The essence​ of scientific reasoning​

5 August, 2018 at 11:02 | Posted in Theory of Science & Methodology | Leave a comment

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-holmesFollowing 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 (evidence only counts as evidence in relation to a specific hypothesis) 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.

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Allt — och lite till — du vill veta om kausalitet

12 July, 2018 at 18:00 | Posted in Theory of Science & Methodology | 1 Comment

KAUSALITETRolf Sandahls och Gustav Jakob Peterssons Kausalitet: i filosofi, politik och utvärdering är en synnerligen välskriven och läsvärd genomgång av de mest inflytelserika teorierna om kausalitet som används inom vetenskapen idag.

Tag och läs!

I den positivistiska (hypotetisk-deduktiva, deduktiv-nomologiska) förklaringsmodellen avser man med förklaring en underordning eller härledning av specifika fenomen ur universella lagbundenheter. Att förklara en företeelse (explanandum) är detsamma som att deducera fram en beskrivning av den från en uppsättning premisser och universella lagar av typen ”Om A, så B” (explanans). Att förklara innebär helt enkelt att kunna inordna något under en bestämd lagmässighet och ansatsen kallas därför också ibland ”covering law-modellen”. Men teorierna ska inte användas till att förklara specifika enskilda fenomen utan för att förklara de universella lagbundenheterna som ingår i en hypotetisk-deduktiv förklaring. Den positivistiska förklaringsmodellen finns också i en svagare variant. Det är den probabilistiska förklaringsvarianten, enligt vilken att förklara i princip innebär att visa att sannolikheten för en händelse B är mycket stor om händelse A inträffar. I samhällsvetenskaper dominerar denna variant. Ur metodologisk synpunkt gör denna probabilistiska relativisering av den positivistiska förklaringsansatsen ingen större skillnad.

Den ursprungliga tanken bakom den positivistiska förklaringsmodellen var att den skulle (1) ge ett fullständigt klargörande av vad en förklaring är och visa att en förklaring som inte uppfyllde dess krav i själva verket var en pseudoförklaring, (2) ge en metod för testning av förklaringar, och (3) visa att förklaringar i enlighet med modellen var vetenskapens mål. Man kan uppenbarligen på goda grunder ifrågasätta alla anspråken.

En viktig anledning till att denna modell fått sånt genomslag i vetenskapen är att den gav sken av att kunna förklara saker utan att behöva använda ”metafysiska” kausalbegrepp. Många vetenskapsmän ser kausalitet som ett problematiskt begrepp, som man helst ska undvika att använda. Det ska räcka med enkla, observerbara storheter. Problemet är bara att angivandet av dessa storheter och deras eventuella korrelationer inte förklarar något alls. Att fackföreningsrepresentanter ofta uppträder i grå kavajer och arbetsgivarrepresentanter i kritstrecksrandiga kostymer förklarar inte varför ungdomsarbetslösheten i Sverige är så hög idag. Vad som saknas i dessa ”förklaringar” är den nödvändiga adekvans, relevans och det kausala djup varförutan vetenskap riskerar att bli tom science fiction och modellek för lekens egen skull.

Många samhällsvetare tycks vara övertygade om att forskning för att räknas som vetenskap måste tillämpa någon variant av hypotetisk-deduktiv metod. Ur verklighetens komplicerade vimmel av fakta och händelser ska man vaska fram några gemensamma lagbundna korrelationer som kan fungera som förklaringar. Inom delar av samhällsvetenskapen har denna strävan att kunna reducera förklaringar av de samhälleliga fenomen till några få generella principer eller lagar varit en viktig drivkraft. Med hjälp av några få generella antaganden vill man förklara vad hela det makrofenomen som vi kallar ett samhälle utgör. Tyvärr ger man inga riktigt hållbara argument för varför det faktum att en teori kan förklara olika fenomen på ett enhetligt sätt skulle vara ett avgörande skäl för att acceptera eller föredra den. Enhetlighet och adekvans är inte liktydigt.

Hard and soft science — a flawed dichotomy

11 July, 2018 at 19:08 | Posted in Theory of Science & Methodology | 1 Comment

The distinctions between hard and soft sciences are part of our culture … But the important distinction is really not between the hard and the soft sciences. Rather, it is between the hard and the easy sciences. Easy-to-do science is what those in physics, chemistry, geology, and some other fields do. Hard-to-do science is what the social scientists do and, in particular, it is what we educational researchers do. In my estimation, we have the hardest-to-do science of them all! We do our science under conditions that physical scientists find intolerable. We face particular problems and must deal with local conditions that limit generalizations and theory building-problems that are different from those faced by the easier-to-do sciences …

Context-MAtters_Blog_Chip_180321_093400Huge context effects cause scientists great trouble in trying to understand school life … A science that must always be sure the myriad particulars are well understood is harder to build than a science that can focus on the regularities of nature across contexts …

Doing science and implementing scientific findings are so difficult in education because humans in schools are embedded in complex and changing networks of social interaction. The participants in those networks have variable power to affect each other from day to day, and the ordinary events of life (a sick child, a messy divorce, a passionate love affair, migraine headaches, hot flashes, a birthday party, alcohol abuse, a new principal, a new child in the classroom, rain that keeps the children from a recess outside the school building) all affect doing science in school settings by limiting the generalizability of educational research findings. Compared to designing bridges and circuits or splitting either atoms or genes, the science to help change schools and classrooms is harder to do because context cannot be controlled.

David Berliner

Amen!

