The Keynes-Ramsey-Savage debate on probability

22 July, 2015 at 08:35 | Posted in Economics | 23 Comments

Neoclassical economics nowadays usually assumes that agents that have to make choices under conditions of uncertainty behave according to Bayesian rules, axiomatized by Ramsey (1931) and Savage (1954) – that is, they maximize expected utility with respect to some subjective probability measure that is continually updated according to Bayes theorem. If not, they are supposed to be irrational, and ultimately – via some “Dutch book” or “money pump”argument – susceptible to being ruined by some clever “bookie”.

calvin-math-atheist3-2Bayesianism reduces questions of rationality to questions of internal consistency (coherence) of beliefs, but – even granted this questionable reductionism – do rational agents really have to be Bayesian? As I have been arguing elsewhere (e. g. here, here and here) there is no strong warrant for believing so.

In many of the situations that are relevant to economics one could argue that there is simply not enough of adequate and relevant information to ground beliefs of a probabilistic kind, and that in those situations it is not really possible, in any relevant way, to represent an individual’s beliefs in a single probability measure.

Say you have come to learn (based on own experience and tons of data) that the probability of you becoming unemployed in Sweden is 10 %. Having moved to another country (where you have no own experience and no data) you have no information on unemployment and a fortiori nothing to help you construct any probability estimate on. A Bayesian would, however, argue that you would have to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1, if you are rational. That is, in this case – and based on symmetry – a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed.

That feels intuitively wrong though, and I guess most people would agree. Bayesianism cannot distinguish between symmetry-based probabilities from information and symmetry-based probabilities from an absence of information. In these kinds of situations most of us would rather say that it is simply irrational to be a Bayesian and better instead to admit that we “simply do not know” or that we feel ambiguous and undecided. Arbitrary an ungrounded probability claims are more irrational than being undecided in face of genuine uncertainty, so if there is not sufficient information to ground a probability distribution it is better to acknowledge that simpliciter, rather than pretending to possess a certitude that we simply do not possess.

I think this critique of Bayesianism is in accordance with the views of John Maynard Keynes’ A Treatise on Probability (1921) and General Theory (1937). According to Keynes we live in a world permeated by unmeasurable uncertainty – not quantifiable stochastic risk – which often forces us to make decisions based on anything but rational expectations. Sometimes we “simply do not know.” Keynes would not have accepted the view of Bayesian economists, according to whom expectations “tend to be distributed, for the same information set, about the prediction of the theory.” Keynes, rather, thinks that we base our expectations on the confidence or “weight” we put on different events and alternatives. To Keynes expectations are a question of weighing probabilities by “degrees of belief”, beliefs that have preciously little to do with the kind of stochastic probabilistic calculations made by the rational agents modeled by Bayesian economists.

Stressing the importance of Keynes’ view on uncertainty John Kay writes in Financial Times:

Keynes believed that the financial and business environment was characterised by “radical uncertainty”. The only reasonable response to the question “what will interest rates be in 20 years’ time?” is “we simply do not know” …

For Keynes, probability was about believability, not frequency. He denied that our thinking could be described by a probability distribution over all possible future events, a statistical distribution that could be teased out by shrewd questioning – or discovered by presenting a menu of trading opportunities. In the 1920s he became engaged in an intellectual battle on this issue, in which the leading protagonists on one side were Keynes and the Chicago economist Frank Knight, opposed by a Cambridge philosopher, Frank Ramsey, and later by Jimmie Savage, another Chicagoan.

Keynes and Knight lost that debate, and Ramsey and Savage won, and the probabilistic approach has maintained academic primacy ever since. A principal reason was Ramsey’s demonstration that anyone who did not follow his precepts – anyone who did not act on the basis of a subjective assessment of probabilities of future events – would be “Dutch booked” … A Dutch book is a set of choices such that a seemingly attractive selection from it is certain to lose money for the person who makes the selection.

