Tuesday, December 15, 2015

Remarks on Abduction

I have been thinking about the notion of abduction recently. Not the kidnapping variety, silly. Rather, the kind that begins an inquiry process with a hunch or hypothesis made on the basis of an observation. Charles Sanders Peirce, “may his tribe increase” (i.e., there should be more logicians and more pragmatists) noticed that people often formed hypotheses about the general relationships among things based on a case or observation. While valid deductive reasoning establishes conclusions with certainty and valid inductive reasoning establishes conclusions with probability, abductive reasoning does not establish a conclusion at all. Rather, it suggests a hypothesis that might be further investigated. One might argue that while Arthur Conan Doyle had Doctor Watson say to Sherlock Holmes on many occasions, “brilliant deduction, Sherlock,” what Watson should have said was “insightful abduction, Sherlock.” There is a fair amount of controversy with regard to abduction and its relationship to other forms of inference. I cannot claim to understand all sides of the various critiques of the various forms of abduction. I refer interested readers (i.e., those bored with these ruminations) to the Stanford Encyclopedia of Philosophy entry on abduction – see http://plato.stanford.edu/entries/abduction/. One can also find an excellent entry on Charles Sanders Peirce in the encyclopedia – see http://plato.stanford.edu/entries/peirce/#dia.

My interest in abduction is somewhat different and focuses on what might be called a naturalistic account of epistemology – how people come to know and understand things. In “Questions Concerning Faculties Claimed for Man” (yes, silly, it applies to women, as well; see https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA103#v=onepage&q&f=false), Peirce questions capabilities assumed to be inherent in humans: (a) intuition, (b) intuitive self consciousness, (c) intuitive ability to distinguish subjective elements of different kinds of cognition, (d) introspective ability, (e) the ability to think without signs, (f) whether a sign said to be of something incognizable can have any meaning, and (g) whether there is any cognition not determined by previous cognition. Peirce’s exploration of these questions led him to conclude that (1) there is no power of introspection – knowledge of the internal world posited by introspections comes to one by hypothetical reasoning (probably of the abductive variety) about external facts or observations; (2) there is no power of intuition – rather, mental actions have the form of inference (even though the inference itself may not be stated or made explicit); (3) no thinking without signs (i.e.,  interpretation requires the use and manipulation of signs – spoiler alert – more on this soon); and (4) we cannot know what we cannot know (i.e., there is no reason to believe that there are unknowable things).

That last conclusion reminds me of Wittgenstein’s closing remark in the Tractatus Logico-Philosophicus – “7. What we cannot speak about we must pass over in silence.” Others have noted similarities between Peirce and Wittgenstein, although those similarities might be construed as incidental rather than deeply significant. There is Peirce’s works on mathematical logic and Wittgenstein's derivation of two-valued logic (a.k.a., Boolean algebra) in a footnote in  the Tractatus, for example. It seems that both Peirce and Wittgenstein (and others) saw a connection between the laws of mathematical logic and the laws governing human thought and reasoning. I personally see a connection of sorts that binds both to what I earlier called a naturalistic epistemology. Peirce’s extension of thinking beyond the strict confines of mathematical logic came in the form of his notion of abduction – the idea that people often form an hypothesis based on limited observations and then may go on to explore that hypothesis. Wittgenstein’s extension beyond the strict confines of mathematical logic came in the form of language games that proceed according to rules (typically implicit and dynamic) determined by a community of speakers. Ironically, while Peirce is often cited by many constructivists, he argued that introspection and intuition should not be regarded as the basis of human knowledge. On the contrary, while Wittgenstein is often cited by many constructivists as an objectivist, it is Wittgenstein who argued that we create internal representations to make sense of things we experience (Remark 2.1 in the Tractatus) and who developed the notion of language games in Philosophical Investigations in recognition that we engage in discourse with others based on those internal representations (which are not directly observable or knowable). In spite of those ironies, both eventually came to consider what people actually do in the process of coming to form beliefs and understand experiences. If one accepts that general conclusion, then both can be regarded as naturalistic epistemologists.