When applying deductivist thinking to economics, mainstream economists set up their easy-to-do  ‘as if’ models based on a set of tight axiomatic assumptions from which consistent and precise inferences are made. The beauty of this procedure is, of course, that if the axiomatic premises are true, the conclusions necessarily follow. The snag is that if the models are to be real-world relevant, we also have to argue that their precision and rigour still holds when they are applied to real-world situations. They often do not, and one of the main reasons for that is that context matters. When addressing real-world systems, the idealizations and abstractions necessary for the deductivist machinery to work simply do not hold.

If the real world is fuzzy, vague and indeterminate, then why should our models build upon a desire to describe it as precise and predictable? The logic of idealization is a marvellous tool in an easy-to-do science like physics, but a poor guide for action in real-world systems in which concepts and entities are without clear boundaries and continually interact and overlap.

Uncertainty heuristics

27 June, 2018 at 09:56 | Posted in Theory of Science & Methodology | Leave a comment

 

Is 0.999… = 1?

1 June, 2018 at 09:11 | Posted in Theory of Science & Methodology | 5 Comments

What is 0.999 …, really? Is it 1? Or is it some number infinitesimally less than 1?

The right answer is to unmask the question. What is 0.999 …, really? It appears to refer to a kind of sum:

.9 + + 0.09 + 0.009 + 0.0009 + …

9781594205224M1401819961But what does that mean? That pesky ellipsis is the real problem. There can be no controversy about what it means to add up two, or three, or a hundred numbers. But infinitely many? That’s a different story. In the real world, you can never have infinitely many heaps. What’s the numerical value of an infinite sum? It doesn’t have one — until we give it one. That was the great innovation of Augustin-Louis Cauchy, who introduced the notion of limit into calculus in the 1820s.

The British number theorist G. H. Hardy … explains it best: “It is broadly true to say that mathematicians before Cauchy asked not, ‘How shall we define 1 – 1 – 1 + 1 – 1 …’ but ‘What is 1 -1 + 1 – 1 + …?'”

No matter how tight a cordon we draw around the number 1, the sum will eventually, after some finite number of steps, penetrate it, and never leave. Under those circumstances, Cauchy said, we should simply define the value of the infinite sum to be 1.

I have no problem with solving problems in mathematics by ‘defining’ them away. In pure mathematics — and logic — you are always allowed to take an epistemological view on problems and ‘axiomatically’ decide that 0.999… is 1. But how about the real world? In that world, from an ontological point of view, 0.999… is never 1! Although mainstream economics seems to take for granted that their epistemology based models rule the roost even in the real world, economists ought to do some ontological reflection when they apply their mathematical models to the real world, where indeed “you can never have infinitely many heaps.”

In econometrics we often run into the ‘Cauchy logic’ —the data is treated as if it were from a larger population, a ‘superpopulation’ where repeated realizations of the data are imagined. Just imagine there could be more worlds than the one we live in and the problem is ‘fixed.’

Accepting Haavelmo’s domain of probability theory and sample space of infinite populations – just as Fisher’s ‘hypothetical infinite population,’ of which the actual data are regarded as constituting a random sample”, von Mises’s ‘collective’ or Gibbs’s ‘ensemble’ – also implies that judgments are made on the basis of observations that are actually never made!

Infinitely repeated trials or samplings never take place in the real world. So that cannot be a sound inductive basis for a science with aspirations of explaining real-world socio-economic processes, structures or events. It is — just as the Cauchy mathematical logic of ‘defining’ away problems — not tenable.

In social sciences — including economics — it is always wise to ponder C. S. Peirce’s remark that universes are not as common as peanuts …

Diversity bonuses — the idea

28 May, 2018 at 12:43 | Posted in Theory of Science & Methodology | Leave a comment


If you’d like to learn more on the issue, have a look at James Surowiecki’s The Wisdom of Crowds (Anchor Books, 2005) or Scott Page’s The Diversity Bonus (Princeton University Press, 2017). For an illustrative example, see here.

The evidential sine qua non

24 May, 2018 at 18:10 | Posted in Theory of Science & Methodology | Leave a comment

612090-W-Edwards-Deming-Quote-In-God-we-trust-all-others-bring-data

The poverty of deductivism

17 March, 2018 at 17:52 | Posted in Theory of Science & Methodology | 4 Comments

guaThe idea that inductive support is a three-place relation among hypothesis H, evidence e, and background factors Ki rather than a two-place relation between H and e has some drastic philosophical implications, which partly explains why philosophers of science have been so reluctant to endorse it. The inductivist program … aimed at doing for inductive inferences what logicians had done for deductive ones … Once the Ki enter the picture, the issue of inductive support becomes contextualized: one cannot answer it by merely looking at the features of e and H. An empirical investigation is necessary in order to establish whether the context is ‘right’ for e to be truly confirming evidence for H or not … Scientists’ knowledge of the context and circumstances of research is required in order to assess the validity of scientific inferences​.

Scientific realism and inference​ to the best explanation

17 March, 2018 at 09:14 | Posted in Theory of Science & Methodology | 11 Comments

In 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 to reveal what this reality that is the object of science actually looks like.

darScience is made possible by the fact that there are structures that are durable and largely 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 would as a critical realist argue that the main task of science is not to detect event-regularities between observed facts. Rather, that task must be conceived as identifying the underlying structure and forces that produce the observed events.

Instead of building models based on logic-axiomatic, topic-neutral, context-insensitive and non-ampliative​ deductive reasoning — as in mainstream economic theory — it would be much more fruitful and relevant to apply inference to the best explanation.

People 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

Abduction — the induction that constitutes the essence​ of scientific reasoning

15 March, 2018 at 17:15 | Posted in Theory of Science & Methodology | 3 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 factually strongly warranted and truth-producing.

holmes-quotes-about-holmesFollowing 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 cours, 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.

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