I used to tell students who queried the premise of “rational” behaviour in financial markets – where rational means are based on Bayesian subjective probabilities – that people had to behave in this way because if they did not, people would devise schemes that made money at their expense. I now believe that observation is correct but does not have the implication I sought. People do not behave in line with this theory, with the result that others in financial markets do devise schemes that make money at their expense.

Although this on the whole gives a succinct and correct picture of Keynes’s view on probability, I think it’s necessary to somewhat qualify in what way and to what extent Keynes “lost” the debate with the Bayesians Frank Ramsey and Jim Savage.

In economics it’s an indubitable fact that few mainstream neoclassical economists work within the Keynesian paradigm. All more or less subscribe to some variant of Bayesianism. And some even say that Keynes acknowledged he was wrong when presented with Ramsey’s theory. This is a view that has unfortunately also been promulgated by Robert Skidelsky in his otherwise masterly biography of Keynes. But I think it’s fundamentally wrong. Let me elaborate on this point (the argumentation is more fully presented in my book John Maynard Keynes (SNS, 2007)).

It’s a debated issue in newer research on Keynes if he, as some researchers maintain, fundamentally changed his view on probability after the critique levelled against his A Treatise on Probability by Frank Ramsey. It has been exceedingly difficult to present evidence for this being the case.

Ramsey’s critique was mainly that the kind of probability relations that Keynes was speaking of in Treatise actually didn’t exist and that Ramsey’s own procedure  (betting) made it much easier to find out the “degrees of belief” people were having. I question this both from a descriptive and a normative point of view.

What Keynes is saying in his response to Ramsey is only that Ramsey “is right” in that people’s “degrees of belief” basically emanates in human nature rather than in formal logic.

Patrick Maher, former professor of philosophy at the University of Illinois, even suggests that Ramsey’s critique of Keynes’s probability theory in some regards is invalid:

Keynes’s book was sharply criticized by Ramsey. In a passage that continues to be quoted approvingly, Ramsey wrote:

“But let us now return to a more fundamental criticism of Mr. Keynes’ views, which is the obvious one that there really do not seem to be any such things as the probability relations he describes. He supposes that, at any rate in certain cases, they can be perceived; but speaking for myself I feel confident that this is not true. I do not perceive them, and if I am to be persuaded that they exist it must be by argument; moreover, I shrewdly suspect that others do not perceive them either, because they are able to come to so very little agreement as to which of them relates any two given propositions.” (Ramsey 1926, 161)

I agree with Keynes that inductive probabilities exist and we sometimes know their values. The passage I have just quoted from Ramsey suggests the following argument against the existence of inductive probabilities. (Here P is a premise and C is the conclusion.)

P: People are able to come to very little agreement about inductive proba- bilities.
C: Inductive probabilities do not exist.

P is vague (what counts as “very little agreement”?) but its truth is still questionable. Ramsey himself acknowledged that “about some particular cases there is agreement” (28) … In any case, whether complicated or not, there is more agreement about inductive probabilities than P suggests.

Ramsey continued:

“If … we take the simplest possible pairs of propositions such as “This is red” and “That is blue” or “This is red” and “That is red,” whose logical relations should surely be easiest to see, no one, I think, pretends to be sure what is the probability relation which connects them.” (162)

I agree that nobody would pretend to be sure of a numeric value for these probabilities, but there are inequalities that most people on reflection would agree with. For example, the probability of “This is red” given “That is red” is greater than the probability of “This is red” given “That is blue.” This illustrates the point that inductive probabilities often lack numeric values. It doesn’t show disagreement; it rather shows agreement, since nobody pretends to know numeric values here and practically everyone will agree on the inequalities.

