Deduction, Induction, Abduction. AND retroduction

Two weeks ago I participated in a hackathon organized by Riga Technical University within the framework of FuturICT 2.0 project (Large-scale experiments and simulations for the second generation of FuturICT). During the hackathon I delivered a talk on educational data. The goal of the presentation was rather modest: I wanted the folks there to reflect on the way in which we engage with data in education. Essentially, the message was that we manipulate data and we can do that in different ways depending on the type of inference that we are drawing “from the data”. We can look for confirmations, similarities among phenomena or explanations. I pretty much referred to Peirce’s well-known classification of inferences – deduction, abduction, induction. I did not talk about a forth category, which is retroduction.

After the presentation, I started thinking about how to present these four types of inferences or, better, epistemic activities (activities that deal in one way or another with knowing). I usually use the syllogism to explain the differences, but I was looking for something simpler.

Let me start with deduction. What do we do with deduction? If deduction is used theoretically, it generates predictions that are meant either to confirm a hypothesis or not. It does that by deriving the consequences that logically follow, when we assume that something is the case. From example, all men are mortal. And if I am a man, then I am going to die sooner or later. When it’s used practically, deduction prescribe a certain course of action. The prescription derives from subsuming a case under a general rule. For example, when one is ill, it’s better to stay at home and rest. This means that, if I happen to be ill, I should not go to the party.

So,

deduction predicts or prescribes

Induction is a different matter and perhaps a bit more complicated. Or not so straight-forward as deduction. Here I have to start with an example. Let’s say that I meet a thin man and I discover that he is a runner. Then, I meet a second man who is thin and who is a runner. Then, I meet a third one, who is the same as the previous two. After a few observations I start thinking that runners are thin.  In doing so, I am taking single observations (e.g., the thin man is a runner) and I generalize them. Such generalization – it is very important to note – can be quantitative or qualitative.

Qualitative generalizations are based on numbers. So, I say that I verified that 80 out of 100 runners are thin. Then I generalize that this is true for the entire population of runners in, say, Tartu, which is the city where I live. If in Tartu there are, say, 1000 runners, then I can draw the conclusion that 800 of those are thin.

Qualitative generalizations are different and in a way more interesting. Let’s say that there is a certain disease D that manifests itself with a list of symptoms a, b, c. By making a inductive generalization, I attribute those symptoms to any single instance of that disease D. So, all cases of that disease will have the set of symptom a, b, c.

It’s important to note that induction does not really produce new theoretical knowledge. It allows us to see things as similar. So, it seems that induction is essentially related to making similarity judgements. This can be done independently from the number of observations. If a boy touches the hot stove with his fingers once, he will inductively derive that the next time he does the same, he may expect something similar to happen.  So, the generalization that the induction does is related to similarity.

Induction generalizes and finds similarities

Now comes abduction. Abduction is often mistaken for induction. The example that I have just made is perfect to show the difference with induction. The boy touches the hot stove and he burns his finger. He may assume that the next time he is going to do the same, the same will happen, because the second time will be similar to the first time. However, induction does not tell us anything about the finger. This is done via abduction. When the boy touches the stove, he perceives that his finger burns. That is done via abduction and it deals with the recognition that something is the case. In this case the recognition happens at the perceptual level. It’s performed, in other words, by our senses. Abduction performs an act of synthesis, as it brings under the same umbrella different elements. To make an other example, when we see a face, we don’t see the single individual components of that face. We see the face as a whole, which is in this case a perceptual synthesis of all the elements composing it (most of which we cannot really name). So,

Abduction recognizes wholes

Now comes the last in the list: retroduction. This is still the trickiest of all. So, what I am sharing now is very tentative. In general, I tend to see retroduction as a sort of bag containing different molds. For example, I am not a wine expert. And if you give me a glass of wine, I can’t really say much about it. I can essentially say if I like the wine you give me or not. But if you take a wine expert, he or she will tell you way more than me. Now, we both can recognize that something is wine and not coke. The reason is, to put it simply, that we both have the category “wine” and “coke”. What we do is that we are able to create a synthesis of all the clues that are coming to us when we drink something. However, the wine expert has way more “categories” than me. That’s why he or she recognizes many more differences. It’s a little bit like the doctor. The doctor has a sort of library of diseases, which allows him to make sense of the patient’s symptoms. We can call them symptomatologies. Now, retroduction answers to the question concerning the development of those symptomatologies. So, retroruction does not tell us that this is pneumonia or Lambrusco wine. Retroduction provides the “molds” to then capture things in the world. Or, better, to take them off from the background and bring them to the foreground. So,

