New term, New course
Most of our classes are annualized, but not some electives. For me? Goodbye Combinatorics, Hello Logic.
I met the new class today. All were there, talkative, mildly interested. They liked the book cover.
We want the kids to do 8 credits (four years) of math, but know that not every kid can handle the high end of algebra-geometry-trigonometry-precalculus. So senior electives that carry math credits are a reasonable option. But logic is not only kids avoiding precalc. Some seniors, and a few juniors, choose it as what they hope will either be an interesting or a fun elective. In fact, I don’t intend to disappoint any of them (except for anyone who is thinking of not showing up). And a few are in there since nothing else fit their programs. I would complain (except I am the programmer).
Is it a math class? We use a college text that would usually accompany a logic course in a philosophy department. Perhaps the last 40% is mathematical logic. So it’s a stretch. The other stuff is fun, too. Informal fallacies. Categorical syllogisms. But when we hit the symbolic stuff and breeze through the old Course I and Course II material, and move on to validity testing and indirect proof…
When we meet first period in late May, with senioritis rampant, that’s when the attendence will tell if Logic has proved interesting. I’ll keep you posted.
JD2718 
I wonder which text you’re using. Last semester I found Chapter Zero which I thought had potential, although I have to say I didn’t read the whole thing. It started with logic and proofs, but then took off into proofs in number theory, geometry and such. It was written to have students work and talk more than the teacher, and seemed like something one may use in senior year in high school as well as beginning college.
Anyway, I’d like to ask you to check out some questions I have for teachers if you get a chance, I’ll leave the url.
A logic course sounds fun! As soon as the Math Counts competition is over, I plan to do an intro-to-logic/proofs mini-course with my middle school kids. Not real heavy on mathematical content—after all, these kids haven’t even had algebra. Most of the proofs we analyze come straight from Lewis Carroll’s Symbolic Logic.
When my father in law was an undergraduate he took a course in logic which was the course that convinced him to become a math student. He eventually got his PhD in math.
I suppose that was the anecdote that convinced me that there is more to math than the alg-trig-cal road.
I would love to hear what text(s) you are using, what you need to do to supplement, the typical difficulties that your students have.
Logic is definitely a math course. It plays a big part in some of the courses I teach in college. It’s good for kids to know taht math is more than numbers.
The text is Hurley, and the progression I mentioned (whole language, categorical syllogisms, mathematical logic) follows the flow of the book. It is the text I used as an undergrad (much older edition), and we use about 65- 75% of the material, sticking to about average difficulty. Lewis Carrol’s awful sorites are indeed in the book, and I will teach them, and assign them, but not test them, as pulling one apart could take half an hour.
This text generally would not be used in a college mathematics department. However, the math part is real math, and there is enough there that a math credit, I believe, is quite appropriate.
jd2718 commented on one of my posts, so I came here to see what’s up. I am totally new to WordPress, so am not clear on how this is all going to work out. I have no clear idea for my own site than as a place I can post notes to myself and anyone else who would care.
Anyway, on to the question. I agree that the course, depending on content, could belong more in a math department than a philosophy department. While you would start out with ideas on common logic issues, such as guilt by association, etc, I would assume you would move on to the math side, which might be called ‘propositional calculus’. If you look into how computers are made, you will find they only use the rules of propositional calculus. There is no algebra, trig, and so on. So as you venture into the application of formal logic, you will encounter situations where the object is to reduce a statement to its minimal terms. Or you can progress to state machines, where the machine has memory, and its next state depends on its present state and its inputs.
This leads to a study of things like race conditions and difficulty in answering simple yes/no questions. For example, you can have a light that can be on or off, and ask a student if the light is on or off. If you have the student answer by pushing a button to signify on or off, you can measure how quickly the student can decide. If the light is solidly on or off, the student can decide quickly. But then you can change the situation to where the light changes at some time before you ask the question. A computer could plot the decision time relative to the time between when the light changes and the student is asked to decide. You will find as the time becomes small, the decision time increases. As the time becomes very small, the decision time can become very large. I suspect you see a limit type question approaching here.
In electronic circuitry, exactly the same thing happens. If you ask a circuit to decide yes or no on an input that changed just before you asked, the circuit may in fact be unable to give a valid output in the allocated time. So there is a possibility of no answer or a wrong answer. This is just one example of how embedded logic is in computers, computer logic, and even probability in the case above.
A common question talked about in a logic class is “Have you stopped beating your wife yet?” I don’t remember the proper terminology, but it is posed as an invalid question, one with no answer. Assuming you never did. But maybe if you think about what the question signifies, it does have some mathematical validity. Suppose you got really mad at your wife once, and barely hit her, or almost did. A really long time ago. The words “stopped yet” might infer it will never happen again, or will never happen. So it seems there may be probability attached. And as the history of your likelyhood of hitting her in the past goes to zero, the probability that the question is unanswerable goes to one. Maybe not a lot different that how the limit as x ->5 of 1/(x-5) becomes unanswerable using a string of digits, however long. Don’t know where I came up with this crazy thought, it must be too late to be writing on the internet! :(
And a nice game that should not be overlooked is WFF ‘N PROOF. Sorry for long post.
How is the annualization of classes been for the school? We are having a disscussion about the philosophy behind it now.
would love for you to comment:
http://www.monticohort1.blogspot.com
chilipep,
I agree about the strong connection with computers. We will not get to the right kind of logic for that, but we will set the stage. The math part of the course, a bit over one third, is very valuable.
In the meantime, we will investigate what “valid” means, both informally, with language (including fallacies such as “complex questions” including “have you stopped beating your wife?”), with categorical syllogisms (pulling structure out of language, and analyzing the structures.)
I do have one kid sitting in the room who took the class last year. He will participate a bit with some topics (for review), but mostly he is there to study the math end more in depth. Quantifiers, harder proofs. I might bring him towards the computery ends of things. Brave soul? Nah, he really really wanted it.
Walter, I am not sure what you mean. It’s just what we have always done, except for one term courses. Kiddies who can stay in the same course, do. Juniors and seniors move around. It works out ok.