Ramsey continued:

“Or, perhaps, they may claim to see the relation but they will not be able to say anything about it with certainty, to state if it ismore or less than 1/3, or so on. They may, of course, say that it is incomparable with any numerical relation, but a relation about which so little can be truly said will be of little scientific use and it will be hard to convince a sceptic of its existence.” (162)

Although the probabilities that Ramsey is discussing lack numeric values, they are not “incomparable with any numerical relation.” Since there are more than three different colors, the a priori probability of “This is red” must be less than 1/3 and so its probability given “This is blue” must likewise be less than 1/3. In any case, the “scientific use” of something is not relevant to whether it exists. And the question is not whether it is “hard to convince a sceptic of its existence” but whether the sceptic has any good argument to support his position …

Ramsey concluded the paragraph I have been quoting as follows:

“Besides this view is really rather paradoxical; for any believer in induction must admit that between “This is red” as conclusion and “This is round” together with a billion propositions of the form “a is round and red” as evidence, there is a finite probability relation; and it is hard to suppose that as we accumulate instances there is suddenly a point, say after 233 instances, at which the probability relation becomes finite and so comparable with some numerical relations.” (162)

Ramsey is here attacking the view that the probability of “This is red” given “This is round” cannot be compared with any number, but Keynes didn’t say that and it isn’t my view either. The probability of “This is red” given only “This is round” is the same as the a priori probability of “This is red” and hence less than 1/3. Given the additional billion propositions that Ramsey mentions, the probability of “This is red” is high (greater than 1/2, for example) but it still lacks a precise numeric value. Thus the probability is always both comparable with some numbers and lacking a precise numeric value; there is no paradox here.

I have been evaluating Ramsey’s apparent argument from P to C. So far I have been arguing that P is false and responding to Ramsey’s objections to unmeasurable probabilities. Now I want to note that the argument is also invalid. Even if P were true, it could be that inductive probabilities exist in the (few) cases that people generally agree about. It could also be that the disagreement is due to some people misapplying the concept of inductive probability in cases where inductive probabilities do exist. Hence it is possible for P to be true and C false …

I conclude that Ramsey gave no good reason to doubt that inductive probabilities exist.

Ramsey’s critique made Keynes more strongly emphasize the individuals’ own views as the basis for probability calculations, and less stress that their beliefs were rational. But Keynes’s theory doesn’t stand or fall with his view on the basis for our “degrees of belief” as logical. The core of his theory – when and how we are able to measure and compare different probabilities – he doesn’t change. Unlike Ramsey he wasn’t at all sure that probabilities always were one-dimensional, measurable, quantifiable or even comparable entities.

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  1. Lars,

    Despite the best endeavours of the best mathematicians, there still seems to be a widespread belief – like Ramsey’s immature view – that one needs probability theory in order to do science, or even that one needs probability theory to be rational. David Deutsch’s analysis (as at https://djmarsay.wordpress.com/science/deutschs-constructors/ ) gives the lie to this, without using any sophisticated mathematics.

    The Dutch book argument is valid wherever it can be logically applied – but not elsewhere.

    • Dave,

      I’m having much trouble understanding this paper. For instance, how would CT replace statistical mechanics as the foundation of quantum mechanics?

      • I am not a Physicist, but statistical mechanics is based on the notion of probability distributions and so one has to ask how one knows to which phenomena it can reasonably be applied. One solution is Keynes’, which is to apply it instrumentally and check statistically that it is not falsified. But then one still should be concerned about any new area of application. As a mathematician the term ‘statistical’ mechanics raises alarm bells, because in statistics the proper use of probability is still controversial. Maybe in Physics it doesn’t matter. But Deutsch seems to think that it does. He shows that sometimes the use of probabilities can be reduced to the use of his constructors. Hence instead of being somewhat arbitrary, statistical mechanics could be re-formulated in terms of constructors, giving the same results, but only when the reduction was well founded. My observation that the issues that arise in attempting to reduce QM to CT are similar those that ‘should’ arise in attempting to inform economic policy by mainstream theories. While it may be true that a theory based on probability distributions is good enough for most physics, this may not be the case for economics. And my point is, it may not even be good enough for physics.

      • “As a mathematician the term ‘statistical’ mechanics raises alarm bells, because in statistics the proper use of probability is still controversial. Maybe in Physics it doesn’t matter.”

