Beyond Bayesian probabilism

13 Jan, 2022 at 23:44 | Posted in Theory of Science & Methodology | 7 Comments

Although Bayes’ theorem is mathematically unquestionable, that doesn’t qualify it as indisputably applicable to scientific questions. Bayesian statistics is one thing, and Bayesian epistemology something else. Science is not reducible to betting, and scientific inference is not a branch of probability theory. It always transcends mathematics. The unfulfilled dream of constructing an inductive logic of probabilism — the Bayesian Holy Grail — will always remain unfulfilled.

Bayesian probability calculus is far from the automatic inference engine that its protagonists maintain it is. That probabilities may work for expressing uncertainty when we pick balls from an urn, does not automatically make it relevant for making inferences in science. Where do the priors come from? Wouldn’t it be better in science if we did some scientific experimentation and observation if we are uncertain, rather than starting to make calculations based on often vague and subjective personal beliefs? People have a lot of beliefs, and when they are plainly wrong, we shall not do any calculations whatsoever on them. We simply reject them. Is it, from an epistemological point of view, really credible to think that the Bayesian probability calculus makes it possible to somehow fully assess people’s subjective beliefs? And are — as many Bayesians maintain — all scientific controversies and disagreements really possible to explain in terms of differences in prior probabilities? I strongly doubt it.

unknown I want to know what my personal probability ought to be, partly because I want to behave sensibly and much more importantly because I am involved in the writing of a report which wants to be generally convincing. I come to the conclusion that my personal probability is of little interest to me and of no interest whatever to anyone else unless it is based on serious and so far as feasible explicit information. For example, how often have very broadly comparable laboratory studies been misleading as regards human health? How distant are the laboratory studies from a direct process affecting health? The issue is not to elicit how much weight I actually put on such considerations but how much I ought to put. Now of course in the personalistic  [Bayesian] approach having (good) information is better than having none but the point is that in my view the personalistic probability is virtually worthless for reasoned discussion​ unless it is based on information, often directly or indirectly of a broadly frequentist kind. The personalistic approach as usually presented is in danger of putting the cart before the horse.

David Cox

[Added 21.15: Those interested in these questions, do read Sander Greenland’s insightful comment.]

Bayesianism — the new positivism

12 Jan, 2022 at 23:21 | Posted in Theory of Science & Methodology | 6 Comments

Fact and Method: Miller, Richard W.: 9780691020457: Amazon.com: BooksNo matter how atheoretical their inclination, scientists are interested in relations between properties of phenomena, not in lists of readings from dials of instruments that detect those properties …

Here as elsewhere, Bayesian philosophy of science obscures a difference between scientists’ problems of hypothesis choice and the problems of prediction that are the standard illustrations and applications of probability theory. In the latter situations, such as the standard guessing games about coins and urns, investigators know an enormous amount about the reality they are examining, including the effects of different values of the unknown factor. Scientists can rarely take that much knowledge for granted. It should not be surprising if an apparatus developed to measure degrees of belief in situations of isolated and precisely regimented uncertainty turns out to be inaccurate, irrelevant or incoherent in the face of the latter, much more radical uncertainty.

For all scholars seriously interested in questions on what makes up a good scientific explanation, Richard Miller’s Fact and Method is a must read. His incisive critique of Bayesianism is still unsurpassed.

Given that we study processes that are adequately captured by our statistical models (think of urns, cards, coins, etc), Bayesian reasoning works. The problem, however, is that when we choose among scientific hypotheses, we standardly lack that kind of knowledge. As a consequence — as Miller puts it — “Bayesian inference to the preferred alternative has not resolved, even temporarily, a single fundamental scientific dispute.”