Retroduction reifies

 

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Uncertainty, staged competitions and (the future of) the university

I have finished to read a book that I warmly recommend: Keynes. The Return of the Master by Robert Skiedelsky. In the book there is a section on Uncertainty, which turned out particularly insightful for me.  What Keynes realized – unlike other classical economists – is that uncertainty is always an issue because our livelihood or prosperity depends “on our taking a view of the future”, as Skiedelsky put it. A page later Skiedelsky quoted the master himself from his General Theory:

We simply don’t know. Nevertheless, The necessity for action and decision compels us practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages […].

As Keynes understood, the category “uncertainty” is a tremendously relevant one in order to make certain phenomena belonging to the social realm a bit more intelligible. That is to say, we may see certain phenomena in direct connection to uncertainty. Or, if you will, an attempt to handle the very fact of uncertainty. Here I would like to talk about the status game and the current situation in the so-called academia.

Keir Martin and Thomas Hylland Eriksen from the University of Oslo have recently published an article (which you find here in English translation) dealing with the situation at their university. There is a passage summarizing the present situation, which seems to be afflicting many of us around the world:

a tendency to view the world as a problem to be fixed with spreadsheets leads to the prioritization of hitting the numbers over the nurturance and development of the human environments that those numbers were intended to measure. It is a tendency that if left unchecked can cause immense problems.

Now, several explanations have been advanced, several labels have been pulled out to understand the emergence of such a tendency. I think that what Keynes wrote is extremely relevant. Essentially the spreadsheet-driven strategies and all the rest of that are an institutional response to uncertainty, which is actually the main issue here.

The first point that I would like to raise is that I am afraid that we are not quite sure of what the university (and higher education) is for. First big uncertainty. Let me focus on research here. What is research? In some disciplines people have been quite successful to get the message across that research embodies the ideal of the scientific method and therefore they see themselves as those who can reach the truth or, at least, get nearer to it. Decisions to be made should be supported by evidence and evidence is provided by science. All the rest relies on anecdotes or, even worse, biases that are resistant, yet unreliable. In other cases, research is successfully presented as fundamental for innovation, which contributes to productivity, which means competitive advantage, which means profit for the individual and growth for the state.

Now, while there is a grain of truth in what I have just described, research is way more than that. Research is not just about evidencing. Yes, research is a device that produces evidence. But the question would be then: evidence for what? That is a question of meaning that goes right to the core of the scientific enterprise, which is not just about coming up with evidence supporting certain ideas. We want those ideas to be good. And the evaluation of ideas cannot be reduced to evidencing: it is fundamentally as fallible as the knowledge we produce. If we don’t deal with that kind of uncertainty, we will start playing conservatively. We will just try to prove that something is the case without imagining other cases. An interesting piece of evidence here – pun not intended – is that negative results have virtually disappeared from the scientific publications. Which is a clue pointing to the fact that there is a strong bias in favor of “positive” results, because knowing what is false is not enough. Again, uncertainty coming back from the backdoor.

The second element concerns the people, who gravitate around the university. The uncertainty in this case regards their career. I have heard over the course of the years many people express their concern regarding their future: Will I be able to get a position at the uni? Will I be able to keep my job? Will I ever get the tenure? Will I ever be able to do research with my own team? I am also concerned about my own future, because I love my job.

The proliferation of staged competitions is the response. The word “staged” is keyword here, because what I am talking about here are essentially games like this one:

 

As a university employee I want to know what I have to do in order to keep my job or to progress in my career. Staged competitions reduce uncertainty, because I can now see my career as a game. Just like in any game, there are rules, score, etc. (The game also becomes a way for those on the top of the hierarchy to mobilize people’s energy and channel it into certain desired targets, but let’s leave this aside for the time being). It all becomes predictable.