        It certainly does matter – http://www.ucl.ac.uk/~ucesjph/reality/entropy/text.html – and Deutsch’s CT might be of foundational interest but I can’t see it replacing [non-commutative] probability theory in physics or any other science.

      • phayes provides a useful reference:

        “[T]hose who believe [Bayes’ Theorem] and use it are called Bayesians. Before using it, however the joint p.d.f. has to be assigned. Because Bayes’ theorem is simply a rule for manipulating probabilities, it cannot by itself help us to assign them in the first place, and for that we have to look elsewhere. ”

        “MaxEnt states that the probabilities should be assigned … where {mi} is a suitable measure over the space of possibilities (hypothesis space).”

        In this light I find myself a Bayesian, and arguably more Bayesian than those who use Bayes’ rule as a heuristic, without regard to the small print of the mathematics. (This is, I think, the opposite of common usage.) But the substantial point is in the second paragraph. It may be that in physics there is always ‘a [unique] suitable measure over the space of possibilities’, but in economics, and much of life, I agree with Keynes that this may not always be the case, and it matters.

        I have a paper on this, open for discussion, at http://www.economics-ejournal.org/economics/discussionpapers/2015-43 . I offer an interpretation of Keynes that is Bayesian in the above sense but which can accommodate Turing’s critical instabilities without using a ‘cloaking device’.

  2. Lars,

    The John Kay link to FT does not seem to work. Is there any other way to access the piece.

    • I’ve changed it now. Hope it works🙂

      • It looks like a paid FT subscription is needed. Thanks Lars.

  3. […] via The Keynes-Ramsey-Savage debate on probability | LARS P. SYLL. […]

  4. It is pointless to attempt to disprove reality using mathematics. The literature Dr. Marsay cites asserts, as its premise, the validity of Einstein’s Principle of Locality. “Spooky action at a distance” has been measured experimentally.

    • The terms ‘principle of locality’ and ‘spooky action at a distance’ appear to be inconsistent. Deutsch shows that the actual physics that these words represent are consistent.

      But I agree with your first sentence. It is also pointless trying to prove reality. The best one can do is to prove unreality. I am looking for any claims to have proved the unreality of non-probabilistic uncertainty. Suggestions welcome on my blog: https://djmarsay.wordpress.com/ .

  5. How to consistently start off on the wrong foot
    Comment on ‘The Keynes-Ramsey-Savage debate on probability’
    .
    Economists have the talent to mess up everything they touch. Curiously, everything that works fine in the real sciences does not seem to work in economics. The long standing mathiness discussion corroborates this observation. More than one physicist has wondered about the ‘unreasonable effectiveness of mathematics in the natural sciences’ (Wigner) and this led Velupillai to wonder about the ‘unreasonable ineffectiveness of mathematics in economics.’ The same holds for probability theory and empirical testing.
    .
    In a sense, economists had the bad luck that when Adam Smith started to think about the economy mathematical tools had already proven their unreasonable effectiveness. So economist could not resist to apply them as they found them. It can be said that neoclassical economics has literally been built around calculus (1995). This was the first big mistake.
    .
    “The mathematical language used to formulate a theory is usually taken for granted. However, it should be recognized that most of mathematics used in physics was developed to meet the theoretical needs of physics. … The moral is that the symbolic calculus employed by a scientific theory should be tailored to the theory, not the other way round.” (Wittgenstein, quoted in Schmiechen, 2009, p. 368)
    .
    The whole mathiness discussion is a surface phenomenon that covers the underlying incompetence of economists to create their own mathematical tools. Therefore, a fine distinction has to be made. One can agree with Keynes that constrained optimization is pointless as a formal embodiment of human behavior, but one cannot agree with him that mathematics or formalization is entirely misplaced in economics. The same holds for probability theory.
    .
    The task of Heterodoxy is therefore to quit the bad habit of taking prefabricated tools from the math department and instead to develop their own tools. As a matter of fact this has already been done. For the application of Popper’s idea of propensity to behavior in the economic realm see (2015).
    .
    With regard to Keynes and methodology we should agree that his valuable contributions to economics lay elsewhere (2011).
    .
    “I consider that Keynes had no real grasp of formal economic theorizing (and also disliked it), and that he consequently left many gaping holes in his theory. I none the less hold that his insights were several orders more profound and realistic than those of his recent critics.” (Hahn, 1982, pp. x-xi)
    .
    Egmont Kakarot-Handtke
    .
    References
    Hahn, F. H. (1982). Money and Inflation. Oxford: Blackwell.
    Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN
    Working Paper Series, 1966438: 1–20. URL http://ssrn.com/abstract=1966438.
    Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: Behavior.
    SSRN Working Paper Series, 2600523: 1–17. URL http://papers.ssrn.com/sol3/
    papers.cfm?abstract_id=2600523.
    Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University
    Press.
    Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited,
    volume 1. Norderstedt: Books on Demand, 2nd edition. URL
    http://books.google.de/books?id=3bIkAQAAQBAJ&printsec=frontcover&hl=
    de&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false.