Assume you’re a Bayesian turkey/chicken and hold a nonzero probability belief in the hypothesis H that “people are nice vegetarians that do not eat turkeys/chickens and that every day I see the sun rise confirms my belief.” For every day you survive, you update your belief according to Bayes’ Rule

P(H|e) = [P(e|H)P(H)]/P(e),

where evidence e stands for “not being eaten” and P(e|H) = 1. Given that there do exist other hypotheses than H, P(e) is less than 1 and a fortiori P(H|e) is greater than P(H). Every day you survive increases your probability belief that you will not be eaten. This is totally rational according to the Bayesian definition of rationality. Unfortunately — as Bertrand Russell famously noticed — for every day that goes by, the traditional Christmas dinner also gets closer and closer …

Bayes and the ‘old evidence’ problem

10 Jan, 2022 at 23:32 | Posted in Theory of Science & Methodology | 1 Comment

Among the many achievements of Newton’s theory of gravitation was its prediction of the tides and their relation to the lunar orbit. Presumably the success of this prediction confirmed Newton’s theory, or in Bayesian terms, the observable facts about the tides e raised the probability of Newton’s theory h.

bayes-theorem - Rens van de SchootBut the Bayesian it turns out can make no such claim. Because the facts about the tides were already known when Newton’s theory was formulated, the probability for e was equal to one. It follows immediately that both C (e ) and C (e |h ) are equal to one (the latter for any choice of h ). But then the Bayesian multiplier is also one, so Newton’s theory does not receive any probability boost from its prediction of the tides. As either a description of actual scientific practice, or a prescription for ideal scientific practice, this is surely wrong.

The problem generalizes to any case of “old evidence”: If the evidence e is received before a hypothesis h is formulated then e is incapable of boosting the probability of h by way of conditionalization. As is often remarked, the problem of old evidence might just as well be called the problem of new theories, since there would be no difficulty if there were no new theories, that is, if all theories were on the table before the evidence began to arrive. Whatever you call it, the problem is now considered by most Bayesians to be in urgent need of a solution. A number of approaches have been suggested, none of them entirely satisfactory.

A recap of the problem: If a new theory is discovered midway through an inquiry, a prior must be assigned to that theory. You would think that, having assigned a prior on non-empirical grounds, you would then proceed to conditionalize on all the evidence received up until that point. But because old evidence has probability one, such conditionalization will have no effect. The Bayesian machinery is silent on the significance of the old evidence for the new theory.

Michael Strevens

The fatal flaw of mathematics

21 Nov, 2021 at 18:16 | Posted in Theory of Science & Methodology | 7 Comments

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Gödel’s incompleteness theorems raise important questions about the foundations of mathematics.

The most important concerns the question of how to select the specific systems of axioms that mathematics are supposed to be founded on. Gödel’s theorems irrevocably show that no matter what system is chosen, there will always have to be other axioms to prove previously unproved truths.

This, of course, ought to be of paramount interest for those mainstream economists who still adhere to the dream of constructing a deductive-axiomatic economics with analytic truths that do not require empirical verification. Since Gödel showed that any complex axiomatic system is undecidable and incomplete, any such deductive-axiomatic economics will always consist of some undecidable statements. When not even being able to fulfil the dream of a complete and consistent axiomatic foundation for mathematics, it’s totally incomprehensible that some people still think that could be achieved for economics.

Separating questions of logic and empirical validity may — of course — help economists to focus on producing rigorous and elegant mathematical theorems that people like Lucas and Sargent consider “progress in economic thinking.” To most other people, not being concerned with empirical evidence and model validation is a sign of social science becoming totally useless and irrelevant. Economic theories building on known to be ridiculously artificial assumptions without an explicit relationship with the real world is a dead end. That’s probably also the reason why general equilibrium analysis today (at least outside Chicago) is considered a total waste of time. In the trade-off between relevance and rigour, priority should always be on the former when it comes to social science. The only thing followers of the Bourbaki tradition within economics — like Karl Menger, John von Neumann, Gerard Debreu, Robert Lucas, and Thomas Sargent — has given us are irrelevant model abstractions with no bridges to real-world economies. It’s difficult to find a more poignant example of an intellectual resource waste in science.

