Reader query: Teaching logic and the 'practice of reasoned argument'

A reader asks:

Is there a way to teach propositional logic that more directly ties the subject to the practice of reasoned argument than I am used to? I learned logic myself as an abstract formal set of operations, through practice exercises. (Sure, we interpreted symbols as propositions, but for all that the results were hardly less divorced from the actual practice of reasoning.) I intuited and later learned in more depth how to put these operations into practice in my own thinking as an aid both to conceptual and communicative clarity. But no one ever explicitly taught me that.  

Does anyone know of a textbook, teacher, teaching method, or anything along these lines which(/who) successfully injects the practice of logical thinking, and perhaps even rational dialogue, into the teaching of the formal operations? Or is that simply too much to ask for in a single class? 

I don't think there's anything wrong with a purely formal and abstract approach, by the way. I'm just looking around.

Those more versed in teaching logic: What do you suggest to this reader?

A nice graphic on argumentative fallacies

The talented graphic artists at Information is Beautiful have come up with an attractive and colorful visual display of argumentative fallacies. This could be a useful poster in a logic or critical thinking course.

teaching argument mapping

Colleagues: inspired in part by some of Mara Harrell's research (and of course by the work of Tim van Gelder), I will begin including the teaching of argument mapping in my courses this semester. It seems particularly apt for the Informal Logic course that I teach, but I plan to try it to a more limited extent in my section of Intro to Philosophy, as well.

Rather than representing arguments in the classic

premise A
premise B
premise C
------------
conclusion

format, argument maps use lines, arrows, and boxes to represent visually the relationships between an argument's premises, intermediate conclusions, responses to objections, and main conclusions. I don't know enough sophisticated HTML to code an argument map here. So, for illustration, here's an example courtesy of the Wikipedia entry on argument mapping: http://en.wikipedia.org/wiki/File:Traffic_congestion_straw_man.png (the conclusion is at the top of the map; the supporting premises are below the main conclusion). There are several software tools -- some available gratis; others not -- for creating argument maps. The hand-and-pen method seems to work, too.

I can see several possible advantages to teaching students how to map the arguments they'll encounter. It seems especially useful for more complex arguments and/or for students who describe themselves as visual learners. But I'd like to hear, from anyone who's used or taught argument mapping for a while now, about some of the challenges that you encountered. Did you choose (or avoid) a particular software tool? What were some of the limitations of argument maps? Did you have a way to assess their effectiveness in helping your students reconstruct and evaluate arguments? If so, then what did you find?

Bleg: Online logic materials?

An ISW reader facing an unexpected teaching challenge asks for your help and guidance:

"I've been hired to teach a course titled "Logic" at a small university.

I'll be teaching two courses beginning in less than a month. Today I finally was able to get a look at the textbook (already ordered by them for the course) and some example syllabuses from past instances of the course.

It turns out it will be almost impossible for me to use these syllabuses and this textbook in good conscience. The book simply _isn't_ a logic book. It's more like an Intro to Philosophy textbook, and (I won't name the text but) it's not even a very good book for _that_ purpose. The syllabuses, similarly, do nothing to teach actual logic and focus on writing position papers on various philosophical and personal/religious/political issues.

One option, of course, is simply to pretend it's not a logic class and teach it as an intro course instead. But I was told when I was hired that one reason they were looking for someone to teach these courses was so that they would have someone teaching Logic, Critical Thinking and Philosophy courses who actually _knows_ logic, critical thinking and philosophy in some professional capacity. As such, it seems it is part of my _duty_ (not just my own personal inclination) to correct the curriculum here. Moreover, I suspect that accreditation probably turns in part on whether students in critical thinking and logic classes (core classes) are actually being taught something _about_ logic and critical thinking. So I think it's best for the university itself if I make this adjustment to the curriculum. Also, I think logic is valuable, and that I'd be doing a disservice to my _students_ if I didn't teach it to them.

So. Problem. I have this course to teach in less than a month, and I have no text, and perhaps even more importantly, I have no exercises to give the students to let them have practice with the concepts I'd be teaching.