  6. Here is my response: http://wp.me/p4Q4Lp-9x

  7. We simply do not know — so let us move on
    Comment on ‘The Keynes-Ramsey-Savage debate on probability’
    .
    Science restricts itself to things that can be known. In marked contrast, non-scientists prefer to spend their lifetime with questions that cannot be answered. Let us face the fact, it is not so much solutions that most people are really interested in, it is more the perpetual inconclusive talk about beliefs. Solutions only spoil the fun.
    .
    Economists are traditionally fond of talking about nonentities like equilibrium, utility, or rational expectations. It seems that this bad habit has a debilitating effect also on mathematicians. Our actual question is not whether statistical mechanics is good enough for physics and there is absolutely no need to discuss the finer point of quantum mechanics. Why? Because quantum mechanics and locality and all the rest is irrelevant for economics. All that is relevant about uncertainty and unpredictability is known at least since J. S. Mill and has been stated unmistakably by other well-known people.
    .
    “The phenomena with which this science [of human nature] is conversant being the thoughts, feelings, and actions of human beings, it would have attained the ideal perfection of a science if it enabled us to foretell how an individual would think, feel, or act, throughout life, with the same certainty with which astronomy enables us to predict the places and the occultations of the heavenly bodies. It needs scarcely be stated that nothing approaching to this can be done.” (Mill, 2006, p. 846)
    .
    “The future is unpredictable.” (Feynman, 1992, p. 147)
    .
    “We are very far from being able to predict, even in physics, the precise results of a concrete situation, such as a thunderstorm, or a fire.” (Popper, 1960, p. 139)
    .
    “… it has even been argued that economic explanations involving rational choice are a species of ‘folk psychology’, explaining actions in terms of beliefs and desires, variables that cannot be measured independently of the actual choices we want to predict, so that they are no genuine predictions at all.” (Blaug, 1994, p. 113)
    .
    Keynes only used more words to restate the obvious.
    .
    “The sense in which I am using the term [uncertainty] is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention … About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know.” (Keynes, 1937, p. 214)
    .
    It is remarkable that the representative economist simply does accept the obvious even when politely told by one of the greatest mathematicians.
    .
    “Walras approached Poincaré for his approval. … But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude. … He also wondered about the premises of Walras’s mathematics: It might be reasonable, as a first approximation, to regard men as completely self-interested, but the assumption of perfect foreknowledge ‘perhaps requires a certain reserve’.” (Porter, 1994, p. 154)
    .
    What Walras’s neoclassical heirs can either not see or not accept is that they are in the wrong research program.
    .
    “The failure to find such a law [between desire, belief and action] or any approximation to it that actually improves our ability to predict consumer behaviour any better than Adam Smith could have resulted on the one hand in a reinterpretation of the aims of economic theory away from explaining individual human action, …” (Rosenberg, 1994, p. 224)
    .
    And this is the spoilsport.
    “… if we wish to place economic science upon a solid basis, we must make it completely independent of psychological assumptions and philosophical hypotheses.” (Slutzky, quoted in Mirowski, 1995, p. 362)
    .
    Because economics is definitively ‘not a science of behavior’ (Hudík, 2011), the aim of economic theory has to be changed:
    • Old definition, subjective-behavioral: “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.”
    • New definition, objective-structural: “Economics is the science which studies how the monetary economy works.”
    .
    Why telling the world ad nauseam ‘We simply do not know’ when scientific knowlege about the actual monetary economy is possible?*
    .
    Egmont Kakarot-Handtke
    .
    References
    Blaug, M. (1994). Why I am Not a Constructivist. Confessions of an Unrepetant
    Popperian. In R. E. Backhouse (Ed.), New Directions in Economic Methodology,
    pages 109–136. London, New York, NY: Routledge.
    Feynman, R. P. (1992). The Character of Physical Law. London: Penguin.
    Hudík, M. (2011). Why Economics is Not a Science of Behaviour. Journal of
    Economic Methodology, 18(2): 147–162.
    Keynes, J. M. (1937). The General Theory of Employment. Quarterly Journal of
    Economics, 51(2): 209–223. URL http://www.jstor.org/stable/1882087.
    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.
    Popper, K. R. (1960). The Poverty of Historicism. London, Henley: Routledge and
    Kegan Paul.
    Porter, T. M. (1994). Rigor and Practicality: Rival Ideals of Quantification in
    Nineteenth-Century Economics. In P. Mirowski (Ed.), Natural Images in Economic
    Thought, pages 128–170. Cambridge: Cambridge University Press.
    Rosenberg, A. (1994). What is the Cognitive Status of Economic Theory? In R. E.
    Backhouse (Ed.), New Directions in Economic Methodology, pages 216–235.
    London, New York, NY: Routledge.
    .
    * For cross-references see
    http://axecorg.blogspot.de/2015/04/new-curriculum-cross-references.html

