The raven paradox

4 July, 2017 at 19:03 | Posted in Theory of Science & Methodology | 2 Comments

 

Besides illustrating that it is simply not a good description of how we make inferences in science to assume that non-black armchairs confirm the hypothesis that all ravens are black, Hempel’s paradox — at least in my reading of it — makes a good argument for a causal account of confirmation of empirical generalizations. Contrary to positivist theories of confirmation, the paradox shows that to have a good explanation in sciences, we have to make references to causes. Observed uniformity does not per se confirm generalizations. We also have to be able to show that uniformity does not appear by chance, but is the result of causal forces at work (such as e.g. genes in the case of ravens.

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 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 …

Studying only surface relations won’t do. Not knowing the nature of the causal structures and relations that give rise to what we observe, explanations serve us as badly as the one used by the turkey. Not knowing why things are the way they are, we run the same risk as the Russellian turkey.

No causality, no confirmation/explanation.

What kind of realist am I?

14 June, 2017 at 17:51 | Posted in Theory of Science & Methodology | 1 Comment

Some commentators on this blog seem to be of the opinion that since yours truly is critical of mainstream economics and ask for more relevance and realism I’m bound to be a “naive” realist or empiricist.

Nothing could be further from the truth!

bhaskarIn a time when scientific relativism is expanding, it is important to keep up the claim for not reducing science to a pure discursive level. We have to maintain the Enlightenment tradition of thinking of reality as principally independent of our views of it and of the main task of science as studying the structure of this reality. Perhaps the most important contribution a researcher can make is reveal what this reality that is the object of science actually looks like.

Science is made possible by the fact that there are structures that are durable and are independent of our knowledge or beliefs about them. There exists a reality beyond our theories and concepts of it. It is this independent reality that our theories in some way deal with. Contrary to positivism, I cannot see that the main task of science is to detect event-regularities between observed facts. Rather, the task must be conceived as identifying the underlying structure and forces that produce the observed events.

The problem with positivist social science is not that it gives the wrong answers, but rather that in a strict sense it does not give answers at all. Its explanatory models presuppose that the social reality is ‘closed,’ and since social reality is fundamentally ‘open,’ models of that kind cannot explain anything of what happens in such a universe. Positivist social science has to postulate closed conditions to make its models operational and then – totally unrealistically – impute these closed conditions to society’s real structure.

In the face of the kind of methodological individualism and rational choice theory that dominate positivist social science we have to admit that even if knowing the aspirations and intentions of individuals are necessary prerequisites for giving explanations of social events, they are far from sufficient. Even the most elementary ‘rational’ actions in society presuppose the existence of social forms that it is not possible to reduce to the intentions of individuals.

archerThe overarching flaw with methodological individualism and rational choice theory is basically that they reduce social explanations to purportedly individual characteristics. But many of the characteristics and actions of the individual originate in and are made possible only through society and its relations. Society is not reducible to individuals, since the social characteristics, forces, and actions of the individual are determined by pre-existing social structures and positions. Even though society is not a volitional individual, and the individual is not an entity given outside of society, the individual (actor) and the society (structure) have to be kept analytically distinct. They are tied together through the individual’s reproduction and transformation of already given social structures.

What makes knowledge in social sciences possible is the fact that society consists of social structures and positions that influence the individuals of society, partly through their being the necessary prerequisite for the actions of individuals but also because they dispose individuals to act (within a given structure) in a certain way. These structures constitute the ‘deep structure’ of society.

Our observations and theories are concept-dependent without therefore necessarily being concept-determined. There is a reality existing independently of our knowledge and theories of it. Although we cannot apprehend it without using our concepts and theories, these are not the same as reality itself. Reality and our concepts of it are not identical. Social science is made possible by existing structures and relations in society that are continually reproduced and transformed by different actors.

Explanations and predictions of social phenomena require theory constructions. Just looking for correlations between events is not enough. One has to get under the surface and see the deeper underlying structures and mechanisms that essentially constitute the social system.

The basic question one has to pose when studying social relations and events is what are the fundamental relations without which they would cease to exist. The answer will point to causal mechanisms and tendencies that act in the concrete contexts we study. Whether these mechanisms are activated and what effects they will have in that case it is not possible to predict, since these depend on accidental and variable relations. Every social phenomenon is determined by a host of both necessary and contingent relations, and it is impossible in practice to have complete knowledge of these constantly changing relations. That is also why we can never confidently predict them. What we can do, through learning about the mechanisms of the structures of society, is to identify the driving forces behind them, thereby making it possible to indicate the direction in which things tend to develop.

