A critical realist perspective on evidence-based policies

4 March, 2017 at 12:37 | Posted in Theory of Science & Methodology | Leave a comment


The logical fallacy that good science builds on

21 February, 2017 at 09:45 | Posted in Theory of Science & Methodology | Leave a comment

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

or, in instantiated form

(1) ∀x (Gx => Px)

(2) Pa

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 | Leave a comment

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 | Leave a comment


Probability calculus is no excuse for forgetfulness

28 December, 2016 at 14:16 | Posted in Theory of Science & Methodology | Leave a comment

When we cannot accept that the observations, along the time-series available to us, are independent, or cannot by some device be divided into groups that can be treated as independent, we get into much deeper water. For we have then, in strict logic, no more than one observation, all of the separate items having to be taken together. For the analysis of that the probability calculus is useless; it does not apply. We are left to use our judgement, making sense of what has happened as best we can, in the manner of the historian. Applied economics does then come back to history, after all.

hicksI am bold enough to conclude, from these considerations that the usefulness of ‘statistical’ or ‘stochastic’ methods in economics is a good deal less than is now conventionally supposed. We have no business to turn to them automatically; we should always ask ourselves, before we apply them, whether they are appropriate to the problem at hand. Very often they are not. Thus it is not at all sensible to take a small number of observations (sometimes no more than a dozen observations) and to use the rules of probability to deduce from them a ‘significant’ general law. For we are assuming, if we do so, that the variations from one to another of the observations are random, so that if we had a larger sample (as we do not) they would by some averaging tend to disappear. But what nonsense this is when the observations are derived, as not infrequently happens, from different countries, or localities, or industries — entities about which we may well have relevant information, but which we have deliberately decided, by our procedure, to ignore. By all means let us plot the points on a chart, and try to explain them; but it does not help in explaining them to suppress their names. The probability calculus is no excuse for forgetfulness.

John Hicks’ Causality in economics is an absolute masterpiece. It ought to be on the reading list of every course in economic methodology.

The search for heavy balls in economics

27 December, 2016 at 16:58 | Posted in Theory of Science & Methodology | 3 Comments

One of the limitations with economics is the restricted possibility to perform experiments, forcing it to mainly rely on observational studies for knowledge of real-world economies.

But still — the idea of performing laboratory experiments holds a firm grip of our wish to discover (causal) relationships between economic ‘variables.’ Galileo's falling bodies experimentIf we only could isolate and manipulate variables in controlled environments, we would probably find ourselves in a situation where we with greater ‘rigour’ and ‘precision’ could describe, predict, or explain economic happenings in terms of ‘structural’ causes, ‘parameter’ values of relevant variables, and economic ‘laws.’

Galileo Galilei’s experiments are often held as exemplary for how to perform experiments to learn something about the real world. Galileo’s experiments were according to Nancy Cartwright (Hunting Causes and Using Them, p. 223)

designed to find out what contribution the motion due to the pull of the earth will make, with the assumption that the contribution is stable across all the different kinds of situations falling bodies will get into … He eliminated (as far as possible) all other causes of motion on the bodies in his experiment so that he could see how they move when only the earth affects them. That is the contribution that the earth’s pull makes to their motion.

Galileo’s heavy balls dropping from the tower of Pisa, confirmed that the distance an object falls is proportional to the square of time, and that this law (empirical regularity) of falling bodies could be applicable outside a vacuum tube when e. g. air existence is negligible.

The big problem is to decide or find out exactly for which objects air resistance (and other potentially ‘confounding’ factors) is ‘negligible.’ In the case of heavy balls, air resistance is obviously negligible, but how about feathers or plastic bags?

One possibility is to take the all-encompassing-theory road and find out all about possible disturbing/confounding factors — not only air resistence — influencing the fall and build that in to one great model delivering accurate predictions on what happens when the object that falls is not only a heavy ball, but feathers and plastic bags. This usually amounts to ultimately state some kind of ceteris paribus interpretation of the ‘law.’

