manually. Our personal and corporate debt money, like electricity returning to a battery, can be written off when used and its use accounted for (this to provide negative feedback); but the battery is going flat and it is up to us to use only what we need and (insofar as we can) to help Nature recharge it. (From this point of view rather than one of inter-personal justice or personal dominance, isn’t this common sense)?

  19. davetaylor1
    October 15, 2014 at 11:29 am

    I’m returning to this because Egmont and I (and others) seem to be disagreeing over the meaning of the word ‘induction’, and it is crucial to my own understanding of PID control and position among economists as an ‘outsider’. If we correct what seems to be an error but is not, we make matters worse, not better – as when academics (even in wikipedia) follow a policy of throwing illegitimate (but nevertheless real) babies out with the bathwater instead of, in due course, adopting them. There is also a relevant aspect of science which we haven’t discussed: Insight (as in Archimedes’ “Eureka!” moment). In my own experience this is what Bacon’s inductive methodology of prolonged study and experiment (as perhaps in Newton’s reflections on rural night skies) can lead to.

    I’d overlooked Jbragin’s reaction Mill and Goodman (and Egmont?). This has had me looking back through Chesterton’s “Orthodoxy” (a “greatest in the twentieth century” essay on these issues in the context of Christianity, hence my recommending it above to Steve). The humorous Chesterton, challenging the insanity of academic (scholastic?) logic, answers Goodman directly:

    “The ordinary man has always been sane because the ordinary man has always been a mystic. He has always had one foot on earth and the other in fairyland. He has always left himself to doubt his gods; but (unlike the agnostic of today) free also to believe in them. He has always cared more for truth than consistency. If he saw two truths which seemed to contradict each other, he would take the two truths and the contradiction along with them. His spiritual sight is stereoscopic, like his physical sight: he sees two different pictures at once and yet sees all the better for that”.

    So elsewhere he says he can look at something a thousand times and on the next see what he hadn’t noticed before. Eureka! A gestalt switch! So if computers note control failures and they keep happening more often than expected, one may discover not that every twelfth event may be a failure but that there is a design fault overstressing a component.

    How different this is from what John Stuart Mill is seeing in Egmont’s quotation (re “Shocks”):

    “… while we look at the facts in the concrete, clothed in all the complexity with which nature has surrounded them, and endeavour to elicit a general law by a process of induction from a comparison of details …”.

    Mill’s science is merely descriptive and at best reactionary whereas Bacon’s induces new knowledge. Mine hinges on an S R Ranganathan gestalt in “The Colon Classification”: he seeing abstraction as opposite to generalisation (as in a photographic negative filtering out not irrelevant detail but all colours except those needed to see the picture as it really was). Our brains stop noticing what has become familiar by long use.

    • davetaylor1
      October 15, 2014 at 12:08 pm

      PS. An interesting comparison of usage is that an electric generator uses magnetism to induce electric current, and vice versa in an induction motor. The magnetic and electric forces are not opposites but orthogonal (at right angles) to each other. C.f. a father and mother being complementary to each other despite – in logic – mother being NOT a father. superficially opposites.

      • robert r locke
        October 15, 2014 at 12:19 pm

        This idea fits with what I encountered when looking at the role organizational science played in management of German firms. the problem with organizational science, is that it was “approximate” knowledge, and henceforth, could not be trusted by all interested parties, i.e.,employees and managers. The American solution is to throw the employees out. The German, was to have employees and managers bring their own experts, trained in organizational science, to the discussions.

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