The first round of courses I'm going to teach are compressed. There are only eight three hour meetings, each meeting intended to cover _two normal weeks_ worth of material. Clearly most of the value is going to come from the students working at home on exercises and getting feedback on them.

My current plan is not to run it simply as a Propositional Logic course. I'm going to take a broader approach. It won't be a mere critical thinking course (the students are supposed to have already taken one of those before they take this course) but will take a more in-depth look at the notion of formalized reasoning. The students will be constructing and analyzing actual argument rather than just manipulating formal symbols, but they'll be demonstrating in these constructions and analyses real understanding of the role and value of formalized techniques for dealing with arguments. It's kind of like an applied logic class. (Not just critical thinking, but actual logic, but not just logic, rather, applied logic.)

So here's what I need, and what I haven't been able to find, and which I hope you might be able to help me find by publicizing (anonymously please!) my plight at the blog In Socrates' Wake. I need good exercises designed to help teach the following concepts:

Logical vocabulary (such as validity, soundness, inductive, deductive, inductive strength, argument form, premise, conclusion, etc.)
Fallacies
The formalization of and evaluation of:
--Inductive Generalizations
--Causal Argumentss
--Arguments by Analogy
--(Possibly Abductive arguments, though I haven't thought this one through yet and I'm not sure I'll include such a section in the final course)
--Arguments best formalized in propositional logic (I won't be having the students deal with particularly complicated proofs here)
--Arguments best formalized in categorical logic

My plan right now is for assessment to be through their performance on worksheets and quizzes, as well as very short logical analyses (in English prose) of arguments found "in the wild" so to speak, together with performance on one or two "position papers" in which they're expected to show facility with logical vocabulary and the forms of argument mentioned in the list above.

Some may wonder what I mean by "formalizing" inductive types of arguments like Inductive Generalization and so on. I just mean the notion of abstracting from a specific argument to those characteristics just relevant to evaluating its strength. (That's a description that applies to deductive logic as well of course!) So for example, for an inductive generalization, you'd extract a population, sample, target characteristic, sampling method, and so on. That's what I'd call a "formalization" of an inductive generalization. The big idea of the course is learning how to think through arguments of varying levels of difficulty by learning how to consider them formally, as instances of this or that type of argument, whether they be deductive or inductive.

What I'm _hoping_ for is that there are sets of exercises like this to be found online somewhere that I simply haven't been able to discover. Or that some kind reader of your blog has access to some such sets of exercises in an electronic format that they'd be able to forward to me. Or any other fortunate outcome.

Really, really awesome would be if someone knows of an open-content Logic (or even the right Critical Thinking) textbook online that covers the above topics or roughly the above topics.

Thanks for any advice or help!"

Readers?

Difficulties of Teaching Ancient Philosophy: taking the “Ancient” out of Ancient Philosophy

I am curious if anyone has experimented with alternative and effective methods for teaching Ancient (Greek) Philosophy. I have found it a difficult subject to teach, but over the past few semesters, I have been experimenting with something that has worked surprisingly effectively.

On the first day of my Ancient Greek philosophy class, while most of my students are beginning to realize that the rumors surrounding the course work-load are true, and after I have begun developing some useful terminology, such as “logos” and “nous”, I am typically, but unsurprisingly, met with at least one student in class who simply does not believe that anything I am saying will ever make sense to her. Then, as I begin to develop something of a systematic explanation of Greek Philosophy in the next few days of class, I find that I quickly lose even my best students’ interest. Why does Ancient Greek philosophy feel so…well, ancient? “Because it is!” my students tell me.

My students often remind me that while I see the relevance of these ancient ideas, they barely see the relevance of philosophy itself. So, when I come to class overly eager to tackle Plato’s solution to the Parmenidean/Heraclitean problem of the one and the many, my students quite rightfully want to tackle each other on the way out of the door.