Social mechanisms and inference to the best explanation

5 Nov, 2021 at 14:44 | Posted in Theory of Science & Methodology | 1 Comment

A Realist Philosophy of Social Science : Explanation and Understanding by  Peter T. Manicas (2006, Perfect) for sale online | eBayEpistemologically speaking, all theory is a representation of reality, an intellectual construct, and it is always abstract: it can never catch the full-bodied reality … But if we accept the theory, we accept that the generative mechanism is real. That is, not only could it have produced the outcome, but having ruled out alternative explanations, we believe that it did produce the outcome …

But we must resist an instrumentalist interpretation of social mechanisms, typical of mainstream economics … On this view, the assumptions of the mechanism need not be realistic at all. That is, not only need there be no real persons with all the attributes of the construction, but the assumptions can be contrary to facts known about them.

Peter Manicas is certainly right in emphasizing the need for non-instrumentalist interpretations of social mechanisms — but one could perhaps still wonder how we rule out “alternative explanations” and believe that the generative mechanism we have chosen really “did produce the outcome.”

In science we standardly use a logically non-valid inference — the fallacy of affirming the consequent — of the following form:

(1) p => q
(2) q
————-
p

or, in instantiated form

(1) ∀x (Gx => Px)

(2) Pa
————
Ga

Although logically invalid, it is nonetheless a kind of inference — abduction — that may be factually strongly warranted and truth-producing.

holmes-quotes-about-holmes

Following the general pattern ‘Evidence  =>  Explanation  =>  Inference’we infer something based on what would be the best explanation given the law-like rule (premise 1) and an observation (premise 2). The truth of the conclusion (explanation) is nothing that is logically given, but something we have to justify, argue for, and test in different ways to possibly establish with any certainty or degree. And as always when we deal with explanations, what is considered best is relative to what we know of the world. In the real world, all evidence is relational (e only counts as evidence in relation to a specific hypothesis H) and has an irreducible holistic aspect. We never conclude that evidence follows from a hypothesis simpliciter, but always given some more or less explicitly stated contextual background assumptions. All non-deductive inferences and explanations are necessarily context-dependent.

If we extend the abductive scheme to incorporate the demand that the explanation has to be the best among a set of plausible competing potential and satisfactory explanations, we have what is nowadays usually referred to as inference to the best explanation.

In inference to the best explanation we start with a body of (purported) data/facts/evidence and search for explanations that can account for these data/facts/evidence. Having the best explanation means that you, given the context-dependent background assumptions, have a satisfactory explanation that can explain the evidence better than any other competing explanation — and so it is reasonable to consider the hypothesis to be true. Even if we (inevitably) do not have deductive certainty, our reasoning gives us a license to consider our belief in the hypothesis as reasonable.

Accepting a hypothesis means that you believe it does explain the available evidence better than any other competing hypothesis. Knowing that we — after having earnestly considered and analysed the other available potential explanations — have been able to eliminate the competing potential explanations, warrants and enhances the confidence we have that our preferred explanation is the best explanation, i. e., the explanation that provides us (given it is true) with the greatest understanding.

This, of course, does not in any way mean that we cannot be wrong. Of course, we can. Inferences to the best explanation are fallible inferences — since the premises do not logically entail the conclusion — so from a logical point of view, inference to the best explanation is a weak mode of inference. But if the arguments put forward are strong enough, they can be warranted and give us justified true belief, and hence, knowledge, even though they are fallible inferences. As scientists we sometimes — much like Sherlock Holmes and other detectives that use inference to the best explanation reasoning — experience disillusion. We thought that we had reached a strong conclusion by ruling out the alternatives in the set of contrasting explanations. But — what we thought was true turned out to be false.

That does not necessarily mean that we had no good reasons for believing what we believed. If we cannot live with that contingency and uncertainty, well, then we are in the wrong business. If it is deductive certainty you are after, rather than the ampliative and defeasible reasoning in inference to the best explanation — well, then get into math or logic, not science.

