Home > Uncategorized > The essence​ of scientific reasoning​

The essence​ of scientific reasoning​

from Lars Syll

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 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 logicallygiven, 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.

  1. Prof Dr James Beckman, Germany
    August 6, 2018 at 2:12 pm

    Lars, I was taught a very long time ago by some eminent researchers in California that abduction was just an investigatory tool,they having the same concerns you have just stated.

  2. August 6, 2018 at 3:53 pm

    James, a long time ago I doubt your “eminent researchers in California would have had much experience of developments in logics for artificial intelligence, or even “if … then …” statements in computer programming subject to error checking.

    Lars, your explanations would be less likely to go wrong if you understood logic in the forms of computer circuit logic. In your symbolic derivation here, p is a set but Ga a member of it. apart from that, your comments are probably helpful.

    In the late 70’s we were exploring parallel processing and ICL came up with a Content Addressable Store to enable the police to quickly identify registered vehicles. If all cells were simultaneously compared with the number being investigated, only the one which was the same would react and so become selectable. Here your hypothesis is factual and the real hypothesis concerns the relations between the terms; the issue of “best available explanation” comes into play when the details being looked for are incomplete. The details don’t really matter in this: what I am insisting on is that the concept of logic has moved on since “pen on paper” days. That said, you are talking about abducton and you might find it helpful to see what the inventor of the label , C S Peirce, had to say about it, and about intuition. I’m looking at p.97ff. and p.62ff. in W B Gallie’s “Peirce and Pragmatism”, 1952, Penguin (Pelican).

  3. Robert Locke
    August 6, 2018 at 6:23 pm

    “what we thought was true turned out to be false.”

    In the 1960s I fell under the influence of the Business Historian Alfred D Chandler, Jr. who wrote among other thing, the Pulitzer Prize winning book (1977), the Visible Hand, and a comparative management study, Scale and Scope (1990). By the 1980’s, after studying management education in Germany and Japan, I concluded that what I thought was true, Chandler’s thesis of a convergence on US management and management education, turned out to be illadvisible. By the 1990s, however, people in US business schools had adopted the Chandler thesis. What was I to do? I was invited to a conference in Bologna in1998 by people who pretty much followed Chandler. The essays read at the conference were published as a collection in ENGWALL and VERA ZAMAGNI (eds.), Management Education in Historical Perspective (Manchester and New York: Manchester University Press, 1998. Pp.v + 177. H/back ISBN 0 7190 5183 5.

    One reviewer of the volume, BJARNAR, O. “Management Education in Historical Perspective.” Business History, vol. 41, no. 4, 1999, p. 168, wrote: “There are many reasons to welcome this volume on the creation and role of management education and training. Provided with an informative introduction by Engwall and Zamagni, and concluded by a thought-provoking chapter by the pioneer of this field of research, Robert R. Locke, the chapters are put together in order to both underline long term developments and to cast light on specific formative historical periods and paths reaching into the 1990s.”

    That concluding chapter was “thought-provoking,” perhaps, because within it I concluded that Chandler’s thesis turned out to be wrong. That somewhat shocked people because it amounted to a volt face from what I had said before and what they believed then.

    The point is not that I changed my mind but how people reacted to the change. Chandler and his followers at the Harvard Business School gave me the silent treatment –Understandable, but people in the business school movement continued to build business schools along the US pattern as if no doubts about the desirability of so doing had been raised. That was in the 1990s. Recently, the doubters have considerably multiplied. Turning a thought hypothesis around is like turning a giant oil tanker about; it takes a very strong hand on the wheel and then a long time to see any reaction.

  4. August 6, 2018 at 6:45 pm

    Science carefully talks about “theory” rather than “explanation” because in many fields the best theories are no longer intuitive. Newtonian mechanics was gratifyingly explanatory. Einsteins is barely intuitive, and quantum mechanics just talks about field equations. If economics came up with abstract math models *and they worked* that would be in keeping with advanced sciences not in itself a sign of trouble.

    The other thing to note is that the best as in most accurate theories are not also the most practical. We use relativistic mechanics for space travel and GPS. For everything else, Newton is more practical. We design electronics most of the time with abstractions like current and capacitance, not with QED and Feynman diagrams. So don’t be quick to ditch simplifying models if they work. The key seems to be knowing when they work.

    • Frank Salter
      August 7, 2018 at 7:26 am

      “The key seems to be knowing when they work.”

      When, at the working level, they fail to correspond to the empirical facts, they are rejected as theories. So only what works ‘well-enough’ remains.