Another road to take would be to concentrate on the negligibility assumption and to specify the domain of applicability to be only heavy compact bodies. The price you have to pay for this is that (1) ‘negligibility’ may be hard to establish in open real-world systems, (2) the generalisation you can make from ‘sample’ to ‘population’ is heavily restricted, and (3) you actually have to use some ‘shoe leather’ and empirically try to find out how large is the ‘reach’ of the ‘law.’

In mainstream economics one has usually settled for the ‘theoretical’ road (and in case you think the present ‘natural experiments’ hype has changed anything, remember that to mimic real experiments, exceedingly stringent special conditions have to obtain).

In the end, it all boils down to one question — are there any heavy balls to be found in economics, so that we can indisputably establish the existence of economic laws operating in real-world economies?

As far as I can see there some heavy balls out there, but  not even one single  real economic law.

Economic factors/variables are more like feathers than heavy balls — non-negligible factors (like air resistance and chaotic turbulence) are hard to rule out as having no influence on the object studied.

Galilean experiments are hard to carry out in economics, and the theoretical ‘analogue’ models economists construct and in which they perform their ‘thought-experiments’ build on assumptions that are far away from the kind of idealized conditions under which Galileo performed his experiments. The ‘nomological machines’ that Galileo and other scientists have been able to construct, have no real analogues in economics. The stability, autonomy, modularity, and interventional invariance, that we may find between entities in nature, simply are not there in real-world economies. That’s are real-world fact, and contrary to the beliefs of most mainstream economists, they wont’t go away simply by applying deductive-axiomatic economic theory with tons of more or less unsubstantiated assumptions.

By this I do not mean to say that we have to discard all (causal) theories/laws building on modularity, stability, invariance, etc. But we have to acknowledge the fact that outside the systems that possibly fullfil these requirements/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 econometric problems of autonomy, identification, invariance and structural stability — 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. Setting up convenient circumstances for conducting Galilean experiments may tell us a lot about what happens under those kind 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..

To solve, understand, or explain real-world problems you actually have to know something about them – logic, pure mathematics, data simulations or deductive axiomatics don’t take you very far. Most econometrics and economic theories/models are splendid logic machines. But — applying them to the real-world is a totally hopeless undertaking! The assumptions one has to make in order to successfully apply these deductive-axiomatic theories/models/machines are devastatingly restrictive and mostly empirically untestable– and hence make their real-world scope ridiculously narrow. To fruitfully analyse real-world  phenomena with models and theories you cannot build on patently and known to be ridiculously absurd assumptions.

No matter how much you would like the world to entirely consist of heavy balls, the world is not like that. The world also has its fair share of feathers and plastic bags.

On analytical statistics and critical realism

22 December, 2016 at 12:17 | Posted in Theory of Science & Methodology | 1 Comment

24398683In this paper we began by describing the position of those critical realists who are sceptical about multi-variate statistics … Some underlying assumptions of this sceptical argument were shown to be false. Then a positive case in favour of using analytical statistics as part of a mixed-methods methodology was developed. An example of the interpretation of logistic regression was used to show that the interpretation need not be atomistic or reductionist. However, we also argued that the data underlying such interpretations are ‘ficts’, i.e. are not true in themselves, and cannot be considered to be accurate or true descriptions of reality. Instead, the validity of the interpretations of such data are what social scientists should argue about. Therefore what matters is how warranted arguments are built by the researcher who uses statistics. Our argument supports seeking surprising findings; being aware of the caveat that demi-regularities do not necessarily reveal laws; and otherwise following advice given from the ‘sceptical’ school. However the capacity of multi-variate statistics to provide a grounding for warranted arguments implies that their use cannot be rejected out of hand by serious social researchers.