    • “Why telling the world ad nauseam ‘We simply do not know’ when scientific knowlege about the actual monetary economy is possible?*”

      How can this be done without introducing human beviour?

      In what way is the “knowledge” scientific?
      .

  8. In the history of science, the mathematics often precedes the empirical verification.

    Ramsey’s critique of Keynes is suspect on two counts: firstly, he relates inductive premises and concludes with irrational infinities. One premise must be a deductive rule or covering law in order to draw a valid conclusion. Ramsey does not see this or he does not analyze the premise that consists of a law. Secondly, the key issue in Bayesianism is whether or not you update your beliefs given contradictory evidence. Learning theory specifies that our species recognizes and retains inductions and operates with trial-and-error reasoning, so getting Dutch-booked should be merely an episode and not a pattern. The failure to update beliefs and predictions given contradictory evidence constitutes irrationality.

    • Stubbornly in the wrong research program
      Comment on Fredrick Welfare on ‘The Keynes-Ramsey-Savage debate on probability’
      .
      You say: “The failure to update beliefs and predictions given contradictory evidence constitutes irrationality.”
      .
      Because you do not understand the relationship between theory and evidence, you — as both orthodox and heterodox economists — do not understand what science is all about.
      .
      “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 … I repeat, there is no limit to my astonishment when I reflect how Aristarchus and Copernicus were able to let conquer sense, and in defiance of sense make reason the mistress of their belief.” (Galileo, quoted in Popper, 1994, p. 84)
      .
      The key words are ‘sheer force of intellect.’ And this gives you the explanation why economists are stuck in pointless wish-wash about utility, equilibrium, expected utility, uncertainty, and the abuse of mathematics by formalizing nonentities. There is not much difference between the Ramsey-Keynes debate and the angels-on-a-pinpoint debate of yore.
      .
      Indeed, is there any difference in pseudo-logical hypotheticalness between “angels can fly because they have wings” and “… that people had to behave in this way because if they did not, people would devise schemes that made money at their expense”? And is it not astounding that economists buy these kinds of arguments? And what does this tell you about their ‘sheer force of intellect?’
      .
      Egmont Kakarot-Handtke
      .
      References
      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.