  5. August 6, 2018 at 7:24 pm

    I’m fascinated at the notion of explainability cropping up here and now because in my day job there is evidently a clash coming with artificial intelligence using neural nets. Explainability is already a requirement embedded in aircraft design requirements. If a plane crashes its cause must be inherently, by design, explainable. Autonomous vehicle design was assumed to follow that same regime. But now we have neural net proponents militating for use of this new technology to identify objects, which will affect decisions; braking,steering etc.
    These life and death decisions will rely on a technology that is thoroughly unexplainable. The self learning neural nets are no more explainable than we are. In fact, when you see their edge case mistakes, all you realize is they sure don’t think like us. A very strange new world is coming.

    • August 6, 2018 at 9:54 pm

      In fact, when you see their edge case mistakes, all you realize is they sure don’t think like us. A very strange new world is coming. ~ Peter Blogda

      What does it even mean to “think”? It is one thing to be an machine algorithm, quite another to be a human mind experiencing reality.

      Daniel Robinson, in his classic study of the history of psychology, describes an important example of anti-knowledge with a structure similar to the one noted by Harden in traditional cultures. Surveying the contemporary scene in American university psychology departments, Robinson notes that “hardly a vestige” remains of the program of experimental analysis of consciousness from earlier in the century.

      “But observe the difference between this shift in emphasis or complete abandonment of interest and the changes that have occurred in physics and biology. We do have minds, we are conscious, and we can reflect upon our private experiences because we have them. Unlike phlogiston or the inheritance of acquired characteristics, these phenomena exist and are the most common in human experience. The absence of orthodox Wundtians or Titchenerians or Jamesians, therefore, cannot be attributed to the disappearance of their subjects. Rather, it is to be understood as the result of the inability of the accepted method of psychological inquiry to address these subjects. The contemporary psychologist, if only insensibly, has made a metaphysical commitment to a method and has, per force, eliminated from the domain of significant issues those that cannot be embraced by that method.” (Robinson 1986, p. 398) (Fullbrook, Narrative Fixation in Economics, 2016, 33-34)

      My incompleteness theorem makes it likely that mind is not mechanical, or else mind cannot understand its own mechanism. If my result is taken together with the rationalistic attitude which Hilbert had and which was not refuted by my results, then [we can infer] the sharp result that mind is not mechanical. This is so, because, if the mind were a machine, there would, contrary to this rationalistic attitude, exist number-theoretic questions undecidable for the human mind (Gödel in Wang 1996, Computability: Turing, Godel, Church, and Beyond, 186-187)

      The mathematician Jack Good, formally Turing’s colleague at Bletchley Park, Britain’s wartime code-breaking headquarters, gave a succinct statement of the Mathematical Objection in a 1948 letter to Turing:

      Can you pin-point the fallacy in the following argument? “No machine can exist for which there are no problems that we can solve and it can’t. But we are machines: a contradiction.”

      At the time of Good’s letter Turing was already deeply interested in the Mathematical Objection. More than eighteen months previously he had given a lecture in London, in which he expounded and criticized an argument flowing from his negative result concerning Entsheidungsproblem and concluding that “there is a fundamental contradiction in the idea of a machine with intelligence” (1947, 393).

      (….) Turing believed that

      (Copeland, Jack B. Posy Carl J. and Shagrir Oron, Eds. Computability: Turing, Gödel, Church, and Beyond. Cambridge, Massachusetts: MIT Press; 2013; p. 21.)

      195:6.11 To say that mind “emerged” from matter explains nothing. If the universe were merely a mechanism and mind were unapart from matter, we would never have two differing interpretations of any observed phenomenon. The concepts of truth, beauty, and goodness are not inherent in either physics or chemistry. A machine cannot know, much less know truth, hunger for righteousness, and cherish goodness.

      195:7.3 The inconsistency of the modern mechanist is: If this were merely a material universe and man only a machine, such a man would be wholly unable to recognize himself as such a machine, and likewise would such a machine-man be wholly unconscious of the fact of the existence of such a material universe. The materialistic dismay and despair of a mechanistic science has failed to recognize the fact of the spirit-indwelt mind of the scientist whose very supermaterial insight formulates these mistaken and self-contradictory concepts of a materialistic universe.

      Conceptualizing Cells

      We should all take seriously an assessment of biology made by the physicist David Bohm over 30 years ago (and universally ignored):

      “It does seem odd … that just when physics is … moving away from mechanism, biology and psychology are moving closer to it. If the trend continues … scientists will be regarding living and intelligent beings as mechanical, while they suppose that inanimate matter is to complex and subtle to fit into the limited categories of mechanism.” [D. Bohm, “Some Remarks on the Notion of Order,” in C. H. Waddington, ed., Towards a Theoretical Biology: 2 Sketches. (Edinburgh: Edinburgh Press 1969), p. 18-40.]

