## Why science necessarily involves a logical fallacy

13 February, 2016 at 17:32 | Posted in Theory of Science & Methodology | 5 Comments

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.

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 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.

1. […] of ways and it’s usually fun and insightful to do so. One of these was brought up in the post Why science necessarily involves a logical fallacy by Lars Syll. The idea is that if p implies q, and we observe q, then we intuitively take this as […]

2. I’ll give you a hard time on Inference to the Best Explanation.
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The love-hate relationship to deductive reasoning makes it hard to recognize its proper place in the scheme of scientific inquiry, as does the emphasis on “justifying” belief and the rough analogy between the syllogism and “abduction”, as if these were alternative approaches to knowledge.
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The critical meta-level premise of science is the presumption that the world is a logical place. We presume that there are ordered relationships — governed by logic — among the phenomena we can observe and that knowing about the logical ordering of those relationships increases our power to understand, navigate, manipulate, design and control our world, our environment.
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For the most part, we cannot observe directly those presumably logical relationships; in the nature of things, those relationships are not available for direct inspection. We must guess. In making a conjecture, we are well-advised to try to identify a logical mechanism that ties together what we can observe with what we cannot (or have not yet) observed. In devising a logical conjecture, we have available to discipline imagination the tools of logic or mathematics: we can propose concepts and try to work out the necessary and sufficient elements of a mechanism in a priori analysis.
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A successful conjecture of broad scope may prove to be a very powerful apparatus for the collective human mind, as it becomes a template for problem-solving in many specific circumstances and a means to codify the collection of facts. What exactly we admit to be a “successful” conjecture or conjectural paradigm — and especially why we admit “success” — is an issue for philosophers of science, epistemologists and methodologists, but before we outline those issues, I think it would be helpful to introduce some examples of allegedly successful scientific conjectures, so that there’s a common fund of denotation to guide the discussion.
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I’ll give one example here, though I will not explicate it in full: Little’s Law from queuing theory: L = λW. Cribbing the English language interpretation from Wikipedia: the average number of customers in a stable service system (say, teller service at a bank) L, is the effective arrival rate λ, times the average time that a customer spends in the system, W. It is a simple relationship; Little published a theorem (yes, a deductive argument!) showing that it was quite a robust relationship conceptually and it became the foundation of a more elaborate set of deductive arguments.
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It may be that you had in mind something like Little’s Law, when you wrote, p => q in the original post as the general form for the analogue of a major premise for an abductive “argument”. But, that general form as you wrote it comes across as post hoc, propter hoc, especially when you propose that abductive arguments, if posed as deductive arguments, would be deductive fallacies. It’s just confusing, I think.
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In a real, scientific inquiry, “p => q” isn’t a simple proposition; as in the case of Little’s Law or queuing theory, it is an analysis of mechanism offered as a conjecture. If it has any merit at all, it is a logically elaborated and vetted analysis, with some outline of logically necessary and sufficient factors. The “law-like” relationships identified in such analyses are not usually of the simplified form, effect follows cause.
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We only get the simplified form, effect follows cause in explanations, and that’s one of several good reasons to be suspicious of explanations as expressions of factual “truth” let alone as fertile grounds for growing truth. Explanations simplify analysis into effect follows cause, which may or may not be appropriate in generalizing a factual case, because in constructing explanations, we filter them thru our story-telling instinct for narrative, where one thing follows another. Consequently, explanations tend to be oversimplified and misleading, both because they encourage us to flatten systemic relationships into effect follows cause, and because in filtering explanations through our story-telling instinct, we tend to add moral intent and meanings to smooth over the gaps. It is very easy to shade into alcemy or astrology, to start reasoning about bodily humours and other nonsense to give an explanation at least the form of a good narrative. But, the form of a good narrative without identifying a logical mechanism is religion or hypnosis, not science.
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The idea that scientific inquiry into the factual nature of reality follows a form analogous to, or alternative to, deductive argument mistakes the place of both logic and inquiry.
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Logical analysis never describes reality, so it never yields, on its own mere motion, grounds for believing any alleged and specific fact. The fallacy is thinking analysis is ever sufficient to justify factual belief.
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On the other hand, direct observation, by itself, never reveals the logical relationships of nature (or society’s) mechanisms. We cannot observe cause-and-effect. We can conjecture by means of a priori analysis, and a good conjecture may be very powerful. And, not incidentally, generate some good explanations. So, logical analysis is necessary but insufficient for developing factually descriptive explanations, if you like.
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The feedback loop, where the experience of measurement and disciplined observation, leads the scientist to question the adequacy of an analytic theory, I will leave to another day.

3. I do not understand this post. You start out with this (incorrect) claim:
“In science we standardly use a logically non-valid inference — the fallacy of affirming the consequent”

Then you go on to (correctly) explain that in science functions by reaching “a strong conclusion by ruling out the alternatives in the set of contrasting explanations”, and that we choose to work with ” a satisfactory explanation that can explain the fact/evidence better than any other competing explanation”.

