[Jeffrey]

Perhaps this will evolve into a sub-forum, but I think it's high time CGR had a place to discuss basic logic. I know JerryLove's done some tutorials regarding informal fallacies and John clearly has a grasp of it - and I teach the thing for a living.

I've been asked to write a logic text likely to be implemented in the '09-'10 school year. We use James Nance's Introductory and Intermediate Logic which are capable documents (some of the examples and jokes he uses are not accessible, however).

Our logic program currently exists just as an 8th grade class. In years past, they offered it in 8th and then again in 9th or 10th grade. The current plan is have one semester of logic in 7th, and one in 8th.

So my question for the logic scholars here: what are the non-negotiable topics of logic (deductive, inductive, and recent strains of logical study) that you would want to see taught in a logic course in which you've enrolled your middle school student?

[Nate]

I think the difference between valid/invalid and true/false is probably the most important topic in all of logic. Aside from that, I'd teach as many logical fallacies as possible with as many practical applications to topics and speeches in current events as possible. Teaching symbolic logic isn't going to help most eighth graders, but learning to think critically about what people in the media (or even, and perhaps more importantly, their friends) say is an incomparably useful skill that is almost entirely absent from any middle school curriculum I've ever heard of. I think a really interesting thing would be to have a final project where students would take a news article or a speech or a critical essay and talk about the various logical constructions the author uses or fallacies the author commits. To me, that's much more useful at this kind of grade level than learning about contrapositives and deductive proofs.

[Chrysostom]

Originally Posted by Jeffrey

Perhaps this will evolve into a sub-forum, but I think it's high time CGR had a place to discuss basic logic. I know JerryLove's done some tutorials regarding informal fallacies and John R0berson clearly has a grasp of it - and I teach the thing for a living.

I'd prefer it if you wrote my name R0berson or something for privacy reasons. Were someone to start looking into blog archives they could probably steal my identity. Yeah, though, I took maybe 4 mathematical logic courses and did my senior thesis on a problem in Frege's logic, in addition to all the computer programming. (If you haven't studied Frege formally, he's a serious badass.)

Originally Posted by Jeffrey

So my question for the logic scholars here: what are the non-negotiable topics of logic (deductive, inductive, and recent strains of logical study) that you would want to see taught in a logic course in which you've enrolled your middle school student?

What's the purpose of this logic course? IOW, how is its purpose different from Algebra (which aims to help children learn to think in a certain kind of way)? Or is its purpose basically the same as Algebra? Is the purpose to sharpen reasoning skills, or really to learn logics themselves?

Here is one possible course outline (based on one possible understanding of the task). Don't do induction (or abduction) because that's way too complicated and at best you'll confuse them with words like 'Bayesian'. Leave that for a history of science class that can compare Aristotle and Bacon and Kuhn and so on. Start with a basic propositional logic -- atomic sentences, and, or, if, parentheses. I suspect you may not be able to finish that in the first semester. If you've got time (or maybe 2nd semester), graduate to a basic predicate logic and introduce existential and universal quantifiers. I would avoid sets because that will probably just confuse them. However, I would teach the basics of Aristotle's logic and then compare with the logics you've taught them. At least in the second semester I'd definitely require a working knowledge of reductio ad absurdum and the basic disjunctive proof models. For "fun" you might end up mentioning (but not testing) Godel (teach with a toy example: "This statement is false") or maybe Kripke's use of naming against mind-body identity. If you must teach modal logic (which I don't recommend), have Plantinga for application.

[Jeffrey]

Originally Posted by Chrysostom

I'd prefer it if you wrote my name R0berson or something for privacy reasons.

Baleeted. You're just John now. Sorry for any stress there. My pen name is something intentionally ridiculous so my students and friends would rarely find it (I intend to legally change my name within a decade, anyway).

What's the purpose of this logic course? IOW, how is its purpose different from Algebra (which aims to help children learn to think in a certain kind of way)? Or is its purpose basically the same as Algebra? Is the purpose to sharpen reasoning skills, or really to learn logics themselves?

This is the sort of question I'm trying to get the administration to grapple with. Having never taken formal logic themselves, they don't quite understand the nature of the beast. One could reasonably teach several years of logic - one private school I've examined teaches it at 7th, 9th, and 11th grade, in order to spread the more difficult topics out in later years and not cram it all in 8th grade.

As a result of little direction from my bosses, I view my logic class as:

1) sharpening students' ability to break statements and arguments into their component parts and recognize their categories;
2) recognize the role of implication and consistency in both deductive and inductive thinking;
3) seek the first steps of philosophical thought by first understanding methods of detecting validity and truth.