The Münchhausen Trilemma

9 Oct, 2021 at 15:15 | Posted in Theory of Science & Methodology | 2 Comments

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The term ‘Münchhausen Trilemma’ is used in epistemology to stress the impossibility to prove any truth (even in logic and mathematics). The term was coined by Albert in 1968 in reference to Popper’s Trilemma of dogmatism vs. infinite regress vs. psychologism.

Is gender a social construct?

1 Oct, 2021 at 16:15 | Posted in Theory of Science & Methodology | 6 Comments

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Judith Butler’s theory of identity rests on the idea that there is nothing between the Scylla of the metaphysical ‘modernist’ subject and the Charybdis of the totally deconstructed identity where the subject becomes nothing but a fictitious fantasy. But this can’t be right. The social constructivist anti-essentialism is unsatisfactory and ends up in a idealist ‘slippery slope.’ Just shifting a biologically over-determined concept with a discursively over-determined  concept is not enough to make us understand or explain gender. Merely inverting a reduction and redescribing it do not re-make it. If social science is to have an emancipatory potential it has to go beyond a purely discursive level and get in touch with the structures and powers that operate in the world in which we live. From that critical realist perspective we can also see that there is a middle ground between Scylla and Charybdis where gender/sex/identity are something both biological and socially constructed.

Postmodernist flips

30 Sep, 2021 at 11:23 | Posted in Theory of Science & Methodology | 1 Comment

The Annual Equality Lecture with Professor Andrew Sayer - Social Science  blogI have argued against the postmodern tendency to flip from naive objectivism to relativism and idealism, from totalities to fragments, and from ethnocentrisms to new forms of self-contradictory cultural relativism. A realist approach shows us that we can escape from these alternatives. The Modernist project — and more specifically, critical social science — don’t need foundationalism or notions of absolute truth. They can be not only better understood but furthered through a critical realist interpretation. The new kinds of idealism and relativism that have infected postmodernist thought offer no support to critical social science, to anti-racism and feminism.

Let us update Hume’s taunts against idealism: we will see how idealists — all those who bracket out reality, who imagine that knowledge is purely a matter of rhetoric and power, those who want to throw out reference and representation along with any concept of truth — fare when the meeting is ended. Truth being apparently purely a matter of convention or power and purely internal to theory and nothing to do with representation of some external ‘reality’, it will of course be easy for the anti-realists to change the conventions and leave through (the so-called) solid walls rather than through the doors of realist orthodoxy. And to add a dash of Bachelard, we shall see the difference between the nocturnal philosophies of the idealists and their diurnal realism, when at the end of the meeting, they sheepishly leave by the door.

Andrew Sayer

Postmodern undecidability

29 Sep, 2021 at 13:26 | Posted in Theory of Science & Methodology | 1 Comment

Realism and Social Science: Amazon.co.uk: Sayer, Andrew: 9780761961246:  BooksFor the idealist, the fact that the Inuit have many words for snow while the bush people of the Kalahari desert have none is merely a function of their different languages and has nothing to do with any extra-discursive reality … However, those who claim that reality is a discursive construct don’t believe what they say, for their practice — for example avoiding extra-discursive dangers, such as oncoming cars — shows that they cannot make the world a slave to their discourses …

Part of the function of communicative action and associated material acts is to indicate which of those many possible meanings apply in a given situation. When we read a final demand for payment of our electricity bill and the accompanying threat of disconnection, we could play endless parlour games running through diverse constructions of what this text says, showing off our ability to construe it in imaginative ways. Never-theless, which of the many possible meanings is supposed to apply, is usually pretty clear; if it isn’t, it might register when the lights go out.