What is the problem with that? To put it simply, we academics start playing the game and in doing so we forget that we are supposed to do science, not piling up pieces of papers called “A-journal articles” (which is an outcome, by the way). The less we care about doing good research, the less relevant research becomes for those who are not playing the game. Besides, when everybody starts “playing the game”, things do not necessarily become easier. On the contrary, they become harder and harder. So, uncertainty comes back again from the backdoor. That’s called performativity.

What is the problem here then? The problem concerns the sort of methods we are collectively deploying to face what Keynes called “irreducible uncertainty”. That is, it concerns the design of our institutions, which are in the end supposed to handle such irreducible uncertainty. The two examples that I have just described rely, on the one hand, on the so-called scientific method, on the other, on gamifying the process of distributing costs and benefits. Those are the “methods”. As I noted above, when we apply them, uncertainty comes back from the backdoor.

What would be the solution then? First of all, this is exactly what I am talking about: there are no certain solutions. Or, to put it another way, repressing uncertainty is not a solution. That is clear in the two examples that I presented here. Science itself  is uncertain: it’s the beautiful risk of discovery. Discoveries cannot be predicted, can they? New ways of looking at the world (natural as well as social) will be found along the way, not planned out in project proposals.

Then, careers are uncertain. We don’t know who is going to be the next Einstein. But perhaps we should just try to provide a good work environment to help the expression of people’s creativity and imagination. That would be a good starting point, instead of coming up with all sorts of pseudo games.

 

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Variety-handling, technology and the meta-system

As a wrote in a previous post, I am currently working on a paper with Tony Tonni – educational technologist at Eller Music College here in Tartu. The text we are composing is supposed to provide a case study, in which we illustrate how a few ideas coming from cybernetics (notably, from Stafford Beer’s work) can be used to understand the role of a educational technologist in an educational institution at different levels of abstraction – that is, practically and theoretically. The case study is built around Tony’s challenge to handle  a videoconferencing system for remote regular one-to-one music tuition, which involved a pair composed of an accordion student and his teacher. Essentially, what we are trying to show is that the educational technologist is a variety-handler. And we do that by providing “ethnographically rich” examples coming from the field.

The main thesis that the educational technologist is (or should be) a variety-handler is meant to be something practical. In other words, we would like to show practically what that means. There are also some broader implications that concern the way in which we see technology. And that’s even more exciting. The kind of narrative that we propose in the paper is essentially based on the idea that technology (or I should say technological innovation) provides us with new options for (the organization of) learning and teaching). And that’s called variety. The proliferation of options (another key term) may turn out to be challenging for the educational institution (a school, for example), because it essentially means that its members can do things in (many) different ways. However, the proliferation of options does not automatically translate into something good or better. Conversely, it may create confusion and a lot more work to do, which may overburden the people in the organization and distract them from their core business – teaching and learning. Essentially, more options means more decisions to make, more tools to test, more of everything. That is not necessarily bad, yet…

Within such a scenario, what should we do with technology? In a recent post Mark Johnson writes that we should look at the system “people plus technology”. To do that, though, we need a meta-system, which is essentially something outside of the system. Now, according to Mark, the problem is when we put technology in the meta-system “to amplify the uncertainty mop” (uncertainty here refers to the fact that we are not sure what option is better than the others). This prompted me to have two kinds of thought, which reflect the duality of the system, which is partly technology, partly people.

The first is that we try to deal with the effects of technology with more technology (read “A.I.”). This is what Alan Watts called “the competition of consciousness”.

In other words, we are trying to match the proliferation of variety by proliferating even more variety. Which eventually means confusion (see my other post). The other thought is that the technology in the meta-system may mean the reduction of people’s ability to express their own variety, because the technology becomes the variety mop that Mark is alluding to in his post. And this essentially means the reduction of variety where we actually don’t want to see that, provided that we all agree that the human potential is something to nurture, indeed, not to destroy.

Let’s go back now to the meta-system. What is that then? Our brain? Is it us – the people? A new form of organization?