This is not affirming the consequent. It is Modus tollens and Bayesian reasoning. Explanations are ruled out for being inconsistent with the evidence. Or if the evidence is consistent with the theory, we assess the probability of the theory given the evidence (which according to Bayes’ rule depends on the probability of the evidence given all the other theories). It isn’t really a matter of a theory being true, just the most probable.

4. Success is the best method
Comment on ‘Why science necessarily involves a logical fallacy’
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When economists, who after more than 200 years have not figured out what exactly the difference between profit and income is, talk about logic things become a bit surreal.
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One outstanding characteristic of Heterodoxy in particular is that deductivism or the axiomatic-deductive method is abhorred. Consequently, other methods are proposed. One among others is abduction.
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This, to be sure, is perfectly legitimate. The question is this: if the abductive method is indeed superior, why not apply it and present concrete results? Success is the best argument. To recall, it were the discoveries of Galileo, Newton or Einstein which cemented the reputation of the axiomatic-deductive method. This method sums up the personal experience of genuine scientists and postulates the primacy of theory over naive empiricism: “This indicates that any attempt logically to derive the basic concepts and laws of mechanics from the ultimate data of experience is doomed to failure.” (Einstein, 1934, p. 166)
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It is a remarkable coincidence that Einstein deduced gravity waves from his theory in 1916 and in our days, 100 years later, they are observed. This success is a fine specimen for the primacy of theory and a smashing refutation of naive empiricism.
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In marked contrast, abduction postulates the primacy of empiricism: “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.” (See intro)
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Now, the fundamental problem is that this may even work satisfactorily on a small scale, but the subject matter of economics is the economy, or more precisely, the world economy. Clearly, the world economy as such cannot be seen or experienced, so there is no other way than to start with a theoretical picture as a first approximation. And this is exactly what Popper has said “And in the social sciences it is even more obvious than in the natural sciences that we cannot see and observe our objects before we have thought about them. For most of the objects of social science, if not all of them, are abstract objects; they are theoretical constructions.” (1960, p. 135)
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Here again we have the primacy of theory. Popper, of course, was not the first to realize this, he got it from an economist: “Since, therefore, it is vain to hope that truth can be arrived at, either in Political Economy or in any other department of the social science, while we look at the facts in the concrete, clothed in all the complexity with which nature has surrounded them, and endeavour to elicit a general law by a process of induction from a comparison of details; there remains no other method than the à priori one, or that of ‘abstract speculation’.” (Mill, 1874, V.55)
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Like nothing else, ‘abstract speculation’ puts the heterodox economist’s teeth on edge. The horror association is the absolutely vacuous formal exercise of general equilibrium theory. This green cheese nonentity, though, is clearly NOT what Mill had in mind when he spoke of ‘abstract speculation’. For him facts had always the last word “The ground of confidence in any concrete deductive science is not the à priori reasoning itself, but the accordance between its results and those of observation à posteriori.” (Mill, 2006, p. 896-897)
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The axiomatic-deductive method implies that the ultimate criterion for the assessment of a theory is empirical proof/refutation. The methodological blunder of standard economics has never been ‘abstract speculation’ but ‘empirically vacuous speculation’ of the type how-many angels-can-dance-on-a-pinpoint.
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The axiomatic-deductive method was never meant to be a fact-free logical exercise. It was Debreu who pushed it down this blind alley. It is fully justified to reject Debreu’s misapplication, but this gives one no good reason to relinquish the method.
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So there is no real need to invent a new method for economics. The scientific method is well-defined and applies here as well “Research is in fact a continuous discussion of the consistency of theories: formal consistency insofar as the discussion relates to the logical cohesion of what is asserted in joint theories; material consistency insofar as the agreement of observations with theories is concerned.” (Klant, 1994, p. 31)
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Logical consistency is secured by applying the axiomatic-deductive method and empirical consistency is secured by applying state-of-the-art testing.
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Economics never rose above logically and empirically inconsistent speculation.
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Egmont Kakarot-Handtke
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References
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science,
1(2): 163–169. URL http://www.jstor.org/stable/184387.
Klant, J. J. (1994). The Nature of Economic Thought. Aldershot, Brookfield, VT:
Edward Elgar.
Mill, J. S. (1874). Essays on Some Unsettled Questions of Political Economy. On
the Definition of Political Economy; and on the Method of Investigation Proper
To It. Library of Economics and Liberty. URL http://www.econlib.org/library/
Mill/mlUQP5.html#EssayV.OntheDefinitionofPoliticalEconomy.
Mill, J. S. (2006). A System of Logic Ratiocinative and Inductive. Being a Connected
View of the Principles of Evidence and the Methods of Scientific Investigation,
volume 8 of Collected Works of John Stuart Mill. Indianapolis, IN: Liberty Fund.
Popper, K. R. (1960). The Poverty of Historicism. London, Henley: Routledge and
Kegan Paul.

5. Lars, I disagree. But I do think that science, as commonly conceived by X, involves a logical fallacy. I’m not sure how large X is, but it does seem to be much too large, and possibly a majority, including politicians, social scientists and most scientists with mouths to feed. I say a bit more in commenting on the Bayesian Philosophy blog, above, and a lot more on my own blog. But I think an important task for academics is to make clear the difference between proper science and pseudo-science.