Facts and values — a critical realist perspective

25 Sep, 2021 at 15:58 | Posted in Theory of Science & Methodology | Comments Off on Facts and values — a critical realist perspective

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Revisiting Myrdal’s ‘solution’ to the problem of value-bias

24 Sep, 2021 at 10:22 | Posted in Theory of Science & Methodology | Comments Off on Revisiting Myrdal’s ‘solution’ to the problem of value-bias

Buy The Possibility of Naturalism: A philosophical critique of the  contemporary human sciences (Classical Texts in Critical Realism) Book  Online at Low Prices in India | The Possibility of Naturalism: A  philosophicalRecognition of the phenomena of rationalization and mystification as the effects of unconscious interference enables us to pinpoint the error in an influential ‘solution’ to the problem of ‘value-bias’, authorized inter alia by Myrdal. On this solution, recognizing that value-neutrality is impossible, all the social scientist needs to do is state his or her own value assumptions fully and explicitly at the beginning of some piece of work so as to put the reader (and possibly also the writer) on their guard. It is not difficult to see that this solution begs the question. For it presupposes that X knows what his or her values are; that is, it presupposes that s/he has the kind of knowledge about him- or herself that ex hypothesi, in virtue of unconscious interference, s/he cannot have about society. Now for X to have such knowledge about him- or herself, s/he would have had to become fully conscious of the formerly unconscious mode of interference, in which case a statement of value assumptions is unnecessary, because objectivity is now possible. Conversely, if X is not conscious of the (unconscious) mode of interference, then any statement of his or her (professed) value assumptions will be worthless. Moreover, one cannot say in general whether any such statement will be more or less misleading. (Thus consider, for instance, what often follows professions of the kind ‘I’m not prejudiced about . . .’ or ‘I’m a tolerant sort of person/true liberal/good democrat . . .’) Mutatis mutandis, similar considerations apply in the case of conscious and semi-conscious modes of interference: avowals are either unnecessary or potentially misleading.

Hume’s Fork

23 Sep, 2021 at 16:59 | Posted in Theory of Science & Methodology | 1 Comment

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How is a philosophy of science possible?

22 Sep, 2021 at 11:00 | Posted in Theory of Science & Methodology | 1 Comment

Amazon.in: Buy Possibility of Naturalism: v. 1: Philosophical Critique of  the Contemporary Human Sciences Book Online at Low Prices in India |  Possibility of Naturalism: v. 1: Philosophical Critique of the ContemporaryWhat is the relation between science and philosophy? Do they compete with one another or speak of different worlds? Neither position is acceptable …

Philosophy is distinguished by the kinds of considerations and arguments it employs. It does not consider a world apart from that of the various sciences. Rather it considers just that world, but from the standpoint of what can be established about it by a priori argument …

Philosophy, like science, produces knowledge. But it is knowledge of the necessary conditions for the production of knowledge — second-order knowledge, if you like. If philosophy is, as I believe it can be, a conceptual science, then like any science it ought to be able to tell us something we did not already know: it ought to be able to surprise us. For, as Marx astutely observed, ‘all science would be superfluous if the outward appearances and essences of things directly coincided.’

Critical realism — making sense of science

19 Sep, 2021 at 23:09 | Posted in Theory of Science & Methodology | 2 Comments

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Jacques Lacan — a severe case of obscurantism

17 Sep, 2021 at 12:48 | Posted in Theory of Science & Methodology | 12 Comments

This so-called crisis. It does not exist' - Jacques Lacan on Psychoanalysis  in 1974To lure the intended or preferred audience into accepting an assertion or set of assertions, the obscurantist should first of all convince the reader that there is indeed a deep and profound insight lurking underneath the surface of his prima facie incomprehensible statements. The obscurantist’s hope is to persuade the intended reader that the hidden treasure, the true meaning, is indeed so valu able and so revealing that he is willing to invest a huge hermeneutic effort in trying to understand whatever his hermeneutic efforts indicate as the “true meaning” of what Lacan says. As Lacan himself put it in a defiant mood: “L’écrit, ça n’est pas à comprendre. C’est bien pour ça que vous n’êtes pas forcés de comprendre les miens. Si vous ne les comprenez pas, tant mieux, ça vous donnera justement l’occasion de les expliquer” (Lacan, 1975, p. 35). What is in normal conversation extrinsic to understanding – acceptance of what is asserted – now triggers the desire to understand: “these pronouncements contain deep truths about myself that I must accept, so what he says must make sense.”

Filip Buekens & Maarten Boudry

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