In order to combat this diluvial dysphoria, I have experimented with a method that not only keeps the students engaged, but also prepares them to think and work in philosophy (and its fun for me too). It is something rather intuitively dissonant: I simply take the "ancient" arguments and put them into modern symbolic notation. Since very few of my students have ever studied anything resembling philosophy before, they move from paralysis to curiosity while I translate Parmenides’ argument for the One, or one of Zeno's paradoxes, into modern symbolic notation.

What I have come to realize, at least for my students, is that they are fascinated by philosophy, particularly how philosophy can take something very seemingly simple (like free will or immortality or the existence of God) and make it entirely baffling, only to put it back together again. Ancient arguments are fun…for me, but my students simply do not immediately see the philosophy behind these antique articulations. When I draw up the arguments in symbolic notation, and walk my students through each argument to show how the arguments work, my students not only begin to reinvigorate their fascination with philosophy, but they also, strangely, begin to take ancient philosophy seriously. It is as if they had found something entirely new that few else have noticed.

I find teaching ancient philosophy to be difficult, and my students may think I am nuts for studying it; so I try to win them over by proving them right. After all, they already think I am crazy for being a philosopher. Prove them right and win them over! This idea was confirmed for me after reading Mark Edmudson’s insights in his NYT article on "good teachers", which Michael Cholbi formerly posted on. Here is an excerpt.

“Why are good teachers strange, uncool, offbeat?Because really good teaching is about not seeing the world the way that everyone else does. Teaching is about being what people are now prone to call “counterintuitive” but to the teacher means simply being honest. Good teachers perceive the world in alternative terms, and they push their students to test out these new, potentially enriching perspectives. Sometimes they do so in ways that are, to say the least, peculiar. The philosophy professor steps in the window the first day of class and asks her students to write down the definition of the word ‘door.’”

I would be very grateful to read your thoughts on such teaching methods and/or alternative ways of teaching Ancient Philosophy.

Helping students with analogical reasoning

Just curious to know if anyone out there has tips for helping students develop the ability to appraise arguments by analogy. Analogies are of course all over in philosophy, especially in ethics, but many of my students struggle to understand how analogies are supposed to support their conclusions and how one might go about criticizing a parcel of analogical reasoning.


Here's one problem in particular that students seem to have. Analogical reasoning procceds by arguing that, because A has feature(s) F and G, and B has feature(s)F, then B has feature G. That's a great simplification of course, but it captures the gist of such reasoning. Many students try to criticize analogical reasoning by pointing out some difference or other between A and B, but the difference they point out doesn't seem to undermine the analogy. (Thomson's abortion article comes to mind here; students are good at pointing out differences between the fetus-mother situation and the violinist-plug in situation, but many of the differences they cite don't do much to undermine what, according to Thomson, is analogous about these two situations). It's as if students fail to appreciate what an analogy is, since they think that one can show an analogy to be weak simply by pointing to any difference at all between the two items. But of course, if there weren't some differences between the analogized items, they would stand in a relation of identity and we wouldn't need to invoke an analogy!

But that's just symptomatic of a larger struggle my students seem to have with figuring out what's going on in analogical reasoning and how to critically engage such reasoning. Any thoughts or tips?

Reductio ad frustratum

I'd be interested to know if anyone out there has some techniques for teaching students reductio ad absurdum. In my experience, what's true of reductio arguments is similar to what I believe Strawson once said about the Euthyphro dilemma: If you get it, you'll likely be pretty good at philosophy, and if you don't, well ...

I'm interested in student understanding of reductio outside of teaching logic per se; on the few occasions I've taught logic I've noticed that it seems to be the one inference rule that large numbers of students have trouble appreciating. This doesn't preclude them from doing proofs using reductio, but they do so mechanically and don't seem to grasp why using that strategy proves a conclusion in the way that they appear to grasp why modus ponens, disjunction, etc., prove a conclusion. But I'm more interested in how to instill an appreciation for reductio in order to help students with their writing. I've encountered many arguments in student papers that would probably be expressed more clearly and forcefully as reductio arguments, but have struggled to help students craft such argumenta in part because the students sometimes don't fully understand reductio anyway.

Thoughts or counsel welcome!