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Submitted by Richard Zach on Thu, 02/21/2013 - 12:33pm

The ASL Committee in Logic Education organized a thought-provoking session this morning at the APA Central Division in New Orleans. There were four presentations and a lively discussion. What are your thoughts?

Andy Arana started things off with observations about salient differences between what we do in intro logic classes vs. what, e.g., mathematics departments do in "discrete mathematics" classes. Discrete math classes, he points out, serve disciplinary ends in mathematics: students learn concepts and techniques that they then go on to use all the time in advanced math courses (e.g., functions and relations, induction). By comparison, logic courses do not serve the same disciplinary ends. Sure, we use arguments all the time in philosophy and sometimes it comes in handy to know that you have to watch the order of your quantifiers or that affirming the consequent is invalid. But much of what we do in introductory formal logic courses does not get used outside of more advanced formal logic courses. Our courses are also very often enrolled by non-majors who satisfy a quantitative reasoning requirement. This raises the important question: why do we teach intro logic the way we do? What concepts and methods do majors and non-majors acquire in our logic courses, and do we teach them the right way for them to get these?

Danielle Macbeth gave an interesting pitch for her particular way of teaching intro logic: as a a history course, reading Aristotle, Kant, Wittgenstein, Frege. She made the provocative claim that formal logic has failed to solve philosophical problems (certainly to the extent that, say, Russell, thought it would). To make logic again of value to a philosophical education, she argued, we should focus on the philosophical advances through a study of its history and specifically of the clarification of the nature of denotation, predication, and the quantifiers. This is, I thought, an interesting persepective: unfortunately it probably can replace intro logic courses only at elite liberal arts colleges where a class with 20 students is "large". But wonderful idea for a more advanced course for majors!

Audrey Yap spoke about stereotype threat in the logic classroom. This is by now a well-worn topic in math and other STEM fields, especially as concerns gender. If students see themselves as belonging to a group that is stereotypically bad at something, they will perform worse. As math and logic are male-dominated and are stereotyped as male (logic even more so than math, perhaps), this is a big issue in the logic classroom, especially when many students take logic in lieu of a mathematics course to fulfil a requirement. What I didn't know about is that another important factor is that even if role models are available, unless succeeding in the field like them is seen as attainable, they hurt rather than help. Math and logic to an extent are like that: if students think you have to be a genius to "get" logic rather than just hard work, it will hurt rather than hinder. Role models are only helpful if students see them as possible futures. The message it took from this is that we should emphasize that logic takes hard work, and possibly present role models (female, of colour) who are successful perhaps not as "genius" logicians but through hard work in something our students aspire to but for which logic was an important preparation.

Susan Vineberg brought it back to Andy's point that we should at least keep in mind, if not actually incorporate into our classroom practice, the application of the methods logic courses train students in. She also compared logical reasoning to mathematical reasoning: in philosophy, like in mathematics, thinking about extreme and near extreme cases is a good strategy to find counterexamples. Other strategies that are useful: partitioning a problem space into cases, considering uniqueness after proving existence, generalizing a result, and self-reference. (E.g., suppose X is real means: X is mind-independent. Now take X = minds.)

In the ensuing discussion, a lot of other topics came up, including, of course, the perennial question of textbooks (Andy pointed out that while, e.g., basically everyone teaches topology from Munkres, everyone basically hates every logic textbook to some degree and they continue to proliferate). Andy also stressed the importance of logic courses for philosophy departments as their highest enrolment classes and hence a crucial part in the administrative justification of the existence of philosophy programs at many schools (and the threat to it would/will pose if logic instructions moves online). This reminded me of a study I've read, possible an Australian education MA thesis from 10 years ago or so, that investigated the effect philosophy (or humanities?) courses had on the improvement of critical thinking skills in undergraduates -- and which, IIRC, showed that only formal logic courses actually did. ~~Please tell me if you know what I'm thinking of, Google is no help!~~ Found it! Claudia Álvarez, "Does philosophy improve critical thinking," MA thesis, University of Melbourne, 2007

- Kalmár's Compleness Proof
- Dana Scott's Favorite Completeness Proof
- Lectures on the Epsilon Calculus
- The Real Reasons Why Philosophers Shouldn't Use LaTeX
- Bringing Logic (and Philosophy, CS) to the Masses
- Proof Formalization in Mathematics: Guest Post by Jeremy Avigad
- Edward Nelson, 1932-2014
- Awodey's "HoTT for Philosophers" on mathtube.org

## Comments

This sounds like a very interesting session.

Was there any discussion of "formal methods" courses, as opposed to logic courses? I believe the University of Edinburgh offers a formal methods course. The idea behind such a course, as I understand, is to present some basic formal tools for future use, such as rudiments of probability theory for reading formal epistemology stuff, modal and counterfactual logic, scope distinctions, definite descriptions, the basics of lambda abstraction and conversion, and so on, perhaps with some techniques such as induction. I'm not sure how much logic is presupposed for such a course. One could do that without going into detailed metatheory. How do/should such courses relate to more traditional logic courses?

The issue about disciplinary needs seems very important. Were there any suggestions for answers to the questions of what majors and non-majors take away from logic courses and what are good ways to teach those things?

We didn't discuss it during the session, which was focussed on a first formal logic course. Personally, I think you do need that before you can talk about counterfactuals. We did talk about using disciplinary examples where the kinds of things you teach in intro logic come up (uantifier alternaton, and obviously valid/invalid inferences).

I mentioned these:

http://www.ucalgary.ca/rzach/blog/2007/01/quantifiers-and-claims-about-i...

http://www.ucalgary.ca/rzach/blog/2009/09/why-study-formal-logic.html

"This raises the important question: why do we teach intro logic the way we do?"

Mathematical-style logic should be required in philosophy so that on those rare occasions when someone with actual intelligence wanders into the program, there is a chance he will be able to eventually say something solid and meaningful and not just yet more of the waffling drivel which characterizes most modern philosophical research.

Will these presentations be published somewhere I'd be interested in using some of these ideas in my own logic classes, especially Dr. Macbeth's teaching logic using the history of philosophy.

"we use arguments all the time in philosophy and sometimes it comes in handy to know that you have to watch the order of your quantifiers or that affirming the consequent is invalid. But much of what we do in introductory formal logic courses does not get used outside of more advanced formal logic courses."

This is why philosophers need to start putting more of their arguments in standard form. We can argue until we're blue in the fact whether a statement is sound but we can recognize immediately that an argument is invalid. Too often philosophers cover up their ignorance behind obscure language. If they would put their arguments in standard form, then it would be much easier to identify what they're saying. So as to practice what I preach:

1. Standardizing arguments helps clarify an authors intentions.

2. Clarity is better than obscurity.

3. Therefore, authors should standardize their arguments.