What brought me to think again about Peirce was a game I sometimes play with my educational technology graduate students and conference audiences. The game is called “Name that Technology.” First I describe a technology (defined as the disciplined application of knowledge to achieve a valued purpose) and then ask who invented it, when, and what it was called. The examples are designed to be very difficult (hardly anyone ever gets even one right) and to remind people that there is a long history to educational technology that precedes the Cloud, the Internet, Social Computing, and Wearable Devices (well, it is true that I used to wear a slide rule clipped to my belt – fastest calculator West of the Pecos was I).  The technology I describe is this: “All digital devices could be constructed using a single logic gate based on a system demonstrated by a philosopher. Who was that philosopher, what was the logic gate, and when did that finding get published?” The answer is Charles Sanders Peirce, of course. It was in 1880 or 1881 in a paper entitled “A Boolean Algebra with One Constant” and that constant (the logic gate) was NOR – the logical operator that is true (or on or 1) only when both operands are false (or off or 0). Yes, one can build a computer using only NOR gates, although it might involve an extremely large number of NOR gates (life is full of trade-offs – I once traded an authenticated Sami knife dated back to the 1930s for a Pentax SLR Spotmatic camera and lenses, the non-digital variety, so there were no logic gates involved).

Peirce also demonstrated that there was a second universal logic gate or single Boolean operator that could generate all of first order, two-valued logic – namely, the NAND gate, which is true (on) only when both operands are false (off). Wittgenstein’s treatment of first order, two-valued logic (a.k.a., Boolean algebra) involves four basic operators: IF-THEN, NOT, AND, OR.

There is yet another similarity to be found in the writings of Peirce and Wittgenstein. As noted previously, Peirce argued that there is no thinking without signs. Wittgenstein says at Remark 5.6 in the Tractatus that “the limits of my language mean the limits of my world.” Signs and symbols are part and parcel of language – without language … without signs … one cannot imagine thought.

Having been drowned (I mean trained) in skepticism, I should point out that those remarks by Peirce and Wittgenstein involve a certain leap – not a leap of faith, but a leap of meaning. From “I cannot imagine X” to “there can be no X” involves a leap beyond the evidence. It amounts to an inverse (or possibly perverse) principle that I hereby dub NABDUCTION (recalling the NOR and NAND gate discussion). Having survived as a skeptical inquirer for more than 40 years, I hereby reject NABDUCTION in all of its various forms. One can suspect that there is no X based on one’s inability to imagine X, but then there are a couple of humbling reminders to consider. First, we are limited beings – most of us, anyway … those of us not running for political office, anyway. Second, there is David Hume’s interesting observation in An Enquiry Concerning Human Understanding that deductive reasoning provides no new information about the world whereas non-deductive reasoning (inductive reasoning and presumably abductive reasoning as well, although Peirce had not then been born) rests on the principle that the future will resemble the past … but that principle cannot be established by either inductive or deductive reasoning. Of course pragmatists and naturalistic epistemologists wiggle out of Hume’s conundrum, but it remains a reminder that we are, after all, limited beings, however much we like to wiggle. The best wigglers, by the way, are politicians who have unearthed a new definition of truth: what is true is simply what they are telling, which is in many cases what people are buying. Your homework, should you accept this assignment, is to compare and contrast the politician’s definition of truth with that of Ruth who tells Naomi, according to non-political accounts, “where you shall go, I will go.” In that latter case, the truth showed itself in the following – something observable … not something intuited nor established by introspection.

Monday, November 16, 2015

On Being a Teacher

I have had these thoughts previously. I have written and spoken about being a teacher previously. It began when I thought about my father, Rabbi Joseph Spector, as a teacher and what he thought about being a rabbi. I have represented his thoughts as follows: “A teacher is the ear that listens, the eye that reflects, the hand that guides, the voice that encourages, the face that does not turn away.” I wanted to be a teacher, but I have strayed from his guidelines. I have come to think of a teacher as someone who helps others to have questions – that is someone who admits to not knowing or understanding something, who commits time and effort to finding likely explanations, who is open to alternative explanations, and who is willing to examine and re-examine assumptions. Rather than a voice that encourages or comforts, my voice has been more one that challenges and provokes.