      The organism is not a machine! Machines are not made of parts that continually turn over and renew; the cell is. A machine is stable because its parts are strongly built and function reliably. The cell is stable for an entirely different reason: It is homeostatic. Perturbed, the cell automatically seeks to reconstitute its inherent pattern. Homeostasis and homeorhesis are basic to all living things, but not machines.

      If not a machine, then what is the cell?

      There appears to be a common thread (theme) running through disparate fields.

      • August 10, 2018 at 12:51 pm

        [Can you pin-point the fallacy in the following argument? “No machine can exist for which there are no problems that we can solve and it can’t. But we are machines: a contradiction.”]

        Humans are a specific type of machine in the same way as an apple is a specific type of fruit – but not vice versa: a fruit is not a specific type of apple. Popkin and Stroll name claiming the latter “the fallacy of division”.

        What makes humans a machine? Arguably, the ability to transmit physical power, meaning we have not only a neural net but neurons capable of transmitting power via muscles to a world beyond our own personal boundaries. The arrangement of the net encodes information, and the intelligence of a neural net is the ability to decode information, not necessarily to act on it. Artificial intelligence is thus best thought of as a servomechanism, which can either inform our own intelligence or control the operation of other physical machines.

  6. Craig
    August 6, 2018 at 10:00 pm

    Scientific reasoning is well and good….but as method it pales in comparison to Wisdom (which contains scientific reasoning). The old/current Paradigm of Inquiry of Science Only needs to become Wisdom-Integration and the current paradigm of Science: Empirical Fragmentary Truth Only must be transcended and become Unitary Integration of All Truths

  7. Helen Sakho
    August 7, 2018 at 1:50 am

    I must admit that I was “abducted” for a few seconds earlier today by Lars’s mathematical formulations and his equally abstract explanations! Holmes did speak English, and he was funny indeed. I do not know (no assumptions whatsoever on my part) how many languages other colleagues do speak, but I do know that many years ago when I did visit Sweden – as always to sort out problems between the Swedes and the immigrants there, I was told by all sides that the Swedes were a bunch of “alcoholic, manic depressive, suicidal, racist so and so’s” who, nonetheless, had opened their doors to migrants due to the negative growth rates, etc. The factors I have written about on this particular place before. Even that “wonderful” era has now passed, very sadly. I also admit that right now I am mediating between the same agents and victims but this time in a refugee Camp! And I quote from a “private” conversation with a former Swedish Development and something Minister that “ When we opened up our doors, we did not know what we were doing! We really are all in deep …now. If you do have any suggestions, please let me have them”. This, by the way, was in an international academic seminar. And this is now from a young mother in the camp “ I cry my eyes out every day. I wait for my young child to go to sleep. I cannot shower…The situation in the Camp is unbearable. I do want to work, but they tell me, you must wait…I was independent and always worked for a living. Here, everyone seems to have a problem amongst themselves, and with the Camp authorities… No work, no chance to start learning the language, no prospect of a family re-union in the near future, no proper doctors, nothing… ”
    No matter how much we shrink, twist, sway, stretch, bend plausible facts, figures and potential justifications for all these, the reality of famine, starvation, unfair treatment (body and soul) belongs to the immigrants. And now? Is the rise of fascism, in society in general or in a refugee camp to be specific, or almost the whole world going to shed natural light on our theories or our practices?
    We must (and this really is an urgent matter) humanise our approach, our teaching, our preaching. I am fully aware that I am preaching to the converted, so, once again, no disrespect to anyone. Let us please teach Economics as a social science, with its limitations and its potential. You did put a smile on my face after a very long day Lars, thank you for that!

    • Rhonda Kovac
      August 9, 2018 at 8:11 pm

      Superb point. Lurking within ‘uncertainty’ in ‘scientific’ measures and methods is is not only drifting from our moral anchor, but also vulnerability to deliberate manipulation and sabotage. No discussion of scientific method is complete without accommodatiing the real-world, human ramifications of it and its applications.

    • August 15, 2018 at 4:47 pm

      ” Is the rise of fascism … going to shed natural light on our theories or our practices?
      We must (and this really is an urgent matter) humanise our approach, our teaching, our preaching. … Let us please teach Economics as a social science … .

      You are right, Helen, you are preaching to the converted, but social science as currently taught, with its methods framed by Hume’s epistemological mistake (“what you see is all you’ve got”), replaces the human character of society with inhuman statistics: essentially voting by self-centred people with little concern for or understanding of humanity. If fascism is all we can see, social science as presently conceived will teach our young that history has ended and there is now no alternative to fascism (spelled ‘capitalism’). Social scientists need to take the components of society to bits, see how human beings work, thus what types of concern motivate different people in different phases of their lives, and set that in its urbanised ecological context. I say again, teachers will get far more understanding from the Myers-Briggs extension of Jungian personality theory (as in “Knowing me, Knowing You”), Thomas D Harris’s explanation of how things can go wrong in growing up (as in “I’m OK, You’re OK”), James Lovelock’s “Gaia” and the Kohr/Schumacher arguments for “Small is Beautiful” than they will from studying the machinations of artificial intelligence in fraudulent stock markets.