This is only my second year teaching logic. Last year's group of 8th graders was resistant in pretty much all of their classes, and as a result we barely made it through both books. This year's group, which features on average less academically gifted students but more common sense and dedicated students, has fared better. We finished the recommended sections of both books and began exploring inductive logic, the scientific method, linguistics - even reading a Lord Dunsany story to show the usage of logical thinking in literature comprehension.

We don't get too much into the history of logic, though I've discovered that students respond well to that. When I can give them a name of the logician who wrote on a topic of logic, it adds a human element. Last year I required them to do biographies of logicians; this year, I did not. Still, we discussed in passing a number of logicians and I was surprised how interested the students were. When they realize people with names, nationalities, etc. helped shape our understanding of logic, there's a human element. However, I tend to stick to the basics.

In terms of non-classical logic, we only start to touch on them. I don't see fuzzy logic or what have you as a threat to classical logic, so we do discuss the basics of probability and at least discuss that there's multi-valued logic out there. We also discuss paradoxes, which a vocal handful adored (the sorites/heap paradox, for one).

This past week, for instance, we wrapped up a discussion of polls by having the students answer the question "What does the [insert school name] community prefer?" Groups were given topics such as "dogs or cats," "Coke or Pepsi," "fall or spring," and put into groups. We discussed the basics of sample size, margin of error, etc. I told them at the beginning that they would not be doing a very rigorous poll, but would simply be exploring the basics. After discussing what the school community entailed, we discussed approaches that would not give accurate data (if the students did not interview anyone under 6th grade, for instance, or if they did not interview any parents or teachers). With a basic direction, I had their groups plan their sample size, record who they asked, and justify why they think their sample was representative of the whole. Some groups interviewed entire classes and quickly got into triple digits. Some groups chose a specific number from each level (elementary, middle, high school, for instance) and had under fifty interviewees, but from a very diverse group.

Friday, we'll discuss the results and relate it to inductive logic. We'll explore limitations. One spirited group chose "Coke or Dr. Pepper," and I discovered they were toying with the idea of tossing out response when Coke began to evidence itself as more popular than Dr. Pepper. This provides a great chance to discuss with both classes how they should be cautious in accepting polled data without looking into methods used.

Many of my students loved the symbolic part of the year, or if not loved, enjoyed the simplicity and their ability to quickly master the basics, then apply that thinking to bodies of text. And as corny as this sounds, it was a treat to see several students who are not "math people" overcome the hurdles during proofs.

The first Nance book ends with informal fallacies, while the second starts off with a review and goes into proper definitions. These less symbolic sections are a good break from the breaking down and symbolizing of arguments and statements. I purposefully introduced inductive logic, linguistics, etc. during proofs so that we could have a "one day on, one day off" approach where more creative or vibrant examples of logic (to speak subjectively) provided breaks for students struggling with rules of inference.

I personally am not a big symbolic logic guy (my gateway to logic was philosophy and literature, whereas the few logic teachers I know claim theirs was math), but I think it's invaluable. It forces students to step out of themselves and view logical thinking in a way that's more than just math. I ascribe to Russell's view that math is a subset of logic, and I do not stay restricted to symbols and proofs. I enjoy the fact that we analyze poetry and Scripture as well as use our P's and Q's. It builds an integrated thinking. Students also enjoy seeing that logical thinking is something they employ in their other classes.

We also did a popular segment where we learned about the role of logic in humor, culminating with students doing video projects (I played a clean clip or two from the humor show "Stella" that used the accent and equivocation fallacies perfectly).

Since you may not be familiar with Nance's texts, here is a sampling of topics:

- Statements and non-statements
- Truth value vs. truth
- Validity
- Relationships between statements (contradiction, contrariety, implication, etc.)
- Arguments, syllogisms, schemas, enthymemes
- Informal fallacies (of form, distraction, ambiguity)
- Logical operators (conjunction, disjunction, negation...)
- Definitions
- Truth tables
- Rules of inference

I tend to emphasize learning symbolic forms, then applying them to real world examples. I don't think I have any quizzes without a "word problem" that requires them draw logical inferences from actual texts, real-life examples, etc.

On our last test, one section will be open-ended. I will just give them invalid arguments (with a few valid ones mixed in!) and tell them to explain why they're invalid or valid. Some students may draw proofs, some may test by counter-example, some will do truth tables. Some problems will require them to draw specifically on truth tables, for instance, but they're equipped with enough practice that some students will just be able to eyeball it.

I tend to allow some of the students to explain their answers in their own words after an initial quiz where they've demonstrated their ability to do truth tables, or schemas, etc. In other words, if a student has thought of a perfect counterexample to prove an OOA-2 argument invalid, they can explain it that way. Another student will simply recognize that two negative premises cannot give us an affirmative conclusion.

[Chrysostom]

Originally Posted by Jeffrey

Baleeted. You're just John now. Sorry for any stress there.