Over the years, I have taught philosophy, computer science, educational technology, program evaluation and related subjects. My first and only academic love was philosophy. I recall using that challenging voice to discourage one of the most inquisitive and brightest students I ever had in class. I had marked up, using a red pen, an innovative dialogue the student had written in the style of Plato – this was prior to the advent of personal computers and the Internet. The student dropped the class after receiving my feedback. When I next saw him some months later, I asked why he dropped when he was doing so well. He said that there was nearly as much of my red ink on the paper as his typewritten black ink. I said that was because I thought his work was especially promising and merited as much constructive feedback as I could manage to offer. He said he took it as general criticism and decided he was not going to do well in the course, even though his paper had been graded very highly. I stopped using red ink after losing the most promising student that I have ever had.

I also reflected on why I had been so challenging in my feedback. I thought about several incidents in which I had received challenging feedback from teachers whom I regarded highly. Challenging feedback seemed to work for (or on) me. Perhaps not everyone is like me (it is certainly true that not everyone likes me). Anyway, I have tried to soften my approach of getting students to have questions a bit.

I have also asked many public school teachers in recent years why they became teachers and remained teachers. These were primarily elementary and middle school teachers working in poorly performing rural schools in the southeastern part of the USA. There was a consistent pattern to their responses involving two things. First, they grew up in those communities and wanted to stay and work there – teaching being the most stable jobs available. Second, they had grown to like many of the children and wanted to help them overcome years of neglect in their education and upbringing.

Is that why I became a teacher? Did I remain in this profession for such praiseworthy reasons? [I wish I could say yes, but that would be a lie.] Those questions reminded me of what Bob Gagné told me more than once while working together at the Human Resources Laboratory in San Antonio – namely, our job was to help people learn. After retiring from Florida State University and while working at the Lab, Bob and his wife Pat had become volunteer tutors to underperforming and underprivileged children in San Antonio. His advice to me was more than high-sounding words – help people learn; he lived those words even after retiring.

Help people learn … and ‘people’ is an inclusive term that includes oneself.

Posted to Building the Scientific Mind - see http://www.learndev.org/BtSM2015.html

Fostering Inquiry, Reasoning and Critical Thinking

J. Michael Spector, PhD, Professor of Learning Technologies, University of North Texas

Observations and Doubts

In many places around the world one can find people with divergent views. In many of those places, tensions have grown considerably and taken the form of hateful language and even violence. Tolerance and an openness to considering alternative views and perspectives seems to be at all-time lows in some places. Advocacy seems to be displacing evidence. Anger seems to be displacing thoughtfulness. What can be done?
Earlier in my career, I thought that I could use reason and logical argumentation to enlighten those suffering from the throes of dogmatism, prejudice and intolerance. I thought that helping others to develop a scientific attitude could help cures the ills of a society suffering from intolerance. Was I wrong to have such thoughts?
What is it to have a scientific attitude? Some might say that it involves considering beliefs and statements that could potentially be shown to be false or mistaken as those beliefs and statements are worth investigating (for those keeping notes, I am thinking about Karl Popper’s Conjectures and Refutations). If the person holding the belief or making the statement is not willing to consider that it could be wrong, then there seems to be little to be gained in pursuing discourse with that person based on an acceptance of the belief or statement if one happens to doubt that belief or statement. This could be called the walk-away strategy. The drawback is that no progress in terms of understanding or openness occurs as a result. I have walked away too many times.
A somewhat different approach involves thinking about what underlies thinking and reasoning. It then occurs to me to revisit Ludwig Wittgenstein’s works. In the Tractatus Logico-Philosophicus (you really should be keeping notes), Wittgenstein observes at remark 2.1 that we picture facts to ourselves. He fails to note that we also picture things that are not factual to ourselves. Nevertheless, the remark that we picture facts to ourselves is the kernel notion in a naturalistic or constructivist epistemology we create internal representations to make sense of things that we experience that are new, unusual or otherwise puzzling. The last remark in the Tractatus is that what we cannot speak about [clearly] we must pass over in silence. As it happened, there was much that Wittgenstein wanted to speak about, as is evident in Philosophical Investigations published after his death. In that posthumous work, he introduced the notion of language games. Not only do we create internal representations to make sense of new and puzzling things, we talk about those representations with others. We engage in language games. Such discourse represents a re-representation of the internal representations that are basically hypothetical entities that no one ever directly observes. These two ideas creating internal representations and engaging in discourse about those representations are the basis of a socio- constructivist epistemology that is prevalent in some educational and philosophical circles.
Then my mind wanders into ancient gardens and I stumble across the works of Sextus Empiricus and Outlines of Pyrrhonism. Since that work was written in Greek, I decided to read it from back to front. After describing what it is to be a skeptic but before I read that part, Sextus argues that being a skeptic will result in peace and tranquility. Is that not odd? Well, in my typical state of anxiety and confusion, it seems highly desirable. How to achieve such intellectual peace and tranquility? I had to read the first part to find an answer to that question.
Basically, becoming a skeptic involves recognizing that many (possibly most) beliefs and statements are open to investigation. A dogmatic position results when one believes something about which there exists a basis for doubt or further investigation; a variant of dogmatism occurs when one believes that there is no possible answer to a question or issue. In both of those cases, no further inquiry can occur and the discourse is cut off (recall the walk-away strategy mentioned earlier). A skeptic, however, is someone who recognizes that further investigation is possible even when the available evidence apparently favors one or another of the many possible beliefs or positions. A skeptic, in the world of Sextus Empiricus, is not held captive by his or her beliefs.
I have to admit that from that conclusion (many or most beliefs are open to further investigation and possible refutation) to intellectual peace and tranquility is a leap at least for me (I have short legs). Nonetheless, I have developed a few suggestions that might lead a student to a path not yet taken.