 

 

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Complexity, complication and educational technology

I am currently working on a paper with Tony Tonni – educational technologist at Eller Music College here in Tartu. The main idea is to show what practically means to say that an educational technologist is a “variety juggler. The label “variety” and all the theoretical jargon we are using comes from Stafford Beer’s work, which we are trying to apply to a specific domain – that of educational technology.

In writing the paper, we have stumbled upon an important issue, which I will try to summarize here. For example, for a teacher, the appearance of new technologies potentially provides new options for doing one’s teaching. This translates into more variety to handle from the teacher’s side. So, a teacher can use this tool to do this, that tool to do that. And if she or she decides to involve students in doing so, we see the exponential growth of possible combinations and re-combinations. In Beer’s terminology that is called “proliferation of variety”.

Beer’s take on variety (From Designing Freedom):

Now, the problem is what having more options actually means. Or what it may actually come to mean in different situations. One idea we have started playing with is that variety may mean that we are dealing with “high-variety” situations, that is, situations with a certain degree of complexity, which, in turn, necessitates the adoption of strategies that are equally “high-variety”.

However, Variety may also mean that things have gotten a lot more complicated. So, we should probably make a distinction between complexity and, say, complication. One way to put it is that complexity is not chaotic. We may find in it a type of organization, which is simply more complex than others. Complication seems to point to a situation in which things went astray. It all became a big mess. Indeed, complexity is sometimes perceived this way. We may get really confused. However, complication seems something different. And this is of pivotal importance for educational technology. Is the proliferation of options (that is variety) something that makes things more complex? Or just more complicated?

 

 

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Uncertainty in teaching

I have been always interested in uncertainty and this very blog has grown out of my interest in trying to address the question concerning what to do when we don’t know what to do, which is decision-making under uncertainty to use a label.

I believe that, when start talking about uncertainty, we will end up sooner or later talking about learning. So, we may say that when we talk about making decision under condition of uncertainty, we need at some level to engage with learning. Which means that learning is the sort of device we use to face uncertainty. But even more than that, learning itself grows out of uncertainty. Which means that learning is something that we do in order to face uncertainty. However, learning itself bears an intimate connection with it. This is the fundamental ambiguity to acknowledge.

In my experience as a lecturer, I always have a plan in mind. Or at least I have a number of things to share with students. I make a selection among the thousands if not millions of the combinations that I can make. In doing so, I simply try to suppress uncertainty: this is the right thing! 

In suppressing uncertainty we basically pull a trick. We do as if there isn’t any. And in doing so we stage ourselves as experts. The ones who are supposed to know, which also means the ones who are immune to uncertainty – we are the righteous.  This sense of righteousness can be dangerous. That’s when we create differences between those who have learnt and those who have not. The success story and the one that was not. We have built self-righteous institutions out of this. Not on the basis of what actually happens.

Another part of me is awakened the moment in which I see I have failed to achieve what I had in mind, when, in other words, reality could not be forced into my own little frame. That’s also the moment in which I get frozen, paralyzed.  I have to change something. Actually there is nothing to change, but something to undo. And that’s where learning comes into place. That is when the teacher starts to learn.

I like the idea that as a teacher I am not superior. I am not granted a privileged status. I do have a role, indeed. I am the one who is willing to learn. Which means, I am the one who is willing to face uncertainty. In other words, to keep that gap open. I refrain from being the one who already knows. I might be the one who has already been there. But there is the place where I have realized that I cannot fool uncertainty (and most likely life). So, what is my role in the end?

I like to think that a teacher is the one who has courage, because his or her main task will be to encourage others. The teacher does not provide epistemological shelter. Out of compassion he or she may do so. But that is always instrumental or a temporary stage. it is important to know that. Courage is what we need to face uncertainty and what we get in return is learning as a process. That is why we need to build educational institutions that deal with uncertainty, instead of suppressing it, doing as if it is not there.

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Educational technology and the analogy with music instruments

Pildiotsingu playing an instrument tulemus

I am interested in developing a vision of educational technology (edtech) that does not fall prey of what we may call “functionalism”. Which is, in short, the idea that views a piece of (educational) technology as a (neutral) means-to-an-end.  Functionalists reduce a piece of technology to the function that it allegedly plays, for example, in class. I say “allegedly”, because very often such “functions” are mere declarations –  well, hot vapor (Mark Johnson drew my attention to that).