The world itself should never be conflated with the knowledge we have of it. Science can only produce meaningful, relevant and realist knowledge if it acknowledges its dependence of  the world out there. Ultimately that also means that the critique yours truly wages against mainstream economics is that it doesn’t take that ontological requirement seriously.

Economic modeling — a realist perspective

28 May, 2017 at 13:37 | Posted in Theory of Science & Methodology | Comments Off on Economic modeling — a realist perspective

411WDSW5BRL._SX331_BO1,204,203,200_To his credit Keynes was not, in contrast to Samuelson, a formalist who was committed to mathematical economics. Keynes wanted models, but for him, building them required ‘ a vigilant observation of the actual working of our system.’ Indeed, ‘to convert a model into a quantitative formula is to destroy its usefulness as an instrument of thought.’ That conclusion can be strongly endorsed!

Modern economics has become increasingly irrelevant to the understanding of the real world. The main reason for this irrelevance is the failure of economists to match their deductive-axiomatic methods with their subject.

In mainstream neoclassical economics internal validity is almost everything and external validity next to nothing. Why anyone should be interested in that kind of theories and models is beyond yours truly’s imagination. As long as mainstream economists do not come up with export licenses for their theories and models to the real world in which we live, they really should not be surprised if people say that this is not science, but autism.

Studying mathematics and logics is interesting and fun. It sharpens the mind. In pure mathematics and logics we do not have to worry about external validity. But economics is not pure mathematics or logics. It’s about society. The real world. Forgetting that, economics is really in danger of becoming — as John Maynard Keynes put it in a letter to Ragnar Frisch in 1935 — “nothing better than a contraption proceeding from premises which are not stated with precision to conclusions which have no clear application.”

Why diversity trumps ability

12 May, 2017 at 08:40 | Posted in Economics, Theory of Science & Methodology | 1 Comment

 

Logical fallacies — the case of Donald Trump

8 May, 2017 at 09:08 | Posted in Theory of Science & Methodology | Comments Off on Logical fallacies — the case of Donald Trump

 

How the laws of physics lie

28 April, 2017 at 21:01 | Posted in Theory of Science & Methodology | 10 Comments

fmaill

Melvyn Bragg and guests — Nancy Cartwright, Mark Buchanan and Frank Close — discuss if there are any Laws of Nature. And if so — are they really ‘facts of life’?

A critical realist perspective on evidence-based policies

4 March, 2017 at 12:37 | Posted in Theory of Science & Methodology | Comments Off on A critical realist perspective on evidence-based policies

 

The logical fallacy that good science builds on

21 February, 2017 at 09:45 | Posted in Theory of Science & Methodology | Comments Off on The logical fallacy that good science builds on

In economics most models and theories build on a kind of argumentation pattern that looks like this:

Premise 1: All Chicago economists believe in REH
Premise 2: Robert Lucas is a Chicago economist
—————————————————————–
Conclusion: Robert Lucas believes in REH

Among philosophers of science this is treated as an example of a logically valid deductive inference (and, following Quine, whenever logic is used in this post, ‘logic’ refers to deductive/analytical logic).

In a hypothetico-deductive reasoning we would use the conclusion to test the law-like hypothesis in premise 1 (according to the hypothetico-deductive model, a hypothesis is confirmed by evidence if the evidence is deducible from the hypothesis). If Robert Lucas does not believe in REH we have gained some warranted reason for non-acceptance of the hypothesis (an obvious shortcoming here being that further information beyond that given in the explicit premises might have given another conclusion).

The hypothetico-deductive method (in case we treat the hypothesis as absolutely sure/true, we rather talk of an axiomatic-deductive method) basically means that we

•Posit a hypothesis
•Infer empirically testable propositions (consequences) from it
•Test the propositions through observation or experiment
•Depending on the testing results either find the hypothesis corroborated or falsified.