      • It is naïve to claim that science is not about evidence, about fact gathering and reconstructing sequences of object change, about description and explanation!

        A theory is a solution to a problem justified with evidence. So evidence is relevant. The claim that Galileo was using his reason in contrast to evidence is nonsense. Galileo had the evidence from Copernicus and from Kepler; the latter was a contemporary. Feyerabend makes all of this clear in Against Method. If you take a minute to read a bit of Kant you can get the distinction between sense and intellect, between sensation and understanding, between experience and logic. Reason is logic.

        Ramsey tries to refute Keynes by claiming two or more inductive probabilities and then drawing some conclusion which is not logical. It is not logical because a logical conclusion is the result of an inductive premise and a deductive premise, no logical conclusion follows without an deductive premise. Of course, the deduction or axiom must be justified separately. (Too often as self-evident!)

        Bayeysian is nothing but the updating of one’s predictions given new evidence, such as the success or failure of one’s last prediction about the same kind of event. Otherwise, one just keeps making the same prediction over and over and being wrong all over again! So, Galileo was not using his “reason” alone, he was using his reason with the new evidence of heliocentrism and rotation of the Earth.

        Galileo was faced with the dilemma of contradicting the bible and religious ways of his times. His demonstrations astounded his detractors but his explanations in words could not be accepted by them, so he had to phrase or word his claims in certain ways to avoid disrespecting the authorities. You might note that Newton used the cover of being a religious scholar to produce his work in science and math!

  9. Frederick, the hallmarks of Bayesianism is not that it updates beliefs, but that it does so in a particular way. If you believe that only the hypotheses {Hi} are possible and you believe that you know what their priors {P(Hi)} and likelihoods {P(E|Hi)} are then you should mechanically update your probabilities using Bayes’ rule, no matter what. In particular, one should gamble solely on the Bayesian probability, taking no account of the weight of evidence, or anything else.

  10. What is “inductive probabilities”?

  11. Appearances and evidence
    Comment on Fredrick Welfare on ‘The Keynes-Ramsey-Savage debate on probability’
    .
    There are two types of evidence. Let us call them common sense evidence and theory guided evidence. J. S. Mill had no good word for the first type.
    .
    “People fancied they saw the sun rise and set, the stars revolve in circles round the pole. We now know that they saw no such thing; what they really saw was a set of appearances, equally reconcileable with the theory they held and with a totally different one. It seems strange that such an instance as this, … , should not have opened the eyes of the bigots of common sense, and inspired them with a more modest distrust of the competency of mere ignorance to judge the conclusions of cultivated thought.” (Mill, 2006, p. 783)
    .
    Accordingly, I do not naively ‘claim that science is not about evidence’ but that economists apply — more often than not — the wrong type of evidence.
    .
    “… 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 deficiency of economics consists, in other words, in the lack of sound theoretical foundations. This in turn is due to the fact that the interplay of induction and deduction is generally not well understood.
    .
    “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)
    .
    Keynes’s problem with regard to inductivism/deductivism was that he eventually hit a wall.
    .
    “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)
    .
    It has to be emphasized that, compared to the vacuous green cheese assumptionism of the so-called Classicals, Keynes’s common sense was a big step forward. However, methodologically Post Keynesians still have some way to go (2011).
    .
    At the moment Post Keynesians are caught in Bacon’s common sense trap.
    “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)
    .
    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.
    Hutchison, T.W. (1960). The Significance and Basic Postulates of Economic Theory. New York, NY: Kelley.
    Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN
    Working Paper Series, 1966438: 1–20. URL http://ssrn.com/abstract=1966438.
    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.
    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.
    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.


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