It seems that the voluminous discussion going under names such as positivism vs. interpretivism, modernism vs. post-modernism, foundatonalism vs. non-foundationalism, and behaviorism, realism and pluralism could benefit from a formalization of the ontological and epistemological models implied by the various positions staked in the discussion. It may be predictably claimed by some of the discussants that the attempt at formalization stakes a position in the contested landscape rather than maps it. I tend to disagree, but do not address this issue. Below is a generic ontological-epistemological formalization framework which allows the description of a wide variety of ontological-epistemological models by setting different values for its parameters. A few specializations, corresponding to radically different situations on the positivist-interpretivist spectrum, are presented.

Setup

Let the “objective, impersonal” universe (that is, all that is observable other than other observers) be a time series of points in an observation space Rr(t) ∈ RT.

In addition the world contains a set of observers I, each with an internal state that develops over time si(t) ∈ S, i ∈ I, t ∈ T. The observations made by each observer at time t depend upon the state of the objective world at this time and upon the state of the observer at the time: fi(t) = f(r(t), si(t)).

The observers can communicate between themselves. These communications are messages of finite length over a certain finite alphabet A, so the communications of observer i at time t is bi(t) ∈ A*. The communication of each observer at each time depend on their state at the time: bi(t) = b(si(t)).

Finally, each observer’s internal state, si can develop based on the observer’s observations and on the history of communications by other observers (and himself): ∆si(t) = s'(si(t), fi(t), Bj(t), j ∈ I), where Bj(t) is the concatenation of all the messages of observer j up to time t: bj(t’), t’ ≤ t.
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Progress

November 26, 2011

It is fair to say, I think, that over the last 40 years or so there has been little progress in the quality of life of the average person in the West, and quite possibly there has been a deterioration. (The only indicator in which there has been steady progress, I think, is longevity.1)

Progressive ideology generally asserts that there is a wide variety of elements of conceivable and feasible policy and technology that would significantly improve average quality of life. It may be further assumed that the pursuit of any of those elements or any combination of those elements can be expected to be fruitful. To some extent this assumption – what may be termed the “parallel progress assumption” – seems to be implicit in much of present-day progressive activism: the agenda is usually very eclectic and often somewhat vague on specifics. While this is partly a tactic that is aimed at maintaining wide appeal, there is also the implication that as long as general principles are agreed to, laying out a detailed workplan is not necessary since progress can be made on any of many items quite independently of each other. While I accept the progressive assumption (i.e., that progress is possible) it appears to me that the parallel progress assumption is incorrect.
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Formal analysis

June 18, 2011

Keynes is rather dismissive of what he calls ‘“mathematical” economics’. The following passage is from chapter 21 of The General Theory:

The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and, after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves. This is the nature of economic thinking. Any other way of applying our formal principles of thought (without which, however, we shall be lost in the wood) will lead us into error. It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section vi of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep “at the back of our heads” the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials “at the back” of several pages of algebra which assume that they all vanish. Too large a proportion of recent “mathematical” economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.

There is much truth in the above, I think, and it is truth that applies not only to “economic thinking” but to any kind of thinking that relies on formalization. Statistical analysis is plagued with this kind of problems. Keynes does lay too much stress on the matter of interaction between factors. The problem with formal methods is not particularly with neglecting various effects – it is that they simply are false in various ways (neglecting various effects is only one of the sources of falsehoods). Informal methods have the same problem, of course – and in addition have problems associated with informality.

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Ricardo offers us the supreme intellectual achievement, unattainable by weaker spirits, of adopting a hypothetical world remote from experience as though it were the world of experience and then living in it consistently. With most of his successors common sense cannot help breaking in — with injury to their logical consistency.

John Maynard Keynes,
The General Theory of Employment, Interest and Money, Appendix to Chapter 14

I found George Englebersten’s book Bare Facts and Naked Truths in a used book shop and was attracted to it because of the interesting (if often wrongheaded) quotations it contained. My favorites are:

Most writers regard the truth as their most valuable possession, and therefore are most economical in its use. –Mark Twain

This kind of thing is frightening to me because it gives me the feeling that the very concept of objective truth is fading out of the world … I am willing to believe that history is for the most part inaccurate and biased, but what is peculiar to our age is the abandonment of the idea that history could be truthfully written. In the past people deliberately lied, or they unconsciously colored what they wrote, or they struggled after the truth, well knowing that they must make many mistakes; but in each case they believed that ‘the facts’ existed and were more or less discoverable. -Orwell

We’ve reached a point where, in an orgy of political correctness, everything is true, and nothing is permitted. -Dean Kuipers

Truths are illusions. -Nietzsche
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Paul Krugman, Princeton economics professor, winner of the Nobel prize in economics for 2008 and New York Times op-ed writer is a person worth paying some attention to. Unlike most other mainstream commentators he does not deal mainly in cliches and often shows respect towards his readers by supporting his positions with hard data. He is also willing to take some risk by, on occasion, pushing against the envelope of mainstream propriety and using impolite words toward people with power.