While I can see why functionalism is deadly wrong in edtech, I struggled finding a way to express a viable alternative. The first idea came from a colleague of mine, Mario Mäeots, who repeatedly told me that the use of technology in education should be meaningful. Or perhaps a better way of putting it would be “pedagogically meaningful”. I started using this label in my courses.

When I presented this idea, I used music as an analogy to convey what I meant by “meaningfulness”. So, I played two pieces. The first was a random beep noise, after which I played Erik Satie’s Once Upon a Time in Paris. The idea was to make them experience that only with the latter we experience meaningfulness. The beep noise is just noise. Nothing we can really make sense of.  That was, as I said, to try to convey what I mean by meaningful or meaningfulness. I actually wanted to avoid to give the impression that by “meaningful use” I meant, again, that a tool had a function and that it was the function that gave meaning to it. To be honest, I don’t think that my attempt was successful. I think that it was largely a failure. (At least students did not think that I lack imagination.)

However, something was working somehow in my mind – perhaps unconsciously, because a month or so later, I got a better idea. Or at least that’s how it looks now to me. The idea came to me after I watched a clip on YouTube, where a famous drummer – Jojo Mayer – described how digital technology changed his way of playing drums.

The idea that came to my mind is that making music has a lot in common – at least analogically – with teaching&learning, which I consider a pair. Meaning, you cannot have one without having the other. Now, the first interesting thing to notice is that music cannot be done without “instruments”. We may lack a piano, guitar – whatever. But we can still make music. For example, we can use our vocal chords or our chest and our hands. The same with teaching&learning. There is no way to teach&learn without instruments.

Second source of analogy, the type of instrument one uses to make music affects the way in which music is experienced. The same very piece of music played with the guitar sounds different when it is played with the piano. That’s because, the instrument is never neutral. The same in teaching&learning. Writing something on a blackboard is not the same as projecting the same thing on a screen. The content might be the same, but not the pedagogical experience.

Thirdly – and this is about functionalism: we say that we play the guitar. We don’t say that we use the guitar. Indeed, we use the guitar. We use our hands, our voice. But the result – what comes out – is “played”. This is a fascinating thing, isn’t it? I think that it’s so because we want to capture some kind of emergent dimension – what we do together with the instrument. Or we want to stress that playing music is not just about pushing buttons. Is it the same as in teaching&learning? Yes. I have experienced on several occasions that good teachers actually play their educational instruments. Because in the end you see that it’s not about using technology for its own sake: technology is integrated smoothly into their practice. Actually, I should say that both teachers and their students are the actual players. (There is in my opinion something mystic in seeing a class that performs. And the performance can be compared to that of an orchestra.)

Fourthly, we are used to identify certain instruments as music instruments. Yes, we can pretend to play pots and pans (I did it) as if they are drums. Yet a drum set is something different. Why? Because a music instrument is not just any instrument. There is a practice that provides the sort of backbone needed to experience it as music. The same in teaching&learning. There are educational instruments. For example, the blackboard is one of those. Have we managed to create new educational instruments? Well, I think that answer is yes. Although we are still playing with pots and pans in a way. I mean, we are still tinkering.

There is a last point I want to bring up. Music is organized in genres. So, for example, there is a genre called electronic music. Is there something similar in teaching&learning? I think so. I mean, I don’t think that teachers and students necessarily need digital technology to have a pedagogical experience. But it’s true that there are people who don’t like, for example, pop music or classic music. They have different preferences. So, it’s harder for them to have a good experience, if their favorite type of music is not played. Perhaps, we see something similar in teaching&learning. Students are used to a certain type of tools. That is, they expect a certain type of “music” to be played. So, it is perhaps convenient to get closer to them and “play” some instruments that they like.

 

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Responsibility, the pedagogical act, and the freedom to learn

In an article that I wrote with a few colleagues of mine, we made the point that the notion of responsibility needs disambiguation, as it may refer to very different pedagogical “scenarios”. Let’s see why.