  8. Rhonda Kovac
    August 9, 2018 at 7:52 pm

    It’s important to acknowledge the uncertainties pointed out here inherent in scientifically drawn conclusions. But the question remains, exactly how damning are those uncertainties to those conclusions. Where THAT is unknown — which is often the case — there is not even a minimal empirical basis for having confidence in those conclusions. The argument in support on science, even as a less that ideal alternative, then descends to a lowly appeal to intuition.

    • Rhonda Kovac
      August 9, 2018 at 11:11 pm

      Sorry for typo. Should read “support of science” (not “support on science”)

  9. August 10, 2018 at 10:11 am

    We are discussing here “the essence of scientific reasoning”, and last night on BBC4 at 10 pm, Professor Brian Cox’s program “Science Britannica” took this down a different path, more akin to the problem of the economist’s establishment shutting out any “unorthodox” methods or conclusions.

    His version of science was like mine. There was everything to be said for “applied” science, focussed on resolving particular problems, but the Royal Society of the scientists included lessons learned from failed experiments as well as successful ones, and these sometimes turned out to be just as valuable. He gave the example of a man trying to synthesise the anti-malaria drug quinine who accidentally discovered the possibility of manufacturing synthetic dyes. Another concerned an experimenter who modelled the sun setting by shining light through a tank of cloudy water, finding that the high energy blue end of the colour spectrum was more likely to be scattered than the less powerful reds, colouring the dark sky blue and the dimming light red. Leaving the experiment for the dust to settle, he also “serendipitously” discovered sterilisation, because the then unknown micro-organisms also settled!

    Cox was arguing, therefore, as I and Kuhn have done, for the need for “blue sky” basic and hence revolutionary science as well as problem-focussed “normal” science – which Cox explained very helpfully in terms of eliminating possibilities. In two examples of this in my own work, our research showed estimating reliability of equipment by summing the failure rates of its components didn’t work that well, but using the same method, unreliability due to design faults stuck out like a sore thumb. In the other we compared different forms of database architecture, but in the days we devoted “non-productively” to keeping up with the literature we found what we were finding worked best reinterpreted as a relational database architecture, which very quickly became ubiquitous.

    Economists need to learn from their mistakes?

  10. August 15, 2018 at 11:09 am

    You’re searching for something that doesn’t exist. There is no essence of scientific reasoning. J.D. Bernal warns about trying to pin down science. “Science throughout is taken in a very broad sense and nowhere do I attempt to cramp it into a definition.” In it earliest uses science merely designated knowledge of any sort. In 1998, the journal Nature described an effort by a group of scientists (mostly physicists) to define science precisely to demonstrate how it was possible to distinguish science from pseudo-science. The group was unable to create a satisfying definition of science. People define and use science in whatever ways meets their needs. Wherever science is kept a mystery in the hands of a select group, often labeled “professionals” it is inevitably linked with the interests of societal elites and becomes cut off from the understandings and the inspirations created by the needs of ordinary persons. In this vein science is simply knowledge about nature and human culture and the associated knowledge-producing activities. This means science in not primarily a theoretical activity but an empirical one. Scientific knowledge owes far more to experiment and “hands-on” trial-and-error than to any form of abstract though. It also means the history of science began when humans asked the first questions about how nature works and why, and how humans work and why.

    • August 15, 2018 at 3:54 pm

      Ken, the discussion isn’t about scientific knowledge, it is about scientific reasoning, so your opening assertion is more or less contradicted by your concluding sentence. What makes scientific reasoning scientific rather than pseudo-scientific is its motivation and dynamic logic: looking for what is not yet known. With Bacon, taking things to bits so one can see what simple empiricism cannot see; as suggested by the theme of Star Wars, “going where no man has been before”. But knowledge having “become” by this process, it can be passed on to those willing to take the trouble to fill in the gaps in their own understanding by recapitulating the motivation and historical context and methods of those who had been there before them.

      • August 16, 2018 at 8:21 am

        Dave, humans create themselves through the cultures they create. Human reasoning/knowledge, whichever you examine is created by humans who then use their creation to examine their creation. This makes human reasoning/knowledge not an object but a process, just like humankind itself. At the same time humans create the meanings (motivation/logic) to explain the cultures and reasoning/knowledge humans create. Yes, these creations are passed to other humans, both within a culture and to other cultures through contacts like trade, war, and diplomacy. The specifics of any cultural creation process must be considered empirically, since each is unique. The version you present may be correct in some situations. But I have no empirical basis for agreeing with you.

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