However, in science we regularly use a kind of ‘practical’ argumentation where there is little room for applying the restricted logical ‘formal transformations’ view of validity and inference. Most people would probably accept the following argument as a ‘valid’ reasoning even though it from a strictly logical point of view is non-valid:

Premise 1: Robert Lucas is a Chicago economist
Premise 2: The recorded proportion of Keynesian Chicago economists is zero
————————————————————————–
Conclusion: So, certainly, Robert Lucas is not a Keynesian economist

How come? Well I guess one reason is that in science, contrary to what you find in most logic text-books, not very many argumentations are settled by showing that ‘All Xs are Ys.’ In scientific practice we instead present other-than-analytical explicit warrants and backings — data, experience, evidence, theories, models — for our inferences. As long as we can show that our ‘deductions’ or ‘inferences’ are justifiable and have well-backed warrants our colleagues listen to us. That our scientific ‘deductions’ or ‘inferences’ are logical non-entailments simply is not a problem. To think otherwise is committing the fallacy of misapplying formal-analytical logic categories to areas where they are pretty much irrelevant or simply beside the point.

Scientific arguments are not analytical arguments, where validity is solely a question of formal properties. Scientific arguments are substantial arguments. If Robert Lucas is a Keynesian or not, is nothing we can decide on formal properties of statements/propositions. We have to check out what the guy has actually been writing and saying to check if the hypothesis that he is a Keynesian is true or not.

Deductive logic may work well — given that it is used in deterministic closed models! In mathematics, the deductive-axiomatic method has worked just fine. But science is not mathematics. Conflating those two domains of knowledge has been one of the most fundamental mistakes made in modern economics.  Applying it to real-world open systems immediately proves it to be excessively narrow and hopelessly irrelevant. Both the confirmatory and explanatory ilk of hypothetico-deductive reasoning fails since there is no way you can relevantly analyze confirmation or explanation as a purely logical relation between hypothesis and evidence or between law-like rules and explananda. In science we argue and try to substantiate our beliefs and hypotheses with reliable evidence — propositional and predicate deductive logic, on the other hand, is not about reliability, but the validity of the conclusions given that the premises are true.

Deduction — and the inferences that goes with it — is an example of ‘explicative reasoning,’  where the conclusions we make are already included in the premises. Deductive inferences are purely analytical and it is this truth-preserving nature of deduction that makes it different from all other kinds of reasoning. But it is also its limitation, since truth in the deductive context does not refer to  a real world ontology (only relating propositions as true or false within a formal-logic system) and as an argument scheme is totally non-ampliative — the output of the analysis is nothing else than the input.

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 strongly warranted and truth-producing.

64800990Following 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 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 a fortiori 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/rival/contrasting 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 fact/evidence better than any other competing explanation — and so it is reasonable to consider/believe 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 in to math or logic, not science.

For realists, the name of the scientific game is explaining phenomena … Realists typically invoke ‘inference to the best explanation’ or IBE … What exactly is the inference in IBE, what are the premises, and what the conclusion? …

It is reasonable to believe that the best available explanation of any fact is true.
F is a fact.
Hypothesis H explains F.
No available competing hypothesis explains F as well as H does.
Therefore, it is reasonable to believe that H is true.

This scheme is valid and instances of it might well be sound. Inferences of this kind are employed in the common affairs of life, in detective stories, and in the sciences …

alan musgravePeople object that the best available explanation might be false. Quite so – and so what? It goes without saying that any explanation might be false, in the sense that it is not necessarily true. It is absurd to suppose that the only things we can reasonably believe are necessary truths …

People object that being the best available explanation of a fact does not prove something to be true or even probable. Quite so – and again, so what? The explanationist principle – “It is reasonable to believe that the best available explanation of any fact is true” – means that it is reasonable to believe or think true things that have not been shown to be true or probable, more likely true than not.

Alan Musgrave

The best advice you will get this year

1 January, 2017 at 17:16 | Posted in Theory of Science & Methodology | Comments Off on The best advice you will get this year

huntingGetting it right about the causal structure of a real system in front of us is often a matter of great importance. It is not appropriate to offer the authority of formalism over serious consideration of what are the best assumptions to make about the structure at hand …

Where we don’t know, we don’t know. When we have to proceed with little information we should make the best evaluation we can for the case at hand — and hedge our bets heavily; we should not proceed with false confidence having plumped either for or against some specific hypothesis … for how the given system works when we really have no idea.