Lucas in his book on responsibility argues that responsibility establishes a triadic relationship: I am responsible for something to somebody. In our article we called this “answerability” to stress that this conception of responsibility always involves in one way or the other to respond to somebody (for something). There are a few things that I may draw from that, which has important consequences for education – I believe.

The first is that what we are held responsibility for should be known in advance. This implies that this something I am responsible for should be described or made fully explicit. This is typical of contractual relations. In education, these are the learning objectives. What is it that the student will eventually acquire? Skills, competences – all these should be fully described in a specific way.

The second thing is that, if I am held responsible for something, then this something should be within my reach. Say, that I am appointed to make coffee for breakfast. So, I am responsible for preparing it. However, if the next morning the coffee machine breaks down, then, I cannot be held responsible. As far as education is concerned, this is a very interesting point. Learning is interpreted by some as acquiring certain skills, knowledge or competences defined beforehand. That is what a student is responsible for. But here comes the third actor in the triad. If I am held responsible for making coffee, as I said, that should be within my reach. Indeed, the machine may get broken. Yet there is another condition under which I may not be able to fulfill my “duty”. And that is when I don’t know how to make coffee. When, in other words, I have to learn. Being in such a state is a quite interesting one. And the reason is this: I may not be able to make coffee now, but I can learn and be able to make afterwards.

If that is the case, then there must be somebody who should teach me or, at least, assist me in the process. In schooling this role is fulfilled by the teacher. Interestingly, the teacher is in the pedagogical process that one the student responds to. But because of the pedagogical relationship the teacher is also the one becoming responsible for the students’ learning process. The teacher is, in other words, responsible for bringing the student into the state of knowing. The teacher is the one who posses pedagogical knowledge. That is, the kind of knowledge that would in theory allow the student to get to know what he/she has to know. At the same time, the teacher is also the subject supposed to know. That is, the state the student should achieve. So, the student responds to her.

So, to go back to my example. I am supposed to make coffee. But I lack the skill to do so. Therefore, a teacher is appointed to teach me how to make coffee. The teacher has pedagogical knowledge. That is, she tells me what to do in order to learn the skill. My responsibility now is not to make coffee, but to follow her instructions, which would allow me to acquire the skill. So, I am now responsible to her, while at the same time she has become (temporarily) responsible for me making coffee. This is what Lucas calls the “upward spiral of responsibility”, which seems to be a fundamental element of schooling.

Now, it goes without saying that the upward spiral establishes the conditions for hierarchy to emerge, because different people become engaged with one another in a sort of co-dependent relationship of duties – I respond to you, you respond to her, etc..  Some would call this “chain of fools”.

We can use responsibility as answerability to describe the state of affairs in education. But is there another way to interpret responsibility?

As I said, answerability establishes a triadic relationship: I am responsible for doing something to a third party. If I am not capable yet to fulfill my duty, then the third party becomes responsible for my learning process, whereas I become responsible for following what the third party – my teacher – tells me.

We can, though, deconstruct this. And that can be done, if we do not interpret responsibility as something related to an outcome to achieve or secure (e.g. making coffee). But as a process. Or, more specifically, as a type of engagement while doing something, which, though, may not be entirely specified. If we go back to the example of coffee – a trivial one, indeed – we may say that, if I am responsible for breaksfast, then what that means is that I am the one who will be taking care of preparing breakfast. I may make coffee, bake a cake, make toasts, etc..What counts is not so much what I am going to prepare as my own engagement, which eventually will lead to preparing something.

This is quite a radical departure from the triadic relationship. We may say that we are still somehow responsible to somebody for doing something. Yet such connections are somehow relaxed or loosened up. What counts is more something coming out of oneself rather than mere compliance. This has indeed very important repercussions on education and the way in which we may conceive it. For example, the learner is not necessarily to be seen as an executor of the teacher’s plan (for his own good, indeed). Conversely,  the student becomes a subject of a process that is essentially open to his “will to learn”. In other words, to educational trajectories that very much depend on his own ideas and plans, not teachers’, school’s or society’s. The teacher then is not taking responsibility for the learner’s learning process. Conversely, she becomes an ally of the student in the process.

Continue…

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