Of course, he is not without faults. Of course, none of us is. The point is that Krugman’s faults are not too different than those of many of his colleagues. In other words, while Krugman is somewhat of an exquisite specimen of the mainstream intellectual, he is still very much such a specimen.

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As Phillip Davis writes (reprinted in the IMS Bulletin), scholarly authors are driven to publish in journals because that is the way to have their work noticed and readers read journals because these provide some measure of quality assurance. Davis is wrong, however, on multiple counts, when he concludes: “This system is not intended to be fair and democratic, but it saves the time of the reader and functions to help consensus building in science. For those who feel that this perpetuates hegemony, let them eat cake.”

The academic publishing system is intended to be fair; the current system (though better than nothing) performs poorly as a time saving tool for the reader; “consensus forming” (i.e., suppressing non-conventional thought) is not a legitimate function of a scientific communication channel; and, finally, there is no reason to dismiss people who are unhappy with the current system with “let them eat cake”: there is a better way to run the scholarly publishing system.

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Steven Levitt has risen to stardom by riding on the overblown rhetoric resting on the overblown claims of Freakonomics. It is, unfortunately, in the nature of popular books that they oversimplify and over-claim. Academic literature is supposed to be different: rigorous, cautious and, of course, peer-reviewed for accuracy.

Of course, if all those attributes really applied, a career like that of Levitt would have been impossible, since the econometric methodology he employs is far too weak to be able to produce with any credibility the kind of results Levitt is aiming at. It is clear, therefore, that within the community within which Levitt works, some standards of critical thought have been suspended. However, even when credulity is being stretched and poorly supported statements are taken as proven, one may still hope for the superficial ground rules to apply. Specifically, for example, one hopes that when previous research is cited and summarized the findings of the research are fairly represented.

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The term “censorship” describes the act of suppressing certain ideas by those who control some distribution channels. Despite regular attempts by interested parties to limit the term to describe very restricted or extreme cases of suppression of ideas, the term is usually, and very reasonably, understood to cover any attempt at reducing the circulation of an idea, by any person or organization. The negative view, which most of the population, as well as official ideology, take of censorship therefore encompasses any such activity. According to this view, the desirable media system is democratic – i.e., one which allows all people an equal opportunity at presenting their ideas and having them considered by others.

The implicit universal rejection of censorship notwithstanding, much of the communication patterns that dominate Western society are inherently censoring activities. The members of the elite group that influences (to varying degrees) the content of wide circulation media – publishers, broadcasters, advertisers, editors and reporters – routinely make decisions that amount to suppressing some communications, containing certain ideas, in favor of other communications, containing different ideas. Those decisions, although usually purporting to reflect only objective accepted standards, are in reality almost completely subjective. They therefore reflect the ideas and biases of the very select and atypical group of people who make them.

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Below is my page-by-page summary of Kuhn’s 1967 postscript to The Structure of Scientific Revolutions.

The following points seem to me to contain the essence of Kuhn’s thesis:

Exemplars:

  1. Exemplars (solved problems) are an important component of any specific scientific world-view. Without exemplars the laws and theories have little empirical content. The exemplars teach practitioners how to attach the relevant abstractions to elements of particular problems and how to see a variety of situations as being alike.
  2. The intuitive knowledge of which situations are alike is analyzable but not by specifying rules since it is perceptual rather than interpretive knowledge. It is similar to other knowledge of perception: e.g., identifying certain light patterns as all representing swans. Perceptual knowledge is selected for “success” – success in survival in the primitive case, success in puzzle solving in the scientific case.
  3. The situation may be similar in non-scientific schools (e.g., art).

Revolutions:

  1. Scientific revolutions – “a special sort of change in scientific thinking involving a certain sort of reconstruction of group commitments” – occur regularly on the smaller scale (within communities of dozens to hundreds).
  2. Crisis is the usual mechanism inducing revolutions. Crises supply a self-correcting mechanism which ensures that the rigidity of normal science will not forever go unchallenged.
  3. Judgments of scientific values – simplicity, consistency and compatibility – can vary greatly from individual to individual. Therefore, debates on theory-choice cannot be decided in a formal way. Still, those values constrain the dominant group view. This explains why competing world-views are rare in science but are common in other human activities.

Scientific progress:

  1. Because the commitment by scientists to puzzle-solving success shapes the long-term structure of scientific development (even if the application of this commitment in any particular case is ambiguous and subjective), scientific development, like biological development, is unidirectional and irreversible. When comparing scientific theories held by various scientific specialties to theories held by the specialty from which the former had their origins, “an uncommitted observer” would be able to consistently distinguish the newer theories from the older. The newer theories will enable more accurate, quantitative, predictions, in a wider variety of situations and they will be more esoteric. Differences in simplicity, scope and compatibility with other specialties are not as telling.
  2. Scientific progress is therefore well defined, but, like biological progress, it cannot be said that science comes closer and closer to a certain goal – “reality”. There is no objective reality which stands outside a specific scientific world-view.

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