Trying to get around this lack of knowledge, mainstream economists in their quest for deductive certainty in their models, standardly assume things like ‘independence,’ ‘linearity,’ ‘additivity,’ ‘stability,’ ‘manipulability,’ ‘variation free variables,’ ‘faithfulness,’ ‘invariance,’ ‘implementation neutrality,’ ‘superexogeneity,’ etc., etc.

This can’t be the right way to tackle real-world problems. If those conditions do not hold, almost everything in those models is lost. The price paid for deductively is an exceedingly narrow scope. By this I do not mean to say that we have to discard all (causal) theories/laws building on ‘stability,’ ‘invariance,’ etc. But we have to acknowledge the fact that outside the systems that possibly fullfil these assumptions, they are of little substantial value. Running paper and pen experiments on artificial ‘analogue’ model economies is a sure way of ‘establishing’ (causal) economic laws or solving intricate problems  — in the model-world. But they are pure substitutes for the real thing and they don’t have much bearing on what goes on in real-world open social systems. Deductive systems are powerful. But one single false premise and all power is gone. Setting up convenient circumstances for conducting thought-experiments may tell us a lot about what happens under those kinds of circumstances. But — few, if any, real-world social systems are ‘convenient.’ So most of those systems, theories and models, are irrelevant for letting us know what we really want to know.

Limiting model assumptions in economic science always have to be closely examined. The results we get in models are only as sure as the assumptions on which they build — and if the economist doesn’t give any guidance on how to apply his models to real-world systems he doesn’t deserve our attention. Of course one can always say — as James Heckman — that it is relatively straightforward to define causality “when the causes can be independently varied.” But what good does that do when we know for a fact that real-world causes almost never can be independently varied?

Building models can’t be a goal in itself. Good models are means that makes it possible for us to infer things about the real-world systems they ‘represent.’ If we can’t show that the mechanisms or causes that we isolate and handle in our models are ‘exportable’ to the real-world, they are of limited value to our understanding, explanations or predictions of real economic systems.

The kind of fundamental assumption about the character of material laws, on which scientists appear commonly to act, seems to me to be much less simple than the bare principle of uniformity. They appear to assume something much more like what mathematicians call the principle of the superposition of small effects, or, as I prefer to call it, in this connection, the atomic character of natural law. 3The system of the material universe must consist, if this kind of assumption is warranted, of bodies which we may term (without any implication as to their size being conveyed thereby) legal atoms, such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state. We do not have an invariable relation between particular bodies, but nevertheless each has on the others its own separate and invariable effect, which does not change with changing circumstances, although, of course, the total effect may be changed to almost any extent if all the other accompanying causes are different. Each atom can, according to this theory, be treated as a separate cause and does not enter into different organic combinations in each of which it is regulated by different laws …

The scientist wishes, in fact, to assume that the occurrence of a phenomenon which has appeared as part of a more complex phenomenon, may be some reason for expecting it to be associated on another occasion with part of the same complex. Yet if different wholes were subject to laws qua wholes and not simply on account of and in proportion to the differences of their parts, knowledge of a part could not lead, it would seem, even to presumptive or probable knowledge as to its association with other parts. Given, on the other hand, a number of legally atomic units and the laws connecting them, it would be possible to deduce their effects pro tanto without an exhaustive knowledge of all the coexisting circumstances.

Real-world social systems are usually not governed by stable causal mechanisms or capacities. The kinds of ‘laws’ and relations that e. g. econometrics has established, are laws and relations about entities in models that presuppose causal mechanisms being invariant and atomistic. But — when causal mechanisms operate in the real world they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. If economic regularities obtain they do it as a rule only because we engineered them for that purpose. Outside man-made ‘nomological machines’ they are rare, or even non-existant.

Since there is no absolutely certain knowledge at hand in social sciences — including economics — explicit argumentation and justification ought to play an extremely important role if the purported knowledge claims are to be sustainably warranted. Without careful supporting arguments, building ‘convenient’ analogue models of real-world phenomena accomplishes absolutely nothing.

So we better follow Cartwright’s advice:

Where we don’t know, we don’t know. When we have to proceed with little information we should make the best evaluation we can for the case at hand — and hedge our bets heavily.

Observational studies vs. RCTs

29 December, 2016 at 14:12 | Posted in Theory of Science & Methodology | Comments Off on Observational studies vs. RCTs

 

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