The riddle of induction

8 Oct, 2014 at 15:20 | Posted in Theory of Science & Methodology | 2 Comments

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 …

2 Comments

  1. Phony riddle solved already by J. S. Mill
    Comment on Nassim Taleb’s ‘The riddle of induction’

    What is the core problem of economics? Bagehot made it clear back in 1885:

    “It [Political Economy] is an abstract science which labours under a special hardship. Those who are conversant with its abstractions are usually without a true contact with its facts; those who are in contact with its facts have usually little sympathy with and little cognisance of its abstractions. Literary men who write about it are constantly using what a great teacher calls ‘unreal words,’ — that is, they are using expressions with which they have no complete vivid picture to correspond. They are like physiologists who have never dissected; like astronomers who have never seen the stars; and, is consequence, just when they seem to be reasoning at their best, their knowledge of the facts falls short. Their primitive picture fails them, and their deduction altogether misses the mark — sometimes, indeed, goes astray so far, that those who live and move among the facts boldly say that they cannot comprehend ‘how any one can talk such nonsense.’ Yet, on the other hand, these people who live and move among the facts often, or mostly, cannot of themselves put together any precise reasonings about them.” (Bagehot, 1885, PE.13)

    Take-home message: There are two types of economists but neither has a clue.

    This, indeed, was not news then because J. S. Mill reported already in 1874 about the two classes of inquirers.

    “It has been again and again demonstrated, that those who are accused of despising facts and disregarding experience build and profess to build wholly upon facts and experience; while those who disavow theory cannot make one step without theorizing. But, although both classes of inquirers do nothing but theorize, and both of them consult no other guide than experience, there is this difference between them, and a most important difference it is: that those who are called practical men require specific experience, and argue wholly upwards from particular facts to a general conclusion; while those who are called theorists aim at embracing a wider field of experience, and, having argued upwards from particular facts to a general principle including a much wider range than that of the question under discussion, then argue downwards from that general principle to a variety of specific conclusions.” (Mill, 1874, V. 43)

    Take-home message: There are two types of economists, the upwarders and downwarders, but neither is particularly successful.

    Mill was confronted with a quite unsatisfactory situation. He was well aware of the “backward state” of the social sciences in general and of economics in particular. Being one of the finest methodologists of his time — and far beyond — he took sides.

    “Since, therefore, it is vain to hope that truth can be arrived at, either in Political Economy or in any other department of the social science, 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; there remains no other method than the à priori one, or that of “abstract speculation”.” (Mill, 1874, V.55)

    Mill had the great triumph of the downwarders before his eyes and he certainly concurred with Galileo.

    “I shall never be able to express strongly enough my admiration for the greatness of mind of these men who conceived this [heliocentric] hypothesis and held it to be true. In violent opposition to the evidence of their own senses and by sheer force of intellect, they preferred what reason told them to that which sense experience plainly showed them …” (quoted in Popper, 1994, p. 84)

    In contrast, the defeat of the upwarders was evident and their good advice rung hollow.

    “Bacon, the philosopher of science, was, quite consistently, an enemy of the Copernican hypothesis. Don’t theorize, he said, but open your eyes and observe without prejudice, and you cannot doubt that the Sun moves and that the Earth is at rest.” (Popper, 1994, p. 84)

    Take-home message: Common sense and open eyes can be very misleading in scientific matters.

    Or, as Marx put it: “That in their appearances things are often presented in an inverted way is something fairly familiar in every science, apart from political economy.” (Marx, 1990, p. 677)

    The downwarders of Orthodoxy have failed to explain how the actual economy works. This, however, does not prove that the methodology of the upwarders is superior. Heterodoxy cannot claim that it has performed better.

    The first step for everybody who seriously wants to get out of the phony induction-deduction impasse is to go here: http://www.axec.org/#!axioms/cy2g

    Egmont Kakarot-Handtke

    References
    Bagehot, W. (1885). The Postulates of English Political Economy. Library of
    Economics and Liberty. URL http://www.econlib.org/library/Bagehot/bagPE1.
    html.

    Marx, K. (1990). Capital, volume I. London: Penguin Classics. (1876).

    Mill, J. S. (1874). Essays on Some Unsettled Questions of Political Economy. On
    the Definition of Political Economy; and on the Method of Investigation Proper
    To It. Library of Economics and Liberty. URL http://www.econlib.org/library/
    Mill/mlUQP5.html#EssayV.OntheDefinitionofPoliticalEconomy.

    Popper, K. R. (1994). The Myth of the Framework. In Defence of Science and
    Rationality., chapter Science: Problems, Aims, Responsibilities, pages 82–111.
    London, New York, NY: Routledge.

  2. Personally I would rather have a naïve extrapolation than someone else’s ‘common sense’. The mistake is not so much in extrapolating, but in leaning too heavily on the extrapolation, especially when there are particular reasons to think that it may be unreliable.


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