No stress at all, actually. I think it's unlikely that something will happen, and especially since my first and last name are usually separated on this forum I think it would be more trouble than it's worth to do anything to me. (Unless it were a forum member, of course.)

Originally Posted by Jeffrey

My pen name is something intentionally ridiculous so my students and friends would rarely find it (I intend to legally change my name within a decade, anyway).

The one that starts with an A?

Originally Posted by Jeffrey

This is the sort of question I'm trying to get the administration to grapple with. Having never taken formal logic themselves, they don't quite understand the nature of the beast...

As a result of little direction from my bosses, I view my logic class as:

1) sharpening students' ability to break statements and arguments into their component parts and recognize their categories;
2) recognize the role of implication and consistency in both deductive and inductive thinking;
3) seek the first steps of philosophical thought by first understanding methods of detecting validity and truth.

You knew I had to say it:
4) Reminding everybody that Greco-Roman white people are responsible for everything good in the world.



I do think that my outline above (simple sentential to predicate logic) would accomplish what they're looking for decently, since you start being able to translate language into logic. (To that end, I would definitely teach Russell's theory of descriptions, since it's so simple.) That starts to make even your conversational language more precise. Of course, it also sets you down the old Analytic road of trying to map us onto some ideal logical language...

Did I mention that if I designed a curriculum it would be really, really weird? This is why I am not to be trusted.

Originally Posted by Jeffrey

We finished the recommended sections of both books and began exploring inductive logic, the scientific method, linguistics - even reading a Lord Dunsany story to show the usage of logical thinking in literature comprehension.

Wow, my hat's off to you if you could teach anything about induction and/or abduction to children.

Originally Posted by Jeffrey

We don't get too much into the history of logic, though I've discovered that students respond well to that. When I can give them a name of the logician who wrote on a topic of logic, it adds a human element. Last year I required them to do biographies of logicians; this year, I did not. Still, we discussed in passing a number of logicians and I was surprised how interested the students were. When they realize people with names, nationalities, etc. helped shape our understanding of logic, there's a human element. However, I tend to stick to the basics.

My socio-culturally oriented mind always gravitates toward it and I think you had a great idea by having them write these biographies. Will Durant's The Story of Philosophy was wildly popular (as historical. philosophy goes) because it humanized the philosophers. The only problem might be that there aren't that many logicians until very, very recently. Unless you let them do ancient Hindu logic or something.

Your administrators might like for you to use examples of logical strategies/rules in the Bible. The easiest would be a fortiori.

Originally Posted by Jeffrey

In terms of non-classical logic, we only start to touch on them.

I think that just pointing out that what seems to us like standard logic only came into existence 125 years ago, that everybody used Aristotle's logic for 2 millennia and it seems to us to be very counter-intuitive and clumsy, is worth plenty.

Originally Posted by Jeffrey

Friday, we'll discuss the results and relate it to inductive logic. We'll explore limitations. One spirited group chose "Coke or Dr. Pepper," and I discovered they were toying with the idea of tossing out response when Coke began to evidence itself as more popular than Dr. Pepper. This provides a great chance to discuss with both classes how they should be cautious in accepting polled data without looking into methods used.

Haha, for real. I don't know if I've trusted a single statistic I've read in years.

This would probably be more for an epistemology course, but you might make some mention of the relationship between logic and knowledge/belief if you have time. If you're doing a decent job with inductive reasoning you'll probably have your hands full, though.

Originally Posted by Jeffrey

Many of my students loved the symbolic part of the year, or if not loved, enjoyed the simplicity and their ability to quickly master the basics, then apply that thinking to bodies of text. And as corny as this sounds, it was a treat to see several students who are not "math people" overcome the hurdles during proofs.

I do hope you require that they master:
1. Reduction to absurdity
2. Conditional proof (assume antecedent & derive consequent to prove conditional)
3. Disjunctive proof (prove P from both sides of a true disjunction to prove P)
4. Get Modus Ponens, Tollens, and Affirming The Consequent straight

These are the models I think will expand their thinking the best.

Originally Posted by Jeffrey

We also did a popular segment where we learned about the role of logic in humor, culminating with students doing video projects (I played a clean clip or two from the humor show "Stella" that used the accent and equivocation fallacies perfectly).

Haha, niiice.

Originally Posted by Jeffrey

- Statements and non-statements
- Truth value vs. truth
- Validity
- Relationships between statements (contradiction, contrariety, implication, etc.)
- Arguments, syllogisms, schemas, enthymemes
- Informal fallacies (of form, distraction, ambiguity)
- Logical operators (conjunction, disjunction, negation...)
- Definitions
- Truth tables
- Rules of inference

So, looks like a basic sentential logic intro. I'd add predicate logic if you can, because it helps bridge the gap to normal language. I'd also definitely point out the difference between the material conditional and causation, because it really exposes the major chink in logic's armor.