Wendy Olsen & Jamie Morgan

Bayesianism — a dangerous superficiality

19 December, 2016 at 12:34 | Posted in Theory of Science & Methodology | 4 Comments

419fn8sv1fl-_sx332_bo1204203200_The bias toward the superficial and the response to extraneous influences on research are both examples of real harm done in contemporary social science by a roughly Bayesian paradigm of statistical inference as the epitome of empirical argument. For instance the dominant attitude toward the sources of black-white differential in United States unemployment rates (routinely the rates are in a two to one ratio) is “phenomenological.” The employment differences are traced to correlates in education, locale, occupational structure, and family background. The attitude toward further, underlying causes of those correlations is agnostic … Yet on reflection, common sense dictates that racist attitudes and institutional racism must play an important causal role. People do have beliefs that blacks are inferior in intelligence and morality, and they are surely influenced by these beliefs in hiring decisions … Thus, an overemphasis on Bayesian success in statistical inference discourages the elaboration of a type of account of racial disadavantages that almost certainly provides a large part of their explanation.

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.

wpid-bilindustriella-a86478514bOne of my favourite “problem situating lecture arguments” against Bayesianism goes something like this: Assume you’re a Bayesian turkey 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 …

For more on my own objections to Bayesianism:
Bayesianism — a patently absurd approach to science
Bayesianism — preposterous mumbo jumbo
One of the reasons I’m a Keynesian and not a Bayesian

Postmodern mumbo jumbo soup

24 November, 2016 at 12:11 | Posted in Theory of Science & Methodology | 2 Comments

MUMBO-JUMBO1The move from a structuralist account in which capital is understood to structure social relations in relatively homologous ways to a view of hegemony in which power relations are subject to repetition, convergence, and rearticulation brought the question of temporality into the thinking of structure, and marked a shift from a form of Althusserian theory that takes structural totalities as theoretical objects to one in which the insights into the contingent possibility of structure inaugurate a renewed conception of hegemony as bound up with the contingent sites and strategies of the rearticulation of power.

Judith Butler

Friedman’s methodological folly

19 November, 2016 at 10:59 | Posted in Theory of Science & Methodology | 2 Comments

milton_friedman_1Friedman enters this scene arguing that all we need to do is predict successfully, that this can be done even without realistic theories, and that unrealistic theories are to be preferred to realistic ones, essentially because they can usually be more parsimonious.

The first thing to note about this response is that Friedman is attempting to turn inevitable failure into a virtue. In the context of economic modelling, the need to produce formulations in terms of systems of isolated atoms, where these are not characteristic of social reality, means that unrealistic formulations are more or less unavoidable. Arguing that they are to be preferred to realistic ones in this context belies the fact that there is not a choice …

My own response to Friedman’s intervention is that it was mostly an irrelevancy, but one that has been opportunistically grasped by some as a supposed defence of the profusion of unrealistic assumptions in economics. This would work if successful prediction were possible. But usually it is not.

Tony Lawson

If scientific progress in economics – as Robert Lucas and other latter days followers of Milton Friedman seem to think – lies in our ability to tell ‘better and better stories’ one would of course expect economics journals being filled with articles supporting the stories with empirical evidence confirming the predictions. However, the journals still show a striking and embarrassing paucity of empirical studies that (try to) substantiate these predictive claims. Equally amazing is how little one has to say about the relationship between the model and real world target systems. It is as though explicit discussion, argumentation and justification on the subject isn’t considered to be required.

If the ultimate criterion of success of a model is to what extent it predicts and coheres with (parts of) reality, modern mainstream economics seems to be a hopeless misallocation of scientific resources. To focus scientific endeavours on proving things in models, is a gross misapprehension of what an economic theory ought to be about. Deductivist models and methods disconnected from reality are not relevant to predict, explain or understand real-world economies.

the-only-function-of-economic-forecasting-is-to-make-astrology-look-respectable-quote-1There can be no theory without assumptions since it is the assumptions embodied in a theory that provide, by way of reason and logic, the implications by which the subject matter of a scientific discipline can be understood and explained. These same assumptions provide, again, by way of reason and logic, the predictions that can be compared with empirical evidence to test the validity of a theory. It is a theory’s assumptions that are the premises in the logical arguments that give a theory’s explanations meaning, and to the extent those assumptions are false, the explanations the theory provides are meaningless no matter how logically powerful or mathematically sophisticated those explanations based on false assumptions may seem to be.

George Blackford

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