The Suggestion

As I am close to retiring after more than 40 years in higher education, I am beginning to understand the role of a teacher in fostering inquiry, reasoning and critical thinking. There are two pieces to the puzzle that I am trying to piece together.
The first is the notion of having questions. The job of a teacher is to help students have questions not to help them ask questions or give them answers. To have a question involves (a) admitting that one does not know (with certainty or with extremely high confidence) something, (b) committing time and effort to finding answers, (c) being willing to consider alternative perspectives and approaches, and (d) being willing to revisit the entire process again and again (akin to Socrates asking Crito to explain again why he should escape). It seems to me that all too often students are taught to have answers rather than to have questions. Learning how to have questions should be considered a basic skill, akin to reading Plato’s Symposium, writing love letters, and calculating π (I happen to love transcendental numbers). If this argument is accepted, then inquiry should be introduced early and often in primary and secondary education.
The second piece to this puzzle (which seems very difficult to put together) is a framework that can support a wide variety of inquiries that is to say, cases of having questions. One framework that might fit into this very complicated puzzle (supporting inquiry, reasoning and critical thinking) involves considering argument forms. An argument can be considered a collection of statements (premises) offered in support of another statement (the conclusion). A form of scientific reasoning can be mapped onto this notion of an argument form. Logicians typically distinguish deductive arguments from non- deductive arguments since the criteria for evaluating them are different. That distinction is not necessarily relevant to this brief and tenuous excursion into inquiry learning. The figure below depicts the general form of an argument. The reason for introducing such a framework early in a child’s education is that it can establish a habit of mind namely the habit of thinking of the adequacy of the evidence, the habit of identifying unstated assumptions that might also merit inquiry, and the habit of looking at the implications of what one believes. If those habits are established early in a child’s education, then there is a remote possibility that more children will begin to think scientifically. Perhaps

there is a remote possibility that when those children become adults that they will be free from dogmas that create tension, confusion and strife within society. There is a remote possibility.

Concluding Statement

I cannot pretend to have found answers or even useful paths to follow. I have only been able to create possibilities. With regard to possibilities, I see several varieties. There are bare possibilities, such as the possibility that the number of grains of sand on the shores of Iwo Jima at a particular point in time is an odd number. There are also practical possibilities, such as the possibility of significantly reducing hunger and violence in a particular part of the world. Another practical possibility is that the children of today may indeed become skeptical inquirers (i.e., non-dogmatic investigators) and critical thinkers. That last practical possibility, however, is not likely to occur without the efforts of many of those involved in such efforts as the Building the Scientific Mind enterprise.